Initial commit. Full UI and process of script conversion to Dart

.gitignore

@@ -0,0 +1,45 @@
+# Miscellaneous
+*.class
+*.log
+*.pyc
+*.swp
+.DS_Store
+.atom/
+.build/
+.buildlog/
+.history
+.svn/
+.swiftpm/
+migrate_working_dir/
+
+# IntelliJ related
+*.iml
+*.ipr
+*.iws
+.idea/
+
+# The .vscode folder contains launch configuration and tasks you configure in
+# VS Code which you may wish to be included in version control, so this line
+# is commented out by default.
+#.vscode/
+
+# Flutter/Dart/Pub related
+**/doc/api/
+**/ios/Flutter/.last_build_id
+.dart_tool/
+.flutter-plugins
+.flutter-plugins-dependencies
+.pub-cache/
+.pub/
+/build/
+
+# Symbolication related
+app.*.symbols
+
+# Obfuscation related
+app.*.map.json
+
+# Android Studio will place build artifacts here
+/android/app/debug
+/android/app/profile
+/android/app/release

.metadata

@@ -0,0 +1,42 @@
+# This file tracks properties of this Flutter project.
+# Used by Flutter tool to assess capabilities and perform upgrades etc.
+#
+# This file should be version controlled and should not be manually edited.
+
+version:
+  revision: "c23637390482d4cf9598c3ce3f2be31aa7332daf"
+  channel: "stable"
+
+project_type: app
+
+# Tracks metadata for the flutter migrate command
+migration:
+  platforms:
+    - platform: root
+      create_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+      base_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+    - platform: android
+      create_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+      base_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+    - platform: ios
+      create_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+      base_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+    - platform: macos
+      create_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+      base_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+    - platform: web
+      create_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+      base_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+    - platform: windows
+      create_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+      base_revision: c23637390482d4cf9598c3ce3f2be31aa7332daf
+
+  # User provided section
+
+  # List of Local paths (relative to this file) that should be
+  # ignored by the migrate tool.
+  #
+  # Files that are not part of the templates will be ignored by default.
+  unmanaged_files:
+    - 'lib/main.dart'
+    - 'ios/Runner.xcodeproj/project.pbxproj'

README.md

@@ -0,0 +1,16 @@
+# surface_tension_calculator
+
+App that calculates surface tension based on an image of a droplet
+
+## Getting Started
+
+This project is a starting point for a Flutter application.
+
+A few resources to get you started if this is your first Flutter project:
+
+- [Lab: Write your first Flutter app](https://docs.flutter.dev/get-started/codelab)
+- [Cookbook: Useful Flutter samples](https://docs.flutter.dev/cookbook)
+
+For help getting started with Flutter development, view the
+[online documentation](https://docs.flutter.dev/), which offers tutorials,
+samples, guidance on mobile development, and a full API reference.

analysis_options.yaml

@@ -0,0 +1,28 @@
+# This file configures the analyzer, which statically analyzes Dart code to
+# check for errors, warnings, and lints.
+#
+# The issues identified by the analyzer are surfaced in the UI of Dart-enabled
+# IDEs (https://dart.dev/tools#ides-and-editors). The analyzer can also be
+# invoked from the command line by running `flutter analyze`.
+
+# The following line activates a set of recommended lints for Flutter apps,
+# packages, and plugins designed to encourage good coding practices.
+include: package:flutter_lints/flutter.yaml
+
+linter:
+  # The lint rules applied to this project can be customized in the
+  # section below to disable rules from the `package:flutter_lints/flutter.yaml`
+  # included above or to enable additional rules. A list of all available lints
+  # and their documentation is published at https://dart.dev/lints.
+  #
+  # Instead of disabling a lint rule for the entire project in the
+  # section below, it can also be suppressed for a single line of code
+  # or a specific dart file by using the `// ignore: name_of_lint` and
+  # `// ignore_for_file: name_of_lint` syntax on the line or in the file
+  # producing the lint.
+  rules:
+    # avoid_print: false  # Uncomment to disable the `avoid_print` rule
+    # prefer_single_quotes: true  # Uncomment to enable the `prefer_single_quotes` rule
+
+# Additional information about this file can be found at
+# https://dart.dev/guides/language/analysis-options

android/.gitignore

@@ -0,0 +1,14 @@
+gradle-wrapper.jar
+/.gradle
+/captures/
+/gradlew
+/gradlew.bat
+/local.properties
+GeneratedPluginRegistrant.java
+.cxx/
+
+# Remember to never publicly share your keystore.
+# See https://flutter.dev/to/reference-keystore
+key.properties
+**/*.keystore
+**/*.jks

android/app/build.gradle.kts

@@ -0,0 +1,44 @@
+plugins {
+    id("com.android.application")
+    id("kotlin-android")
+    // The Flutter Gradle Plugin must be applied after the Android and Kotlin Gradle plugins.
+    id("dev.flutter.flutter-gradle-plugin")
+}
+
+android {
+    namespace = "com.upisc.surface_tension_calculator"
+    compileSdk = flutter.compileSdkVersion
+    ndkVersion = flutter.ndkVersion
+
+    compileOptions {
+        sourceCompatibility = JavaVersion.VERSION_11
+        targetCompatibility = JavaVersion.VERSION_11
+    }
+
+    kotlinOptions {
+        jvmTarget = JavaVersion.VERSION_11.toString()
+    }
+
+    defaultConfig {
+        // TODO: Specify your own unique Application ID (https://developer.android.com/studio/build/application-id.html).
+        applicationId = "com.upisc.surface_tension_calculator"
+        // You can update the following values to match your application needs.
+        // For more information, see: https://flutter.dev/to/review-gradle-config.
+        minSdk = flutter.minSdkVersion
+        targetSdk = flutter.targetSdkVersion
+        versionCode = flutter.versionCode
+        versionName = flutter.versionName
+    }
+
+    buildTypes {
+        release {
+            // TODO: Add your own signing config for the release build.
+            // Signing with the debug keys for now, so `flutter run --release` works.
+            signingConfig = signingConfigs.getByName("debug")
+        }
+    }
+}
+
+flutter {
+    source = "../.."
+}

android/app/src/debug/AndroidManifest.xml

@@ -0,0 +1,7 @@
+<manifest xmlns:android="http://schemas.android.com/apk/res/android">
+    <!-- The INTERNET permission is required for development. Specifically,
+         the Flutter tool needs it to communicate with the running application
+         to allow setting breakpoints, to provide hot reload, etc.
+    -->
+    <uses-permission android:name="android.permission.INTERNET"/>
+</manifest>

android/app/src/main/AndroidManifest.xml

@@ -0,0 +1,45 @@
+<manifest xmlns:android="http://schemas.android.com/apk/res/android">
+    <application
+        android:label="surface_tension_calculator"
+        android:name="${applicationName}"
+        android:icon="@mipmap/ic_launcher">
+        <activity
+            android:name=".MainActivity"
+            android:exported="true"
+            android:launchMode="singleTop"
+            android:taskAffinity=""
+            android:theme="@style/LaunchTheme"
+            android:configChanges="orientation|keyboardHidden|keyboard|screenSize|smallestScreenSize|locale|layoutDirection|fontScale|screenLayout|density|uiMode"
+            android:hardwareAccelerated="true"
+            android:windowSoftInputMode="adjustResize">
+            <!-- Specifies an Android theme to apply to this Activity as soon as
+                 the Android process has started. This theme is visible to the user
+                 while the Flutter UI initializes. After that, this theme continues
+                 to determine the Window background behind the Flutter UI. -->
+            <meta-data
+              android:name="io.flutter.embedding.android.NormalTheme"
+              android:resource="@style/NormalTheme"
+              />
+            <intent-filter>
+                <action android:name="android.intent.action.MAIN"/>
+                <category android:name="android.intent.category.LAUNCHER"/>
+            </intent-filter>
+        </activity>
+        <!-- Don't delete the meta-data below.
+             This is used by the Flutter tool to generate GeneratedPluginRegistrant.java -->
+        <meta-data
+            android:name="flutterEmbedding"
+            android:value="2" />
+    </application>
+    <!-- Required to query activities that can process text, see:
+         https://developer.android.com/training/package-visibility and
+         https://developer.android.com/reference/android/content/Intent#ACTION_PROCESS_TEXT.
+
+         In particular, this is used by the Flutter engine in io.flutter.plugin.text.ProcessTextPlugin. -->
+    <queries>
+        <intent>
+            <action android:name="android.intent.action.PROCESS_TEXT"/>
+            <data android:mimeType="text/plain"/>
+        </intent>
+    </queries>
+</manifest>

android/app/src/main/kotlin/com/upisc/surface_tension_calculator/MainActivity.kt

@@ -0,0 +1,5 @@
+package com.upisc.surface_tension_calculator
+
+import io.flutter.embedding.android.FlutterActivity
+
+class MainActivity : FlutterActivity()

android/app/src/main/res/drawable-v21/launch_background.xml

@@ -0,0 +1,12 @@
+<?xml version="1.0" encoding="utf-8"?>
+<!-- Modify this file to customize your launch splash screen -->
+<layer-list xmlns:android="http://schemas.android.com/apk/res/android">
+    <item android:drawable="?android:colorBackground" />
+
+    <!-- You can insert your own image assets here -->
+    <!-- <item>
+        <bitmap
+            android:gravity="center"
+            android:src="@mipmap/launch_image" />
+    </item> -->
+</layer-list>

android/app/src/main/res/drawable/launch_background.xml

@@ -0,0 +1,12 @@
+<?xml version="1.0" encoding="utf-8"?>
+<!-- Modify this file to customize your launch splash screen -->
+<layer-list xmlns:android="http://schemas.android.com/apk/res/android">
+    <item android:drawable="@android:color/white" />
+
+    <!-- You can insert your own image assets here -->
+    <!-- <item>
+        <bitmap
+            android:gravity="center"
+            android:src="@mipmap/launch_image" />
+    </item> -->
+</layer-list>

android/app/src/main/res/values-night/styles.xml

@@ -0,0 +1,18 @@
+<?xml version="1.0" encoding="utf-8"?>
+<resources>
+    <!-- Theme applied to the Android Window while the process is starting when the OS's Dark Mode setting is on -->
+    <style name="LaunchTheme" parent="@android:style/Theme.Black.NoTitleBar">
+        <!-- Show a splash screen on the activity. Automatically removed when
+             the Flutter engine draws its first frame -->
+        <item name="android:windowBackground">@drawable/launch_background</item>
+    </style>
+    <!-- Theme applied to the Android Window as soon as the process has started.
+         This theme determines the color of the Android Window while your
+         Flutter UI initializes, as well as behind your Flutter UI while its
+         running.
+
+         This Theme is only used starting with V2 of Flutter's Android embedding. -->
+    <style name="NormalTheme" parent="@android:style/Theme.Black.NoTitleBar">
+        <item name="android:windowBackground">?android:colorBackground</item>
+    </style>
+</resources>

android/app/src/main/res/values/styles.xml

@@ -0,0 +1,18 @@
+<?xml version="1.0" encoding="utf-8"?>
+<resources>
+    <!-- Theme applied to the Android Window while the process is starting when the OS's Dark Mode setting is off -->
+    <style name="LaunchTheme" parent="@android:style/Theme.Light.NoTitleBar">
+        <!-- Show a splash screen on the activity. Automatically removed when
+             the Flutter engine draws its first frame -->
+        <item name="android:windowBackground">@drawable/launch_background</item>
+    </style>
+    <!-- Theme applied to the Android Window as soon as the process has started.
+         This theme determines the color of the Android Window while your
+         Flutter UI initializes, as well as behind your Flutter UI while its
+         running.
+
+         This Theme is only used starting with V2 of Flutter's Android embedding. -->
+    <style name="NormalTheme" parent="@android:style/Theme.Light.NoTitleBar">
+        <item name="android:windowBackground">?android:colorBackground</item>
+    </style>
+</resources>

android/app/src/profile/AndroidManifest.xml

@@ -0,0 +1,7 @@
+<manifest xmlns:android="http://schemas.android.com/apk/res/android">
+    <!-- The INTERNET permission is required for development. Specifically,
+         the Flutter tool needs it to communicate with the running application
+         to allow setting breakpoints, to provide hot reload, etc.
+    -->
+    <uses-permission android:name="android.permission.INTERNET"/>
+</manifest>

android/build.gradle.kts

@@ -0,0 +1,21 @@
+allprojects {
+    repositories {
+        google()
+        mavenCentral()
+    }
+}
+
+val newBuildDir: Directory = rootProject.layout.buildDirectory.dir("../../build").get()
+rootProject.layout.buildDirectory.value(newBuildDir)
+
+subprojects {
+    val newSubprojectBuildDir: Directory = newBuildDir.dir(project.name)
+    project.layout.buildDirectory.value(newSubprojectBuildDir)
+}
+subprojects {
+    project.evaluationDependsOn(":app")
+}
+
+tasks.register<Delete>("clean") {
+    delete(rootProject.layout.buildDirectory)
+}

android/gradle.properties

@@ -0,0 +1,3 @@
+org.gradle.jvmargs=-Xmx8G -XX:MaxMetaspaceSize=4G -XX:ReservedCodeCacheSize=512m -XX:+HeapDumpOnOutOfMemoryError
+android.useAndroidX=true
+android.enableJetifier=true

android/gradle/wrapper/gradle-wrapper.properties

@@ -0,0 +1,5 @@
+distributionBase=GRADLE_USER_HOME
+distributionPath=wrapper/dists
+zipStoreBase=GRADLE_USER_HOME
+zipStorePath=wrapper/dists
+distributionUrl=https\://services.gradle.org/distributions/gradle-8.10.2-all.zip

android/settings.gradle.kts

@@ -0,0 +1,25 @@
+pluginManagement {
+    val flutterSdkPath = run {
+        val properties = java.util.Properties()
+        file("local.properties").inputStream().use { properties.load(it) }
+        val flutterSdkPath = properties.getProperty("flutter.sdk")
+        require(flutterSdkPath != null) { "flutter.sdk not set in local.properties" }
+        flutterSdkPath
+    }
+
+    includeBuild("$flutterSdkPath/packages/flutter_tools/gradle")
+
+    repositories {
+        google()
+        mavenCentral()
+        gradlePluginPortal()
+    }
+}
+
+plugins {
+    id("dev.flutter.flutter-plugin-loader") version "1.0.0"
+    id("com.android.application") version "8.7.0" apply false
+    id("org.jetbrains.kotlin.android") version "1.8.22" apply false
+}
+
+include(":app")

fonts/OFL.txt

@@ -0,0 +1,93 @@
+Copyright 2020 The Open Sans Project Authors (https://github.com/googlefonts/opensans)
+
+This Font Software is licensed under the SIL Open Font License, Version 1.1.
+This license is copied below, and is also available with a FAQ at:
+http://scripts.sil.org/OFL
+
+
+-----------------------------------------------------------
+SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
+-----------------------------------------------------------
+
+PREAMBLE
+The goals of the Open Font License (OFL) are to stimulate worldwide
+development of collaborative font projects, to support the font creation
+efforts of academic and linguistic communities, and to provide a free and
+open framework in which fonts may be shared and improved in partnership
+with others.
+
+The OFL allows the licensed fonts to be used, studied, modified and
+redistributed freely as long as they are not sold by themselves. The
+fonts, including any derivative works, can be bundled, embedded, 
+redistributed and/or sold with any software provided that any reserved
+names are not used by derivative works. The fonts and derivatives,
+however, cannot be released under any other type of license. The
+requirement for fonts to remain under this license does not apply
+to any document created using the fonts or their derivatives.
+
+DEFINITIONS
+"Font Software" refers to the set of files released by the Copyright
+Holder(s) under this license and clearly marked as such. This may
+include source files, build scripts and documentation.
+
+"Reserved Font Name" refers to any names specified as such after the
+copyright statement(s).
+
+"Original Version" refers to the collection of Font Software components as
+distributed by the Copyright Holder(s).
+
+"Modified Version" refers to any derivative made by adding to, deleting,
+or substituting -- in part or in whole -- any of the components of the
+Original Version, by changing formats or by porting the Font Software to a
+new environment.
+
+"Author" refers to any designer, engineer, programmer, technical
+writer or other person who contributed to the Font Software.
+
+PERMISSION & CONDITIONS
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of the Font Software, to use, study, copy, merge, embed, modify,
+redistribute, and sell modified and unmodified copies of the Font
+Software, subject to the following conditions:
+
+1) Neither the Font Software nor any of its individual components,
+in Original or Modified Versions, may be sold by itself.
+
+2) Original or Modified Versions of the Font Software may be bundled,
+redistributed and/or sold with any software, provided that each copy
+contains the above copyright notice and this license. These can be
+included either as stand-alone text files, human-readable headers or
+in the appropriate machine-readable metadata fields within text or
+binary files as long as those fields can be easily viewed by the user.
+
+3) No Modified Version of the Font Software may use the Reserved Font
+Name(s) unless explicit written permission is granted by the corresponding
+Copyright Holder. This restriction only applies to the primary font name as
+presented to the users.
+
+4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
+Software shall not be used to promote, endorse or advertise any
+Modified Version, except to acknowledge the contribution(s) of the
+Copyright Holder(s) and the Author(s) or with their explicit written
+permission.
+
+5) The Font Software, modified or unmodified, in part or in whole,
+must be distributed entirely under this license, and must not be
+distributed under any other license. The requirement for fonts to
+remain under this license does not apply to any document created
+using the Font Software.
+
+TERMINATION
+This license becomes null and void if any of the above conditions are
+not met.
+
+DISCLAIMER
+THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
+OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
+COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
+DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
+OTHER DEALINGS IN THE FONT SOFTWARE.

ios/.gitignore

@@ -0,0 +1,34 @@
+**/dgph
+*.mode1v3
+*.mode2v3
+*.moved-aside
+*.pbxuser
+*.perspectivev3
+**/*sync/
+.sconsign.dblite
+.tags*
+**/.vagrant/
+**/DerivedData/
+Icon?
+**/Pods/
+**/.symlinks/
+profile
+xcuserdata
+**/.generated/
+Flutter/App.framework
+Flutter/Flutter.framework
+Flutter/Flutter.podspec
+Flutter/Generated.xcconfig
+Flutter/ephemeral/
+Flutter/app.flx
+Flutter/app.zip
+Flutter/flutter_assets/
+Flutter/flutter_export_environment.sh
+ServiceDefinitions.json
+Runner/GeneratedPluginRegistrant.*
+
+# Exceptions to above rules.
+!default.mode1v3
+!default.mode2v3
+!default.pbxuser
+!default.perspectivev3

ios/Flutter/AppFrameworkInfo.plist

@@ -0,0 +1,26 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+  <key>CFBundleDevelopmentRegion</key>
+  <string>en</string>
+  <key>CFBundleExecutable</key>
+  <string>App</string>
+  <key>CFBundleIdentifier</key>
+  <string>io.flutter.flutter.app</string>
+  <key>CFBundleInfoDictionaryVersion</key>
+  <string>6.0</string>
+  <key>CFBundleName</key>
+  <string>App</string>
+  <key>CFBundlePackageType</key>
+  <string>FMWK</string>
+  <key>CFBundleShortVersionString</key>
+  <string>1.0</string>
+  <key>CFBundleSignature</key>
+  <string>????</string>
+  <key>CFBundleVersion</key>
+  <string>1.0</string>
+  <key>MinimumOSVersion</key>
+  <string>12.0</string>
+</dict>
+</plist>

ios/Flutter/Debug.xcconfig

@@ -0,0 +1,2 @@
+#include? "Pods/Target Support Files/Pods-Runner/Pods-Runner.debug.xcconfig"
+#include "Generated.xcconfig"

ios/Flutter/Release.xcconfig

@@ -0,0 +1,2 @@
+#include? "Pods/Target Support Files/Pods-Runner/Pods-Runner.release.xcconfig"
+#include "Generated.xcconfig"

ios/Podfile

@@ -0,0 +1,43 @@
+# Uncomment this line to define a global platform for your project
+# platform :ios, '12.0'
+
+# CocoaPods analytics sends network stats synchronously affecting flutter build latency.
+ENV['COCOAPODS_DISABLE_STATS'] = 'true'
+
+project 'Runner', {
+  'Debug' => :debug,
+  'Profile' => :release,
+  'Release' => :release,
+}
+
+def flutter_root
+  generated_xcode_build_settings_path = File.expand_path(File.join('..', 'Flutter', 'Generated.xcconfig'), __FILE__)
+  unless File.exist?(generated_xcode_build_settings_path)
+    raise "#{generated_xcode_build_settings_path} must exist. If you're running pod install manually, make sure flutter pub get is executed first"
+  end
+
+  File.foreach(generated_xcode_build_settings_path) do |line|
+    matches = line.match(/FLUTTER_ROOT\=(.*)/)
+    return matches[1].strip if matches
+  end
+  raise "FLUTTER_ROOT not found in #{generated_xcode_build_settings_path}. Try deleting Generated.xcconfig, then run flutter pub get"
+end
+
+require File.expand_path(File.join('packages', 'flutter_tools', 'bin', 'podhelper'), flutter_root)
+
+flutter_ios_podfile_setup
+
+target 'Runner' do
+  use_frameworks!
+
+  flutter_install_all_ios_pods File.dirname(File.realpath(__FILE__))
+  target 'RunnerTests' do
+    inherit! :search_paths
+  end
+end
+
+post_install do |installer|
+  installer.pods_project.targets.each do |target|
+    flutter_additional_ios_build_settings(target)
+  end
+end

ios/Runner.xcodeproj/project.pbxproj

@@ -0,0 +1,616 @@
+// !$*UTF8*$!
+{
+	archiveVersion = 1;
+	classes = {
+	};
+	objectVersion = 54;
+	objects = {
+
+/* Begin PBXBuildFile section */
+		1498D2341E8E89220040F4C2 /* GeneratedPluginRegistrant.m in Sources */ = {isa = PBXBuildFile; fileRef = 1498D2331E8E89220040F4C2 /* GeneratedPluginRegistrant.m */; };
+		331C808B294A63AB00263BE5 /* RunnerTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 331C807B294A618700263BE5 /* RunnerTests.swift */; };
+		3B3967161E833CAA004F5970 /* AppFrameworkInfo.plist in Resources */ = {isa = PBXBuildFile; fileRef = 3B3967151E833CAA004F5970 /* AppFrameworkInfo.plist */; };
+		74858FAF1ED2DC5600515810 /* AppDelegate.swift in Sources */ = {isa = PBXBuildFile; fileRef = 74858FAE1ED2DC5600515810 /* AppDelegate.swift */; };
+		97C146FC1CF9000F007C117D /* Main.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 97C146FA1CF9000F007C117D /* Main.storyboard */; };
+		97C146FE1CF9000F007C117D /* Assets.xcassets in Resources */ = {isa = PBXBuildFile; fileRef = 97C146FD1CF9000F007C117D /* Assets.xcassets */; };
+		97C147011CF9000F007C117D /* LaunchScreen.storyboard in Resources */ = {isa = PBXBuildFile; fileRef = 97C146FF1CF9000F007C117D /* LaunchScreen.storyboard */; };
+/* End PBXBuildFile section */
+
+/* Begin PBXContainerItemProxy section */
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+				CLANG_WARN_EMPTY_BODY = YES;
+				CLANG_WARN_ENUM_CONVERSION = YES;
+				CLANG_WARN_INFINITE_RECURSION = YES;
+				CLANG_WARN_INT_CONVERSION = YES;
+				CLANG_WARN_NON_LITERAL_NULL_CONVERSION = YES;
+				CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES;
+				CLANG_WARN_OBJC_LITERAL_CONVERSION = YES;
+				CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR;
+				CLANG_WARN_RANGE_LOOP_ANALYSIS = YES;
+				CLANG_WARN_STRICT_PROTOTYPES = YES;
+				CLANG_WARN_SUSPICIOUS_MOVE = YES;
+				CLANG_WARN_UNREACHABLE_CODE = YES;
+				CLANG_WARN__DUPLICATE_METHOD_MATCH = YES;
+				"CODE_SIGN_IDENTITY[sdk=iphoneos*]" = "iPhone Developer";
+				COPY_PHASE_STRIP = NO;
+				DEBUG_INFORMATION_FORMAT = "dwarf-with-dsym";
+				ENABLE_NS_ASSERTIONS = NO;
+				ENABLE_STRICT_OBJC_MSGSEND = YES;
+				ENABLE_USER_SCRIPT_SANDBOXING = NO;
+				GCC_C_LANGUAGE_STANDARD = gnu99;
+				GCC_NO_COMMON_BLOCKS = YES;
+				GCC_WARN_64_TO_32_BIT_CONVERSION = YES;
+				GCC_WARN_ABOUT_RETURN_TYPE = YES_ERROR;
+				GCC_WARN_UNDECLARED_SELECTOR = YES;
+				GCC_WARN_UNINITIALIZED_AUTOS = YES_AGGRESSIVE;
+				GCC_WARN_UNUSED_FUNCTION = YES;
+				GCC_WARN_UNUSED_VARIABLE = YES;
+				IPHONEOS_DEPLOYMENT_TARGET = 12.0;
+				MTL_ENABLE_DEBUG_INFO = NO;
+				SDKROOT = iphoneos;
+				SUPPORTED_PLATFORMS = iphoneos;
+				SWIFT_COMPILATION_MODE = wholemodule;
+				SWIFT_OPTIMIZATION_LEVEL = "-O";
+				TARGETED_DEVICE_FAMILY = "1,2";
+				VALIDATE_PRODUCT = YES;
+			};
+			name = Release;
+		};
+		97C147061CF9000F007C117D /* Debug */ = {
+			isa = XCBuildConfiguration;
+			baseConfigurationReference = 9740EEB21CF90195004384FC /* Debug.xcconfig */;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				CLANG_ENABLE_MODULES = YES;
+				CURRENT_PROJECT_VERSION = "$(FLUTTER_BUILD_NUMBER)";
+				ENABLE_BITCODE = NO;
+				INFOPLIST_FILE = Runner/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/Frameworks",
+				);
+				PRODUCT_BUNDLE_IDENTIFIER = com.upisc.surfaceTensionCalculator;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OBJC_BRIDGING_HEADER = "Runner/Runner-Bridging-Header.h";
+				SWIFT_OPTIMIZATION_LEVEL = "-Onone";
+				SWIFT_VERSION = 5.0;
+				VERSIONING_SYSTEM = "apple-generic";
+			};
+			name = Debug;
+		};
+		97C147071CF9000F007C117D /* Release */ = {
+			isa = XCBuildConfiguration;
+			baseConfigurationReference = 7AFA3C8E1D35360C0083082E /* Release.xcconfig */;
+			buildSettings = {
+				ASSETCATALOG_COMPILER_APPICON_NAME = AppIcon;
+				CLANG_ENABLE_MODULES = YES;
+				CURRENT_PROJECT_VERSION = "$(FLUTTER_BUILD_NUMBER)";
+				ENABLE_BITCODE = NO;
+				INFOPLIST_FILE = Runner/Info.plist;
+				LD_RUNPATH_SEARCH_PATHS = (
+					"$(inherited)",
+					"@executable_path/Frameworks",
+				);
+				PRODUCT_BUNDLE_IDENTIFIER = com.upisc.surfaceTensionCalculator;
+				PRODUCT_NAME = "$(TARGET_NAME)";
+				SWIFT_OBJC_BRIDGING_HEADER = "Runner/Runner-Bridging-Header.h";
+				SWIFT_VERSION = 5.0;
+				VERSIONING_SYSTEM = "apple-generic";
+			};
+			name = Release;
+		};
+/* End XCBuildConfiguration section */
+
+/* Begin XCConfigurationList section */
+		331C8087294A63A400263BE5 /* Build configuration list for PBXNativeTarget "RunnerTests" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				331C8088294A63A400263BE5 /* Debug */,
+				331C8089294A63A400263BE5 /* Release */,
+				331C808A294A63A400263BE5 /* Profile */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		97C146E91CF9000F007C117D /* Build configuration list for PBXProject "Runner" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				97C147031CF9000F007C117D /* Debug */,
+				97C147041CF9000F007C117D /* Release */,
+				249021D3217E4FDB00AE95B9 /* Profile */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+		97C147051CF9000F007C117D /* Build configuration list for PBXNativeTarget "Runner" */ = {
+			isa = XCConfigurationList;
+			buildConfigurations = (
+				97C147061CF9000F007C117D /* Debug */,
+				97C147071CF9000F007C117D /* Release */,
+				249021D4217E4FDB00AE95B9 /* Profile */,
+			);
+			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
+		};
+/* End XCConfigurationList section */
+	};
+	rootObject = 97C146E61CF9000F007C117D /* Project object */;
+}

ios/Runner.xcodeproj/project.xcworkspace/contents.xcworkspacedata

@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "self:">
+   </FileRef>
+</Workspace>

ios/Runner.xcodeproj/project.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

ios/Runner.xcodeproj/project.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>PreviewsEnabled</key>
+	<false/>
+</dict>
+</plist>

ios/Runner.xcodeproj/xcshareddata/xcschemes/Runner.xcscheme

@@ -0,0 +1,99 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Scheme
+   LastUpgradeVersion = "1510"
+   version = "1.3">
+   <BuildAction
+      parallelizeBuildables = "YES"
+      buildImplicitDependencies = "YES">
+      <BuildActionEntries>
+         <BuildActionEntry
+            buildForTesting = "YES"
+            buildForRunning = "YES"
+            buildForProfiling = "YES"
+            buildForArchiving = "YES"
+            buildForAnalyzing = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "97C146ED1CF9000F007C117D"
+               BuildableName = "Runner.app"
+               BlueprintName = "Runner"
+               ReferencedContainer = "container:Runner.xcodeproj">
+            </BuildableReference>
+         </BuildActionEntry>
+      </BuildActionEntries>
+   </BuildAction>
+   <TestAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      shouldUseLaunchSchemeArgsEnv = "YES">
+      <MacroExpansion>
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "97C146ED1CF9000F007C117D"
+            BuildableName = "Runner.app"
+            BlueprintName = "Runner"
+            ReferencedContainer = "container:Runner.xcodeproj">
+         </BuildableReference>
+      </MacroExpansion>
+      <Testables>
+         <TestableReference
+            skipped = "NO"
+            parallelizable = "YES">
+            <BuildableReference
+               BuildableIdentifier = "primary"
+               BlueprintIdentifier = "331C8080294A63A400263BE5"
+               BuildableName = "RunnerTests.xctest"
+               BlueprintName = "RunnerTests"
+               ReferencedContainer = "container:Runner.xcodeproj">
+            </BuildableReference>
+         </TestableReference>
+      </Testables>
+   </TestAction>
+   <LaunchAction
+      buildConfiguration = "Debug"
+      selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
+      selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
+      launchStyle = "0"
+      useCustomWorkingDirectory = "NO"
+      ignoresPersistentStateOnLaunch = "NO"
+      debugDocumentVersioning = "YES"
+      debugServiceExtension = "internal"
+      enableGPUValidationMode = "1"
+      allowLocationSimulation = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "97C146ED1CF9000F007C117D"
+            BuildableName = "Runner.app"
+            BlueprintName = "Runner"
+            ReferencedContainer = "container:Runner.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </LaunchAction>
+   <ProfileAction
+      buildConfiguration = "Profile"
+      shouldUseLaunchSchemeArgsEnv = "YES"
+      savedToolIdentifier = ""
+      useCustomWorkingDirectory = "NO"
+      debugDocumentVersioning = "YES">
+      <BuildableProductRunnable
+         runnableDebuggingMode = "0">
+         <BuildableReference
+            BuildableIdentifier = "primary"
+            BlueprintIdentifier = "97C146ED1CF9000F007C117D"
+            BuildableName = "Runner.app"
+            BlueprintName = "Runner"
+            ReferencedContainer = "container:Runner.xcodeproj">
+         </BuildableReference>
+      </BuildableProductRunnable>
+   </ProfileAction>
+   <AnalyzeAction
+      buildConfiguration = "Debug">
+   </AnalyzeAction>
+   <ArchiveAction
+      buildConfiguration = "Release"
+      revealArchiveInOrganizer = "YES">
+   </ArchiveAction>
+</Scheme>

ios/Runner.xcworkspace/contents.xcworkspacedata

@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<Workspace
+   version = "1.0">
+   <FileRef
+      location = "group:Runner.xcodeproj">
+   </FileRef>
+</Workspace>

ios/Runner.xcworkspace/xcshareddata/IDEWorkspaceChecks.plist

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>IDEDidComputeMac32BitWarning</key>
+	<true/>
+</dict>
+</plist>

ios/Runner.xcworkspace/xcshareddata/WorkspaceSettings.xcsettings

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>PreviewsEnabled</key>
+	<false/>
+</dict>
+</plist>

ios/Runner/AppDelegate.swift

@@ -0,0 +1,13 @@
+import Flutter
+import UIKit
+
+@main
+@objc class AppDelegate: FlutterAppDelegate {
+  override func application(
+    _ application: UIApplication,
+    didFinishLaunchingWithOptions launchOptions: [UIApplication.LaunchOptionsKey: Any]?
+  ) -> Bool {
+    GeneratedPluginRegistrant.register(with: self)
+    return super.application(application, didFinishLaunchingWithOptions: launchOptions)
+  }
+}

ios/Runner/Assets.xcassets/AppIcon.appiconset/Contents.json

@@ -0,0 +1,122 @@
+{
+  "images" : [
+    {
+      "size" : "20x20",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-20x20@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "20x20",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-20x20@3x.png",
+      "scale" : "3x"
+    },
+    {
+      "size" : "29x29",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-29x29@1x.png",
+      "scale" : "1x"
+    },
+    {
+      "size" : "29x29",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-29x29@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "29x29",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-29x29@3x.png",
+      "scale" : "3x"
+    },
+    {
+      "size" : "40x40",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-40x40@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "40x40",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-40x40@3x.png",
+      "scale" : "3x"
+    },
+    {
+      "size" : "60x60",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-60x60@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "60x60",
+      "idiom" : "iphone",
+      "filename" : "Icon-App-60x60@3x.png",
+      "scale" : "3x"
+    },
+    {
+      "size" : "20x20",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-20x20@1x.png",
+      "scale" : "1x"
+    },
+    {
+      "size" : "20x20",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-20x20@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "29x29",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-29x29@1x.png",
+      "scale" : "1x"
+    },
+    {
+      "size" : "29x29",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-29x29@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "40x40",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-40x40@1x.png",
+      "scale" : "1x"
+    },
+    {
+      "size" : "40x40",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-40x40@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "76x76",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-76x76@1x.png",
+      "scale" : "1x"
+    },
+    {
+      "size" : "76x76",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-76x76@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "83.5x83.5",
+      "idiom" : "ipad",
+      "filename" : "Icon-App-83.5x83.5@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "size" : "1024x1024",
+      "idiom" : "ios-marketing",
+      "filename" : "Icon-App-1024x1024@1x.png",
+      "scale" : "1x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}

ios/Runner/Assets.xcassets/LaunchImage.imageset/Contents.json

@@ -0,0 +1,23 @@
+{
+  "images" : [
+    {
+      "idiom" : "universal",
+      "filename" : "LaunchImage.png",
+      "scale" : "1x"
+    },
+    {
+      "idiom" : "universal",
+      "filename" : "LaunchImage@2x.png",
+      "scale" : "2x"
+    },
+    {
+      "idiom" : "universal",
+      "filename" : "LaunchImage@3x.png",
+      "scale" : "3x"
+    }
+  ],
+  "info" : {
+    "version" : 1,
+    "author" : "xcode"
+  }
+}

ios/Runner/Assets.xcassets/LaunchImage.imageset/README.md

@@ -0,0 +1,5 @@
+# Launch Screen Assets
+
+You can customize the launch screen with your own desired assets by replacing the image files in this directory.
+
+You can also do it by opening your Flutter project's Xcode project with `open ios/Runner.xcworkspace`, selecting `Runner/Assets.xcassets` in the Project Navigator and dropping in the desired images.

ios/Runner/Base.lproj/LaunchScreen.storyboard

@@ -0,0 +1,37 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="12121" systemVersion="16G29" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" launchScreen="YES" colorMatched="YES" initialViewController="01J-lp-oVM">
+    <dependencies>
+        <deployment identifier="iOS"/>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="12089"/>
+    </dependencies>
+    <scenes>
+        <!--View Controller-->
+        <scene sceneID="EHf-IW-A2E">
+            <objects>
+                <viewController id="01J-lp-oVM" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="Ydg-fD-yQy"/>
+                        <viewControllerLayoutGuide type="bottom" id="xbc-2k-c8Z"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="Ze5-6b-2t3">
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <subviews>
+                            <imageView opaque="NO" clipsSubviews="YES" multipleTouchEnabled="YES" contentMode="center" image="LaunchImage" translatesAutoresizingMaskIntoConstraints="NO" id="YRO-k0-Ey4">
+                            </imageView>
+                        </subviews>
+                        <color key="backgroundColor" red="1" green="1" blue="1" alpha="1" colorSpace="custom" customColorSpace="sRGB"/>
+                        <constraints>
+                            <constraint firstItem="YRO-k0-Ey4" firstAttribute="centerX" secondItem="Ze5-6b-2t3" secondAttribute="centerX" id="1a2-6s-vTC"/>
+                            <constraint firstItem="YRO-k0-Ey4" firstAttribute="centerY" secondItem="Ze5-6b-2t3" secondAttribute="centerY" id="4X2-HB-R7a"/>
+                        </constraints>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="iYj-Kq-Ea1" userLabel="First Responder" sceneMemberID="firstResponder"/>
+            </objects>
+            <point key="canvasLocation" x="53" y="375"/>
+        </scene>
+    </scenes>
+    <resources>
+        <image name="LaunchImage" width="168" height="185"/>
+    </resources>
+</document>

ios/Runner/Base.lproj/Main.storyboard

@@ -0,0 +1,26 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="10117" systemVersion="15F34" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" initialViewController="BYZ-38-t0r">
+    <dependencies>
+        <deployment identifier="iOS"/>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="10085"/>
+    </dependencies>
+    <scenes>
+        <!--Flutter View Controller-->
+        <scene sceneID="tne-QT-ifu">
+            <objects>
+                <viewController id="BYZ-38-t0r" customClass="FlutterViewController" sceneMemberID="viewController">
+                    <layoutGuides>
+                        <viewControllerLayoutGuide type="top" id="y3c-jy-aDJ"/>
+                        <viewControllerLayoutGuide type="bottom" id="wfy-db-euE"/>
+                    </layoutGuides>
+                    <view key="view" contentMode="scaleToFill" id="8bC-Xf-vdC">
+                        <rect key="frame" x="0.0" y="0.0" width="600" height="600"/>
+                        <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
+                        <color key="backgroundColor" white="1" alpha="1" colorSpace="custom" customColorSpace="calibratedWhite"/>
+                    </view>
+                </viewController>
+                <placeholder placeholderIdentifier="IBFirstResponder" id="dkx-z0-nzr" sceneMemberID="firstResponder"/>
+            </objects>
+        </scene>
+    </scenes>
+</document>

ios/Runner/Info.plist

@@ -0,0 +1,49 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>CFBundleDevelopmentRegion</key>
+	<string>$(DEVELOPMENT_LANGUAGE)</string>
+	<key>CFBundleDisplayName</key>
+	<string>Surface Tension Calculator</string>
+	<key>CFBundleExecutable</key>
+	<string>$(EXECUTABLE_NAME)</string>
+	<key>CFBundleIdentifier</key>
+	<string>$(PRODUCT_BUNDLE_IDENTIFIER)</string>
+	<key>CFBundleInfoDictionaryVersion</key>
+	<string>6.0</string>
+	<key>CFBundleName</key>
+	<string>surface_tension_calculator</string>
+	<key>CFBundlePackageType</key>
+	<string>APPL</string>
+	<key>CFBundleShortVersionString</key>
+	<string>$(FLUTTER_BUILD_NAME)</string>
+	<key>CFBundleSignature</key>
+	<string>????</string>
+	<key>CFBundleVersion</key>
+	<string>$(FLUTTER_BUILD_NUMBER)</string>
+	<key>LSRequiresIPhoneOS</key>
+	<true/>
+	<key>UILaunchStoryboardName</key>
+	<string>LaunchScreen</string>
+	<key>UIMainStoryboardFile</key>
+	<string>Main</string>
+	<key>UISupportedInterfaceOrientations</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>UISupportedInterfaceOrientations~ipad</key>
+	<array>
+		<string>UIInterfaceOrientationPortrait</string>
+		<string>UIInterfaceOrientationPortraitUpsideDown</string>
+		<string>UIInterfaceOrientationLandscapeLeft</string>
+		<string>UIInterfaceOrientationLandscapeRight</string>
+	</array>
+	<key>CADisableMinimumFrameDurationOnPhone</key>
+	<true/>
+	<key>UIApplicationSupportsIndirectInputEvents</key>
+	<true/>
+</dict>
+</plist>

ios/Runner/Runner-Bridging-Header.h

@@ -0,0 +1 @@
+#import "GeneratedPluginRegistrant.h"

ios/RunnerTests/RunnerTests.swift

@@ -0,0 +1,12 @@
+import Flutter
+import UIKit
+import XCTest
+
+class RunnerTests: XCTestCase {
+
+  func testExample() {
+    // If you add code to the Runner application, consider adding tests here.
+    // See https://developer.apple.com/documentation/xctest for more information about using XCTest.
+  }
+
+}

lib/main.dart

@@ -0,0 +1,34 @@
+import 'package:flutter/material.dart';
+import 'package:surface_tension_calculator/routes/route_generator.dart';
+import 'package:surface_tension_calculator/routes/routes.dart';
+import 'package:surface_tension_calculator/utils/snackbar_utils.dart';
+
+void main() {
+  WidgetsFlutterBinding.ensureInitialized();
+
+  runApp(const MyApp());
+}
+
+class MyApp extends StatelessWidget {
+  const MyApp({super.key});
+
+  @override
+  Widget build(BuildContext context) {
+    return MaterialApp(
+      scaffoldMessengerKey: SnackBarUtils.scaffoldKey,
+      title: 'Surface Tension Calculator',
+      theme: ThemeData(
+        fontFamily: 'Montserrat',
+        useMaterial3: true,
+        appBarTheme: const AppBarTheme(
+          centerTitle: true,
+          iconTheme: IconThemeData(color: Colors.white),
+          elevation: 0,
+        ),
+        colorScheme: ColorScheme.fromSeed(seedColor: Colors.deepPurple),
+      ),
+      initialRoute: MainUIRoutes.homeScreen,
+      onGenerateRoute: RouteGenerator.generateRoute,
+    );
+  }
+}

lib/models/stc_output.dart

@@ -0,0 +1,64 @@
+class STCOutput {
+  String negCoordFile;
+  String posCoordFile;
+  double syringeWidth;
+  String radiusCurvRange;
+  String shapeFactorRange;
+  String initXCoordRange;
+  String initAngleRange;
+  int paramCombinations;
+  int numProcessors;
+  double juza;
+  List<double> bestOutput;
+  double lowestRMSD;
+  double surfaceTension;
+  double bestRadiusOfCurvature;
+  double bestShapeFactor;
+  double bestInitialXCoordinate;
+  double bestInitialAngle;
+  double elapsedTime;
+
+  STCOutput({
+    required this.negCoordFile,
+    required this.posCoordFile,
+    required this.syringeWidth,
+    required this.radiusCurvRange,
+    required this.shapeFactorRange,
+    required this.initXCoordRange,
+    required this.initAngleRange,
+    required this.paramCombinations,
+    required this.numProcessors,
+    required this.juza,
+    required this.bestOutput,
+    required this.lowestRMSD,
+    required this.surfaceTension,
+    required this.bestRadiusOfCurvature,
+    required this.bestShapeFactor,
+    required this.bestInitialXCoordinate,
+    required this.bestInitialAngle,
+    required this.elapsedTime,
+  });
+
+  static STCOutput clearOutput() {
+    return STCOutput(
+      negCoordFile: '',
+      posCoordFile: '',
+      syringeWidth: 0,
+      radiusCurvRange: '',
+      shapeFactorRange: '',
+      initXCoordRange: '',
+      initAngleRange: '',
+      paramCombinations: 0,
+      numProcessors: 0,
+      juza: 0,
+      bestOutput: [],
+      lowestRMSD: 0,
+      surfaceTension: 0,
+      bestRadiusOfCurvature: 0,
+      bestShapeFactor: 0,
+      bestInitialXCoordinate: 0,
+      bestInitialAngle: 0,
+      elapsedTime: 0,
+    );
+  }
+}

lib/res/assets.dart

@@ -0,0 +1,4 @@
+abstract class Assets {
+  static const String _assetPath = 'assets';
+  static const String logo = '$_assetPath/ISC_Logo_White.png';
+}

lib/res/strings.dart

@@ -0,0 +1,22 @@
+abstract class Strings {
+  static const sampleOut =
+      'Negative Cooridnate File  : water-drop_Negative.dat\n'
+      'Positive Cooridnate File  : water-drop_Positive.dat\n'
+      'Syringe Width (millimeter): 0.8049999999999999\n'
+      'Radius of Curvature Range : 0.0001-2.0001 (interval: 20)\n'
+      'Shape Factor Range        : 0.0001-1.0001 (interval: 20)\n'
+      'Initial X Coordinate Range: 0.0001-0.5001 (interval: 5)\n'
+      'Initial Angle Range       : 0.0001-0.5001 (interval: 5)\n'
+      'Parameter Combinations    : 10000\n'
+      'Number of Process to Use  : 8\n'
+      'Juza 5-Plane (1/H) Std.Dev: 0.005252355255611812\n'
+      'minimization success\n'
+      'best output: [0.003522111582892356, 0.8302552101788515, 0.4880084250271468, 0.059397867545048805, 0.08677238094443798]\n\n'
+      'Lowest RMSD               : 0.003522111582892356\n'
+      'Computed Surface Tension  : 16.67287006223331\n'
+      'Best Radius of Curvature  : 0.8302552101788515\n'
+      'Best Shape Factor         : 0.4880084250271468\n'
+      'Best Initial X Coordinate : 0.059397867545048805\n'
+      'Best Initial Angle        : 0.08677238094443798\n'
+      'Lapsed Time in Seconds    : 0.18291211128234863';
+}

lib/routes/route_generator.dart

@@ -0,0 +1,49 @@
+import 'package:flutter/material.dart';
+import 'package:surface_tension_calculator/routes/routes.dart';
+
+import '../screens/home_screen.dart';
+
+class RouteGenerator {
+  static Route<dynamic> generateRoute(RouteSettings settings) {
+    // Getting arguments passed in while calling Navigator.pushNamed
+    final args = settings.arguments;
+
+    switch (settings.name) {
+      case MainUIRoutes.homeScreen:
+        return MaterialPageRoute<dynamic>(
+          settings: settings,
+          builder: (_) => const HomeScreen(),
+        );
+      case MainUIRoutes.resultsScreen:
+        // if (args is Map && args['student'] is Student) {
+        //   return MaterialPageRoute(
+        //       settings: settings,
+        //       builder: (_) => DashboardScreen(student: args['student']));
+        // } else {
+        return _errorRoute();
+      // }
+
+      default:
+        // If there is no such named route in the switch statement
+        return _errorRoute();
+    }
+  }
+
+  static Route<dynamic> _errorRoute() {
+    return MaterialPageRoute(
+      builder: (_) {
+        return Scaffold(
+          appBar: AppBar(title: const Text('Error')),
+          body: const Column(
+            mainAxisAlignment: MainAxisAlignment.center,
+            crossAxisAlignment: CrossAxisAlignment.stretch,
+            children: [
+              Icon(Icons.construction_rounded, size: 65),
+              Center(child: Text('This page is under construction.')),
+            ],
+          ),
+        );
+      },
+    );
+  }
+}

lib/routes/routes.dart

@@ -0,0 +1,4 @@
+class MainUIRoutes {
+  static const homeScreen = '/home';
+  static const resultsScreen = '/results';
+}

lib/screens/home_screen.dart

@@ -0,0 +1,309 @@
+import 'dart:io';
+
+import 'package:file_picker/file_picker.dart';
+import 'package:flutter/material.dart';
+import 'package:flutter/services.dart';
+import 'package:surface_tension_calculator/models/stc_output.dart';
+
+import '../res/assets.dart';
+
+class HomeScreen extends StatefulWidget {
+  const HomeScreen({super.key});
+
+  @override
+  State<HomeScreen> createState() => _HomeScreenState();
+}
+
+class _HomeScreenState extends State<HomeScreen> {
+  PlatformFile? _imageFile;
+  STCOutput out = STCOutput.clearOutput();
+  static const String scriptPath = 'scripts/img_V01.exe';
+
+  Future<void> _pickImage() async {
+    try {
+      FilePickerResult? result = await FilePicker.platform.pickFiles(
+        type: FileType.image,
+      );
+      if (result == null) return;
+
+      setState(() {
+        _imageFile = result.files.first;
+      });
+    } catch (e) {}
+  }
+
+  Future<void> _computeSTC() async {
+    final List<String> args = [
+      '-img',
+      _imageFile!.path ?? '',
+      '-out',
+      'water-drop',
+      '-proc',
+      '8',
+    ];
+
+    await Process.run(scriptPath, args);
+
+    out = STCOutput(
+      negCoordFile: 'negCoordFile',
+      posCoordFile: 'posCoordFile',
+      syringeWidth: 0.123,
+      radiusCurvRange: 'asd',
+      shapeFactorRange: 'asd',
+      initXCoordRange: 'asd',
+      initAngleRange: 'asd',
+      paramCombinations: 123,
+      numProcessors: 123,
+      juza: 12.09,
+      bestOutput: [0.123, 12.213],
+      lowestRMSD: 0.123,
+      surfaceTension: 0.123,
+      bestRadiusOfCurvature: 0.123,
+      bestShapeFactor: 0.123,
+      bestInitialXCoordinate: 123.123,
+      bestInitialAngle: 234.123,
+      elapsedTime: 12.12345,
+    );
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      body: SizedBox.expand(
+        child: Container(
+          padding: const EdgeInsets.only(top: 35.0, left: 25, right: 25),
+          color: Color(0xFF7B1113),
+          child: Column(
+            children: [
+              buildHeader(),
+              const SizedBox(height: 20),
+              Container(
+                padding: const EdgeInsets.all(25),
+                decoration: BoxDecoration(
+                  color: Colors.grey.shade300,
+                  borderRadius: BorderRadius.circular(30),
+                ),
+                child: IntrinsicHeight(
+                  child: Row(
+                    children: [
+                      buildLeftImage(),
+                      const SizedBox(width: 20),
+                      const VerticalDivider(width: 20),
+                      const SizedBox(width: 20),
+                      buildRightResults(),
+                    ],
+                  ),
+                ),
+              ),
+              const SizedBox(height: 20),
+              buildFooter(),
+            ],
+          ),
+        ),
+      ),
+    );
+  }
+
+  Widget buildFooter() {
+    return Center(
+      child: Text(
+        '\u00a9 2025 UP Intelligent Systems Center',
+        style: TextStyle(color: Colors.white),
+      ),
+    );
+  }
+
+  Widget buildHeader() {
+    return IntrinsicHeight(
+      child: Row(
+        mainAxisAlignment: MainAxisAlignment.start,
+        children: [
+          const SizedBox(width: 20),
+          Image.asset(Assets.logo, height: 70),
+          const SizedBox(width: 10),
+          const VerticalDivider(),
+          const SizedBox(width: 10),
+          Text(
+            'SURFACE TENSION CALCULATOR',
+            style: TextStyle(
+              fontSize: 45,
+              fontWeight: FontWeight.w500,
+              color: Colors.white,
+            ),
+          ),
+        ],
+      ),
+    );
+  }
+
+  Column buildLeftImage() {
+    return Column(
+      children: [
+        if (_imageFile == null)
+          Container(
+            height: 400,
+            width: 500,
+            decoration: BoxDecoration(
+              color: Colors.grey.shade500,
+              borderRadius: BorderRadius.circular(30),
+            ),
+            child: Center(child: Text('No image uploaded')),
+          ),
+        if (_imageFile != null)
+          Container(
+            height: 400,
+            width: 500,
+            decoration: BoxDecoration(
+              color: Colors.grey.shade500,
+              borderRadius: BorderRadius.circular(30),
+            ),
+            child: Image.memory(Uint8List.fromList(_imageFile!.bytes!)),
+          ),
+        const SizedBox(height: 15),
+        Row(
+          children: [
+            ElevatedButton(
+              onPressed: _pickImage,
+              child: Text('Upload Droplet Image'),
+            ),
+            const SizedBox(width: 10),
+            ElevatedButton(
+              onPressed: _imageFile == null ? null : _computeSTC,
+              child: Text('Compute Surface Tension'),
+            ),
+          ],
+        ),
+      ],
+    );
+  }
+
+  Widget buildRightResults() {
+    return Column(
+      crossAxisAlignment: CrossAxisAlignment.start,
+      children: [
+        Text(
+          'Results:',
+          style: TextStyle(fontSize: 30, fontWeight: FontWeight.w600),
+        ),
+        const SizedBox(height: 10),
+        SingleChildScrollView(child: buildResults()),
+        // Text(out),
+      ],
+    );
+  }
+
+  Widget buildResults() {
+    return Row(
+      children: [
+        buildOutputFields(),
+        const SizedBox(width: 10),
+        Column(
+          crossAxisAlignment: CrossAxisAlignment.start,
+          children: [
+            Text(out.posCoordFile),
+            Text(out.posCoordFile),
+            Text(out.syringeWidth.toString()),
+            Text(out.radiusCurvRange),
+            Text(out.shapeFactorRange),
+            Text(out.initXCoordRange),
+            Text(out.initAngleRange),
+            Text(out.paramCombinations.toString()),
+            Text(out.numProcessors.toString()),
+            Text(out.juza.toString()),
+            Text(''),
+            Text(''),
+            Text(out.bestOutput.toString()),
+            Text(''),
+            Text(out.lowestRMSD.toString()),
+            Text(out.surfaceTension.toString()),
+            Text(out.bestRadiusOfCurvature.toString()),
+            Text(out.bestShapeFactor.toString()),
+            Text(out.bestInitialXCoordinate.toString()),
+            Text(out.bestInitialAngle.toString()),
+            Text(out.elapsedTime.toString()),
+          ],
+        ),
+      ],
+    ); //Text(Strings.sampleOut);
+  }
+
+  Column buildOutputFields() {
+    return Column(
+      crossAxisAlignment: CrossAxisAlignment.start,
+      children: [
+        Text(
+          'Negative Coordinate File: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Positive Coordinate File: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Syringe Width (millimeter): ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Radius of Curvature: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Shape Factor Range: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Initial X Coordinate: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Initial Angle Range: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Parameter Combinations: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Number of Process: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Juza 5-Plane (1/H) Std.Dev: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(''),
+        Text(
+          'minimization success',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text('best output: ', style: TextStyle(fontWeight: FontWeight.w600)),
+        Text('', style: TextStyle(fontWeight: FontWeight.w600)),
+        Text('Lowest RMSD: ', style: TextStyle(fontWeight: FontWeight.w600)),
+        Text(
+          'Computed Surface Tension: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Best Radius of Curvature: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Best Shape Factor: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Best Initial X Coordinate: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Best Initial Angle: ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+        Text(
+          'Lapsed Time (seconds): ',
+          style: TextStyle(fontWeight: FontWeight.w600),
+        ),
+      ],
+    );
+  }
+}

lib/scripts/compute_st.dart

@@ -0,0 +1,361 @@
+import 'dart:io';
+import 'dart:math';
+import 'package:scidart/scidart.dart';
+
+import 'extract_edge_coordinate.dart';
+import 'find_optimal_params_bashforthadams.dart';
+import 'juszas_equation.dart';
+import 'minimize_params_optimization.dart';
+
+void computeST(List<String> sysArgs) {
+  // Initial variable definitions
+  String imageFilePath = "";
+  String outputFileName = "";
+  String posPointsFileName = "";
+  String negPointsFileName = "";
+  int processCount = 2;
+  double syringeWidth = 0.70 * 1.15;
+  double minaRadcurv = 0.0001;
+  double maxaRadcurv = 2.0001;
+  double minbShapefact = 0.0001;
+  double maxbShapefact = 1.0001;
+  double minX = 0.0001;
+  double maxX = 0.5001;
+  double mintAngle = 0.0001;
+  double maxtAngle = 0.5001;
+  int aStep = 20;
+  int bStep = 20;
+  int xStep = 5;
+  int tStep = 5;
+
+  int imageFlag = 0;
+  int posFileFlag = 0;
+  int negFileFlag = 0;
+  int outFlag = 0;
+  int counter = 0;
+  int solveMethod = 0;
+
+  // Argument processing loop.
+  while (counter <= sysArgs.length - 1) {
+    String currentOption = sysArgs[counter];
+    String currentValue = "";
+    try {
+      currentValue = sysArgs[counter + 1];
+    } catch (e) {
+      exit(0);
+    }
+
+    if (currentOption == "-help") {
+      exit(0);
+    } else if (currentOption == "-img") {
+      imageFilePath = currentValue;
+      imageFlag = 1;
+    } else if (currentOption == "-filep") {
+      posPointsFileName = currentValue;
+      posFileFlag = 1;
+    } else if (currentOption == "-filen") {
+      negPointsFileName = currentValue;
+      negFileFlag = 1;
+    } else if (currentOption == "-out") {
+      outputFileName = currentValue;
+      outFlag = 1;
+    } else if (currentOption == "-proc") {
+      processCount = int.parse(currentValue);
+    } else if (currentOption == "-syrg") {
+      syringeWidth = double.parse(currentValue);
+    } else if (currentOption == "-a") {
+      minaRadcurv = double.parse(currentValue);
+    } else if (currentOption == "-A") {
+      maxaRadcurv = double.parse(currentValue);
+    } else if (currentOption == "-b") {
+      minbShapefact = double.parse(currentValue);
+    } else if (currentOption == "-B") {
+      maxbShapefact = double.parse(currentValue);
+    } else if (currentOption == "-x") {
+      minX = double.parse(currentValue);
+    } else if (currentOption == "-X") {
+      maxX = double.parse(currentValue);
+    } else if (currentOption == "-t") {
+      mintAngle = double.parse(currentValue);
+    } else if (currentOption == "-T") {
+      maxtAngle = double.parse(currentValue);
+    } else if (currentOption == "-ai") {
+      aStep = int.parse(currentValue);
+    } else if (currentOption == "-bi") {
+      bStep = int.parse(currentValue);
+    } else if (currentOption == "-xi") {
+      xStep = int.parse(currentValue);
+    } else if (currentOption == "-ti") {
+      tStep = int.parse(currentValue);
+    } else if (currentOption == "-solver") {
+      solveMethod = int.parse(currentValue);
+    } else {
+      exit(0);
+    }
+    counter = counter + 2;
+  }
+
+  if (outFlag == 0 && imageFlag == 1) {
+    print("Output file name not set. (-out)");
+    exit(0);
+  }
+  if (imageFlag == 1 && ((posFileFlag == 1) || (negFileFlag == 1))) {
+    print("Image(-img) can not be set with files option (-filep, -filen).");
+    print("Either set image only or files only.");
+    exit(0);
+  }
+  if (imageFlag == 0 &&
+      ((posFileFlag == 1 && negFileFlag == 0) ||
+          (posFileFlag == 0 && negFileFlag == 1))) {
+    print(
+      "File inputs (-filep, -filen) should both be set if image input is not set.",
+    );
+    exit(0);
+  }
+
+  // Calculate ARange_radCurv
+  List<double> ARange_radCurv = [];
+  double a = minaRadcurv;
+  double ahop = (maxaRadcurv - minaRadcurv) / (aStep - 1);
+  while (a <= maxaRadcurv) {
+    ARange_radCurv.add(a);
+    a += ahop;
+    if (ahop == 0.0) {
+      break;
+    }
+  }
+  if ((maxaRadcurv - ARange_radCurv[ARange_radCurv.length - 1] - ahop).abs() <
+          0.000001 &&
+      ahop != 0.0) {
+    ARange_radCurv.add(maxaRadcurv);
+  }
+
+  // Calculate bRange_shapeFact
+  List<double> brangeShapefact = [];
+  double b = minbShapefact;
+  double bhop = (maxbShapefact - minbShapefact) / (bStep - 1);
+  while (b <= maxbShapefact) {
+    brangeShapefact.add(b);
+    b += bhop;
+    if (bhop == 0) {
+      break;
+    }
+  }
+  if ((maxbShapefact - brangeShapefact[brangeShapefact.length - 1] - bhop)
+              .abs() <
+          0.000001 &&
+      bhop != 0.0) {
+    brangeShapefact.add(maxbShapefact);
+  }
+
+  // Calculate XRange
+  List<double> XRange = [];
+  double x = minX;
+  double xhop = (maxX - minX) / (xStep - 1);
+  while (x <= maxX) {
+    XRange.add(x);
+    x += xhop;
+    if (xhop == 0) {
+      break;
+    }
+  }
+  if ((maxX - XRange[XRange.length - 1] - xhop).abs() < 0.000001 &&
+      xhop != 0.0) {
+    XRange.add(maxX);
+  }
+
+  // Calculate TRange_angle
+  List<double> TRange_angle = [];
+  double t = mintAngle;
+  double thop = (maxtAngle - mintAngle) / (tStep - 1);
+  while (t <= maxtAngle) {
+    TRange_angle.add(t);
+    t += thop;
+    if (thop == 0.0) {
+      break;
+    }
+  }
+  if ((maxtAngle - TRange_angle[TRange_angle.length - 1] - thop).abs() <
+          0.000001 &&
+      thop != 0.0) {
+    TRange_angle.add(maxtAngle);
+  }
+
+  print("\n");
+  if (imageFlag == 1) {
+    print("Image File                : $imageFilePath");
+    print("Output Name               : $outputFileName");
+    print("Negative Coordinate File  : ${outputFileName}_Negative.dat");
+    print("Positive Coordinate File  : ${outputFileName}_Positive.dat");
+    print("Syringe Width (millimeter): $syringeWidth");
+  } else {
+    print("Negative Coordinate File  : $negPointsFileName");
+    print("Positive Coordinate File  : $posPointsFileName");
+  }
+  print(
+    "Radius of Curvature Range : $minaRadcurv-$maxaRadcurv (interval: ${ARange_radCurv.length})",
+  );
+  print(
+    "Shape Factor Range        : $minbShapefact-$maxbShapefact (interval: ${brangeShapefact.length})",
+  );
+  print("Initial X Coordinate Range: $minX-$maxX (interval: ${XRange.length})");
+  print(
+    "Initial Angle Range       : $mintAngle-$maxtAngle (interval: ${TRange_angle.length})",
+  );
+  print(
+    "Parameter Combinations    : ${ARange_radCurv.length * brangeShapefact.length * XRange.length * TRange_angle.length}",
+  );
+  print("Number of Process to Use  : $processCount");
+
+  List<List<double>> posEdgePts;
+  List<List<double>> negEdgePts;
+
+  if (imageFlag == 1) {
+    var result = extractEdgeCoordinate(
+      imageFilePath,
+      outputFileName,
+      syringeWidth,
+    );
+    posEdgePts = result[0];
+    negEdgePts = result[1];
+    double deScaledMaxWidth = result[2];
+    List<double> dmsDiameters = List<double>.from(result[3]);
+
+    double HInv1 = HJuza(dmsDiameters[7] / deScaledMaxWidth, 0.8);
+    double HInv2 = HJuza(dmsDiameters[8] / deScaledMaxWidth, 0.9);
+    double HInv3 = HJuza(dmsDiameters[9] / deScaledMaxWidth, 1.0);
+    double HInv4 = HJuza(dmsDiameters[10] / deScaledMaxWidth, 1.1);
+    double HInv5 = HJuza(dmsDiameters[11] / deScaledMaxWidth, 1.2);
+    double HInvM = (0.20) * (HInv1 + HInv2 + HInv3 + HInv4 + HInv5);
+    double HInvSD = sqrt(
+      (0.20) *
+          ((HInv1 - HInvM) * (HInv1 - HInvM) +
+              (HInv2 - HInvM) * (HInv2 - HInvM) +
+              (HInv3 - HInvM) * (HInv3 - HInvM) +
+              (HInv4 - HInvM) * (HInv4 - HInvM) +
+              (HInv5 - HInvM) * (HInv5 - HInvM)),
+    );
+    print("Juza 5-Plane (1/H) Std.Dev: $HInvSD");
+  } else {
+    posEdgePts = [];
+    try {
+      List<String> positiveLines = File(posPointsFileName).readAsLinesSync();
+      for (var Line in positiveLines) {
+        List<String> coordinate = Line.split(RegExp(r'\s+'));
+        //print(coordinate);
+        posEdgePts.add([
+          double.parse(coordinate[0]),
+          double.parse(coordinate[1]),
+        ]);
+      }
+    } catch (e) {
+      print("Error reading positive points file.");
+      exit(0);
+    }
+    negEdgePts = [];
+    try {
+      List<String> negativeLines = File(negPointsFileName).readAsLinesSync();
+      for (var Line in negativeLines) {
+        List<String> coordinate = Line.split(RegExp(r'\s+'));
+        //print(Coordinate);
+        negEdgePts.add([
+          double.parse(coordinate[0]),
+          double.parse(coordinate[1]),
+        ]);
+      }
+    } catch (e) {
+      print("Error reading negative points file.");
+      exit(0);
+    }
+  }
+
+  // Nested function bruteForce
+  List<dynamic> bruteForce() {
+    List<List<double>> posList = [];
+    List<List<double>> negList = [];
+    for (int processNo = 0; processNo < processCount; processNo++) {
+      posList.add(posEdgePts);
+      negList.add(negEdgePts);
+      //print(processNo);
+    }
+
+    List<List<double>> aRanges = [];
+    for (int processNo = 0; processNo < processCount; processNo++) {
+      aRanges.add([]);
+    }
+
+    int i = 0;
+    for (var A in ARange_radCurv) {
+      aRanges[i % processCount].add(A);
+      i += 1;
+    }
+
+    List<List<dynamic>> bestParams = []; // will store candidate tuples
+    List<int> ticksQueue = []; // simulate ticks
+
+    // Simulate process creation and execution.
+    for (int processNo = 0; processNo < processCount; processNo++) {
+      // In a real multiprocessing environment, each process would run concurrently.
+      // Here, we directly call the function.
+      findOptimalParameters(
+        posList[processNo],
+        negList[processNo],
+        aRanges[processNo],
+        brangeShapefact,
+        XRange,
+        TRange_angle,
+        bestParams,
+        ticksQueue,
+      );
+    }
+
+    stdout.write("\rParameter Search Progress : 0%");
+    stdout.flush();
+    int count = 0;
+    int totalTicks = ARange_radCurv.length;
+    // Simulate receiving ticks.
+    while (count < totalTicks) {
+      // Since ticks have been already added, just increment Count.
+      if (ticksQueue.isNotEmpty) {
+        ticksQueue.removeAt(0);
+        count += 1;
+        stdout.write(
+          "\rParameter Search Progress : ${(100 * (count / totalTicks)).toInt()}%",
+        );
+        stdout.flush();
+      }
+    }
+    print("");
+
+    List<dynamic> bestOutput = [999999999, 1, 1, 1, 1];
+    for (var output in bestParams) {
+      if (output[0] < bestOutput[0]) {
+        bestOutput = output;
+      }
+    }
+    return bestOutput;
+  }
+
+  // Nested function Optimize
+  List<dynamic> optimize() {
+    return optimizeParameters(posEdgePts, negEdgePts, 0.95, 0.3, 0.1, 0.2);
+  }
+
+  // Record start time
+  var startTime = DateTime.now();
+
+  // Choose which solver to use.
+  List<dynamic> bestOutput = (solveMethod != 1) ? optimize() : bruteForce();
+
+  print("best output: $bestOutput");
+
+  print("\nLowest RMSD               : ${bestOutput[0]}");
+  // Computed Surface Tension: 9.8*bestOutput[1]/bestOutput[2]
+  print("Computed Surface Tension  : ${9.8 * bestOutput[1] / bestOutput[2]}");
+  print("Best Radius of Curvature  : ${bestOutput[1]}");
+  print("Best Shape Factor         : ${bestOutput[2]}");
+  print("Best Initial X Coordinate : ${bestOutput[3]}");
+  print("Best Initial Angle        : ${bestOutput[4]}");
+  var elapsed = DateTime.now().difference(startTime).inSeconds;
+  print("Lapsed Time in Seconds    : $elapsed");
+}

lib/scripts/extract_edge_coordinate.dart

@@ -0,0 +1,344 @@
+import 'dart:io';
+import 'dart:math';
+
+List<dynamic> extractEdgeCoordinate(
+  String imageFilePath,
+  String outputFileName,
+  double syringeWidth,
+) {
+  // Detect the edges of the image.
+  // All edge pixels will white(255) and rest of the pixels will be black(0).
+  List<List<dynamic>> Image = CV2.imread(imageFilePath, CV2.IMREAD_COLOR);
+  List<List<int>> EdgeImage = CV2.Canny(Image, 100, 200);
+
+  // Find the first edge point (white pixel).
+  // It is assumed that first edge point part of the syringe.
+  int NumOfRow = EdgeImage.length;
+  int NumOfCol = EdgeImage[0].length;
+  List<int> EdgePoint = [0, 0];
+  int EdgePointFlag = 0;
+  for (int RowIndex = 0; RowIndex < NumOfRow; RowIndex++) {
+    for (int ColIndex = 0; ColIndex < NumOfCol; ColIndex++) {
+      if (EdgeImage[RowIndex][ColIndex] == 255) {
+        EdgePoint = [RowIndex, ColIndex];
+        EdgePointFlag = 1;
+        break;
+      }
+    }
+    if (EdgePointFlag == 1) {
+      break;
+    }
+  }
+
+  // Color the all the syringe and droplet pixels differently (70).
+  // Determine the left-most, right-most, and bottom droplet pixels.
+  EdgeImage[EdgePoint[0]][EdgePoint[1]] = 70;
+  List<List<int>> DropletEdgePoints = [];
+  DropletEdgePoints.add(EdgePoint);
+  int LeftMostCol = 9999999999;
+  int RightMostCol = 0;
+  int BottomMostRow = 0;
+  int BottomMostRow2 = 0;
+  int CenterCol = 0;
+
+  while (DropletEdgePoints.length != 0) {
+    List<int> CurrentPoint = DropletEdgePoints[0];
+    DropletEdgePoints.remove(CurrentPoint);
+    List<List<int>> NeighborPoints = [];
+    for (int RowOffset = -3; RowOffset < 4; RowOffset++) {
+      for (int ColOffset = -3; ColOffset < 4; ColOffset++) {
+        if (RowOffset != 0 || ColOffset != 0) {
+          NeighborPoints.add([
+            CurrentPoint[0] + RowOffset,
+            CurrentPoint[1] + ColOffset,
+          ]);
+        }
+      }
+    }
+    for (List<int> point in NeighborPoints) {
+      int PointRow = point[0];
+      int PointCol = point[1];
+      if ((0 <= PointRow && PointRow < NumOfRow) &&
+          (0 <= PointCol && PointCol < NumOfCol)) {
+        if (EdgeImage[PointRow][PointCol] == 255) {
+          DropletEdgePoints.add([PointRow, PointCol]);
+          EdgeImage[PointRow][PointCol] = 70;
+          if (PointRow > BottomMostRow) {
+            BottomMostRow = PointRow;
+          }
+          if (PointCol > RightMostCol) {
+            RightMostCol = PointCol;
+          }
+          if (PointCol < LeftMostCol) {
+            LeftMostCol = PointCol;
+          }
+        }
+      }
+    }
+  }
+
+  CenterCol = (LeftMostCol + RightMostCol) ~/ 2;
+  for (int Row = 0; Row < BottomMostRow + 1; Row++) {
+    if (EdgeImage[Row][CenterCol] == 70) {
+      BottomMostRow2 = Row;
+    }
+  }
+  BottomMostRow = BottomMostRow2;
+
+  // Determine the transition row between the syringe pixels and the droplet pixels.
+  int PreviousWidth = 0;
+  int WidthIncCount = 5;
+  List<int> WidthHistory = List.filled(WidthIncCount + 1, 0);
+  int TransitionRow = 0;
+
+  for (int Row = 0; Row < BottomMostRow; Row++) {
+    int LeftEdgeCol = 0;
+    int RightEdgeCol = 9999999;
+    for (int Col = LeftMostCol - 1; Col < RightMostCol + 1; Col++) {
+      if (EdgeImage[Row][Col] == 70) {
+        LeftEdgeCol = Col;
+        break;
+      }
+    }
+    for (int Col = RightMostCol + 1; Col >= LeftMostCol - 1; Col--) {
+      if (EdgeImage[Row][Col] == 70) {
+        RightEdgeCol = Col;
+        break;
+      }
+    }
+    int CurrentWidth = RightEdgeCol - LeftEdgeCol;
+    if ((CurrentWidth != PreviousWidth) &&
+        (0 < CurrentWidth) &&
+        (CurrentWidth < (9999999 - NumOfCol))) {
+      for (int i = 0; i < WidthIncCount; i++) {
+        WidthHistory[i] = WidthHistory[i + 1];
+      }
+      WidthHistory[WidthIncCount] = CurrentWidth;
+    }
+    int WidthIncreaseCount = 0;
+    for (int i = 0; i < WidthIncCount; i++) {
+      if (WidthHistory[i] < WidthHistory[i + 1]) {
+        WidthIncreaseCount += 1;
+      }
+    }
+    if (WidthIncreaseCount == WidthIncCount) {
+      TransitionRow = Row;
+      break;
+    }
+    if ((0 < CurrentWidth) && (CurrentWidth < (9999999 - NumOfCol))) {
+      PreviousWidth = CurrentWidth;
+    }
+  }
+
+  // Determine the width of the syringe in terms of pixel count
+  int WidthSum = 0;
+  int WidthCount = 0;
+  int SyringeLevel = (0.75 * TransitionRow).toInt();
+  for (int Row = 0; Row < TransitionRow; Row++) {
+    int RightEdgeCol = 9999999;
+    int LeftEdgeCol = 0;
+    for (int Col = LeftMostCol; Col < CenterCol + 1; Col++) {
+      if (EdgeImage[Row][Col] == 70) {
+        EdgeImage[Row][Col] = 255;
+        LeftEdgeCol = Col;
+        break;
+      }
+    }
+    for (int Col = RightMostCol; Col > CenterCol - 1; Col--) {
+      if (EdgeImage[Row][Col] == 70) {
+        EdgeImage[Row][Col] = 255;
+        RightEdgeCol = Col;
+        break;
+      }
+    }
+    int CurrentWidth = RightEdgeCol - LeftEdgeCol;
+    if (WidthCount <= SyringeLevel) {
+      if ((0 < CurrentWidth) && (CurrentWidth < (9999999 - NumOfCol))) {
+        WidthSum += CurrentWidth;
+        WidthCount += 1;
+      }
+    }
+  }
+  double AverageWidth = (WidthSum.toDouble()) / (WidthCount.toDouble());
+
+  // Extract the pixel coordinates of all droplet pixels (color: 70)
+  List<List<int>> PositiveEdgePoints = [];
+  List<List<int>> NegativeEdgePoints = [];
+  for (int Row = BottomMostRow; Row > TransitionRow - 1; Row--) {
+    for (int Col = LeftMostCol; Col < CenterCol + 1; Col++) {
+      if (EdgeImage[Row][Col] == 70) {
+        NegativeEdgePoints.add([Row, Col]);
+        break;
+      }
+    }
+    for (int Col = RightMostCol; Col > CenterCol; Col--) {
+      if (EdgeImage[Row][Col] == 70) {
+        PositiveEdgePoints.add([Row, Col]);
+        break;
+      }
+    }
+  }
+
+  // Scale the point coordinates by using the syringe length
+  double SyringeWidth = syringeWidth;
+  double ScalingFactor = SyringeWidth / AverageWidth;
+  List<List<double>> ScaledNegativeEdgePoints = [];
+  String negativeFileName = outputFileName + "_Negative.dat";
+  IOSink NegativeCoordinatesFile = File(negativeFileName).openWrite();
+  for (List<int> point in NegativeEdgePoints) {
+    int Row = point[0];
+    int Col = point[1];
+    double Row2 = (ScalingFactor * (BottomMostRow - Row).toDouble()) + 0.0001;
+    double Col2 = ScalingFactor * (Col - CenterCol).toDouble();
+    NegativeCoordinatesFile.write("$Col2 $Row2\n");
+    ScaledNegativeEdgePoints.add([Col2, Row2]);
+  }
+  NegativeCoordinatesFile.close();
+
+  List<List<double>> ScaledPositiveEdgePoints = [];
+  String positiveFileName = "${outputFileName}_Positive.dat";
+  IOSink PositiveCoordinatesFile = File(positiveFileName).openWrite();
+  for (List<int> point in PositiveEdgePoints) {
+    int Row = point[0];
+    int Col = point[1];
+    double Row2 = (ScalingFactor * (BottomMostRow - Row).toDouble()) + 0.0001;
+    double Col2 = ScalingFactor * (Col - CenterCol).toDouble();
+    PositiveCoordinatesFile.write("$Col2 $Row2\n");
+    ScaledPositiveEdgePoints.add([Col2, Row2]);
+  }
+  PositiveCoordinatesFile.close();
+
+  // Draw the detected edge points of the droplet.
+  // List<List<dynamic>> Image2 = deepCopy(Image);
+  for (int Row = 0; Row < NumOfRow; Row++) {
+    for (int Col = 0; Col < NumOfCol; Col++) {
+      Image[Row][Col] = 0;
+      // For EdgeImage, since it is a separate 2D list of ints, set to 0.
+      EdgeImage[Row][Col] = 0;
+    }
+  }
+  for (List<int> Point in PositiveEdgePoints) {
+    Image[Point[0]][Point[1]] = [0, 0, 255];
+    EdgeImage[Point[0]][Point[1]] = 255;
+  }
+  for (List<int> Point in NegativeEdgePoints) {
+    Image[Point[0]][Point[1]] = [0, 0, 255];
+    EdgeImage[Point[0]][Point[1]] = 255;
+  }
+
+  // Draw the center column of the drop
+  CV2.line(
+    Image,
+    Point(CenterCol.toDouble(), TransitionRow.toDouble()),
+    Point(CenterCol.toDouble(), BottomMostRow.toDouble()),
+    [0, 255, 0],
+    1,
+  ); // image, start, end, color(BGR), thickness
+
+  double MaxWidthRatio = 0.0;
+  for (int Row = BottomMostRow; Row > TransitionRow - 1; Row--) {
+    int RightCol = 99999;
+    int LeftCol = -1;
+    for (int Col = LeftMostCol; Col < CenterCol + 1; Col++) {
+      if (EdgeImage[Row][Col] == 255) {
+        LeftCol = Col;
+        break;
+      }
+    }
+    for (int Col = RightMostCol; Col > CenterCol; Col--) {
+      if (EdgeImage[Row][Col] == 255) {
+        RightCol = Col;
+        break;
+      }
+    }
+    double WidthRatio =
+        (RightCol - LeftCol).toDouble() /
+        (RightMostCol - LeftMostCol).toDouble();
+    if (WidthRatio < 1.0 && WidthRatio > MaxWidthRatio) {
+      MaxWidthRatio = WidthRatio;
+    }
+  }
+
+  List<List<int>> RowWithMaxWidth = [];
+  for (int Row = BottomMostRow; Row > TransitionRow - 1; Row--) {
+    int RightCol = 99999;
+    int LeftCol = -1;
+    for (int Col = LeftMostCol; Col < CenterCol + 1; Col++) {
+      if (EdgeImage[Row][Col] == 255) {
+        LeftCol = Col;
+        break;
+      }
+    }
+    for (int Col = RightMostCol; Col > CenterCol; Col--) {
+      if (EdgeImage[Row][Col] == 255) {
+        RightCol = Col;
+        break;
+      }
+    }
+    double WidthRatio =
+        (RightCol - LeftCol).toDouble() /
+        (RightMostCol - LeftMostCol).toDouble();
+    if (WidthRatio == MaxWidthRatio) {
+      RowWithMaxWidth.add([Row, LeftCol, RightCol]);
+    }
+  }
+
+  // Draw the main diameter
+  int n = RowWithMaxWidth.length;
+  n = (n / 2).toInt();
+  int Row = RowWithMaxWidth[n][0];
+  int LeftCol = RowWithMaxWidth[n][1];
+  int RightCol = RowWithMaxWidth[n][2];
+  CV2.line(
+    Image,
+    Point(LeftCol.toDouble(), Row.toDouble()),
+    Point(RightCol.toDouble(), Row.toDouble()),
+    [0, 255, 0],
+    1,
+  );
+
+  // Measure and draw the ten diameters
+  List<int> Diameters = [];
+  int MaxWidth = RightMostCol - LeftMostCol;
+  for (int i = 1; i < 13; i++) {
+    for (int Col = LeftMostCol; Col < CenterCol + 1; Col++) {
+      if (EdgeImage[BottomMostRow - (i * MaxWidth ~/ 10)][Col] == 255) {
+        LeftCol = Col;
+        break;
+      }
+    }
+    for (int Col = RightMostCol; Col > CenterCol; Col--) {
+      if (EdgeImage[BottomMostRow - (i * MaxWidth ~/ 10)][Col] == 255) {
+        RightCol = Col;
+        break;
+      }
+    }
+    Diameters.add(RightCol - LeftCol);
+    CV2.line(
+      Image,
+      Point(
+        LeftCol.toDouble(),
+        (BottomMostRow - (i * MaxWidth ~/ 10)).toDouble(),
+      ),
+      Point(
+        RightCol.toDouble(),
+        (BottomMostRow - (i * MaxWidth ~/ 10)).toDouble(),
+      ),
+      [255, 0, 0],
+      1,
+    );
+  }
+
+  // Scale the 12 drop diameters
+  for (int i = 0; i < 12; i++) {
+    Diameters[i] = (Diameters[i] * ScalingFactor).toInt();
+  }
+  double ScaledMaxWidth = ScalingFactor * MaxWidth.toDouble();
+  // double ScaledUpWidth = ScalingFactor * (RightCol - LeftCol).toDouble();
+  return [
+    ScaledPositiveEdgePoints,
+    ScaledNegativeEdgePoints,
+    ScaledMaxWidth,
+    Diameters,
+  ];
+}

lib/scripts/find_optimal_params_bashforthadams.dart

@@ -0,0 +1,63 @@
+import 'dart:math';
+
+import 'package:surface_tension_calculator/scripts/rk4.dart';
+
+/// ========== FINDING OPTIMAL PARAMETERS for BASHFORTH-ADAMS SOLUTION ==========
+void findOptimalParameters(
+  List<double> posEdgePoints,
+  List<double> negEdgePoints,
+  List<double> aRangeRadCurv,
+  List<double> bRangeShapeFact,
+  List<double> xRange,
+  List<double> tRangeAngle,
+  List<dynamic> params,
+  List<dynamic> ticks,
+) {
+  var rk4PosTable = makeRK4Table(posEdgePoints);
+  var rk4NegTable = makeRK4Table(negEdgePoints);
+
+  double minimumRMSD = 999999.0;
+  List<double> bestParameters = [0, 0, 0, 0];
+
+  for (var aRadCurv in aRangeRadCurv) {
+    for (var bShapeFact in bRangeShapeFact) {
+      for (var x in xRange) {
+        for (var tAngle in tRangeAngle) {
+          double fTotalDiffSquared = 0.0;
+          rk4PosTable[0][3] = x;
+          rk4PosTable[0][4] = tAngle;
+          rk4NegTable[0][3] = x;
+          rk4NegTable[0][4] = tAngle;
+          fTotalDiffSquared += bashforthAdamsRK4(
+            rk4PosTable,
+            aRadCurv,
+            bShapeFact,
+            1.0,
+          );
+          fTotalDiffSquared += bashforthAdamsRK4(
+            rk4NegTable,
+            aRadCurv,
+            bShapeFact,
+            -1.0,
+          );
+
+          double currentRMSD = sqrt(
+            fTotalDiffSquared / (posEdgePoints.length + negEdgePoints.length),
+          );
+          if (currentRMSD < minimumRMSD) {
+            minimumRMSD = currentRMSD;
+            bestParameters = [aRadCurv, bShapeFact, x, tAngle];
+          }
+        }
+        ticks.add("#");
+      }
+    }
+  }
+
+  double aRadCurv = bestParameters[0];
+  double bShapeFact = bestParameters[1];
+  double x = bestParameters[2];
+  double tAngle = bestParameters[3];
+  // double st = (9.8 * aRadCurv) / bShapeFact;
+  params.add((minimumRMSD, aRadCurv, bShapeFact, x, tAngle));
+}

lib/scripts/img_V01.py

@@ -0,0 +1,799 @@
+#!/usr/bin/env python
+
+# Surface Tension Calculation via Pendant Drop Method (Bashforth-Adams)
+# Created by    : Ren Tristan A. de la Cruz
+# Created on    : 2016 July 26
+# Last Modified : 2025 January 27
+# Contact       : rentristandelacruz@gmail.com
+# Contact       : radelacruz@up.edu.ph
+
+# ========== IMPORTS ==========
+
+import math
+import copy
+import time
+import sys
+import cv2
+import multiprocessing
+import numpy as np
+import scipy.optimize #as spo
+
+# ========== READ THE IMAGE & EXTRACT THE EDGE COORDINATES ==========
+
+def ExtractEdgeCoordinate(_ImageFilePath, _OutputFileName, _SyringeWidth):
+
+    # Detect the edges of the image. 
+    # All edge pixels will white(255) and rest of the pixels will be black(0).
+    Image = cv2.imread(_ImageFilePath, cv2.IMREAD_COLOR)
+    EdgeImage = cv2.Canny(Image, 100, 200)
+
+    # Find the first edge point (white pixel). 
+    # It is assumed that first edge point part of the syringe.
+    NumOfRow, NumOfCol = EdgeImage.shape
+    EdgePoint = (0, 0)
+    EdgePointFlag = 0
+    for RowIndex in range(NumOfRow):
+        for ColIndex in range(NumOfCol):
+            if EdgeImage[RowIndex, ColIndex] == 255:
+                EdgePoint = (RowIndex, ColIndex)
+                EdgePointFlag = 1
+                break
+        if EdgePointFlag == 1:
+            break
+
+
+    # Color the all the syringe and droplet pixels differently (70). 
+    # Determine the left-most, right-most, and bottom droplet pixels.
+    EdgeImage[EdgePoint] = 70
+    DropletEdgePoints = []
+    DropletEdgePoints.append(EdgePoint)
+    LeftMostCol    = 9999999999
+    RightMostCol   = 0
+    BottomMostRow  = 0
+    BottomMostRow2 = 0
+    CenterCol      = 0
+
+    while (len(DropletEdgePoints) != 0):
+        CurrentPoint = DropletEdgePoints[0]
+        DropletEdgePoints.remove(CurrentPoint)
+        NeighborPoints = []
+        for RowOffset in range(-3,4, 1):
+            for ColOffset in range(-3,4,1):
+                if(RowOffset != 0 or ColOffset != 0):
+                    NeighborPoints.append((CurrentPoint[0]+RowOffset, CurrentPoint[1]+ColOffset))
+        for PointRow, PointCol in NeighborPoints:
+            if (0 <= PointRow and PointRow < NumOfRow) and (0 <= PointCol and PointCol < NumOfCol):
+                if EdgeImage[PointRow][PointCol] == 255:
+                    DropletEdgePoints.append((PointRow, PointCol))
+                    EdgeImage[PointRow, PointCol] = 70
+                    if PointRow > BottomMostRow:
+                        BottomMostRow = PointRow
+                    if PointCol > RightMostCol:
+                        RightMostCol = PointCol
+                    if PointCol < LeftMostCol:
+                        LeftMostCol = PointCol
+
+    CenterCol = (LeftMostCol + RightMostCol)//2
+    for Row in range(BottomMostRow + 1):
+        if EdgeImage[Row][CenterCol] == 70:
+            BottomMostRow2 = Row
+    BottomMostRow = BottomMostRow2
+
+
+    # Determine the transition row between the syringe pixels and the droplet pixels.
+    PreviousWidth = 0
+    WidthIncCount = 5
+    WidthHistory  = [0]*(WidthIncCount+1)
+    TransitionRow = 0
+
+    for Row in range(BottomMostRow):
+        LeftEdgeCol = 0
+        RightEdgeCol = 9999999
+        for Col in range(LeftMostCol-1, RightMostCol+1, 1):
+            if EdgeImage[Row,Col] == 70:
+                LeftEdgeCol = Col
+                break
+        for Col in range(RightMostCol+1, LeftMostCol-1, -1):
+            if EdgeImage[Row,Col] == 70:
+                RightEdgeCol = Col
+                break
+        CurrentWidth = RightEdgeCol - LeftEdgeCol
+        if (CurrentWidth != PreviousWidth) and (0 < CurrentWidth) and (CurrentWidth < (9999999-NumOfCol)):
+            for i in range(WidthIncCount):
+                WidthHistory[i] = WidthHistory[i+1]
+            WidthHistory[WidthIncCount] = CurrentWidth
+        WidthIncreaseCount = 0
+        for i in range(WidthIncCount):
+            if WidthHistory[i] < WidthHistory[i+1]:
+                WidthIncreaseCount += 1
+        if WidthIncreaseCount == WidthIncCount:
+            TransitionRow = Row
+            break
+        if (0 < CurrentWidth) and (CurrentWidth < (9999999-NumOfCol)):
+            PreviousWidth = CurrentWidth
+
+
+    # Determine the width of the syringe in terms of pixel count
+    WidthSum   = 0
+    WidthCount = 0
+    SyringeLevel = int(0.75 * TransitionRow)
+    for Row in range(TransitionRow):
+        RightEdgeCol = 9999999
+        LeftEdgeCol  = 0
+        for Col in range(LeftMostCol, CenterCol + 1, 1):
+            if EdgeImage[Row, Col] == 70:
+                 EdgeImage[Row, Col] = 255
+                 LeftEdgeCol = Col
+                 break
+        for Col in range(RightMostCol, CenterCol - 1, -1):
+            if EdgeImage[Row, Col] == 70:
+                 EdgeImage[Row, Col] = 255
+                 RightEdgeCol = Col
+                 break
+        CurrentWidth = RightEdgeCol - LeftEdgeCol
+        if WidthCount <= SyringeLevel:
+            if (0 < CurrentWidth) and (CurrentWidth < (9999999-NumOfCol)):
+                WidthSum += CurrentWidth
+                WidthCount += 1
+    AverageWidth = float(WidthSum)/float(WidthCount)
+
+
+    # Extract the pixel coordinates of all droplet pixels (color: 70)
+    PositiveEdgePoints = []
+    NegativeEdgePoints = []
+    for Row in range(BottomMostRow, TransitionRow-1 ,-1):
+        for Col in range(LeftMostCol, CenterCol + 1, 1):
+           if EdgeImage[Row, Col] == 70:
+                NegativeEdgePoints.append((Row, Col))
+                break
+        for Col in range(RightMostCol, CenterCol, -1):
+            if EdgeImage[Row, Col] == 70:
+                PositiveEdgePoints.append((Row, Col))
+                break
+
+
+    # Scale the point coordinates by using the syringe length
+    SyringeWidth = _SyringeWidth
+    ScalingFactor = SyringeWidth/AverageWidth
+    ScaledNegativeEdgePoints = [] 
+    NegativeCoordinatesFile = open(_OutputFileName+"_Negative.dat", 'w')
+    for Row, Col in NegativeEdgePoints:
+        Row2 = (ScalingFactor*float(BottomMostRow-Row)) + 0.0001
+        Col2 = ScalingFactor*float(Col - CenterCol)
+        NegativeCoordinatesFile.write(str(Col2) + " " + str(Row2) + "\n")
+        ScaledNegativeEdgePoints.append((Col2,Row2))
+    NegativeCoordinatesFile.close()
+
+    ScaledPositiveEdgePoints = []
+    PositiveCoordinatesFile = open(_OutputFileName+"_Positive.dat", 'w')
+    for Row, Col in PositiveEdgePoints:
+        Row2 = (ScalingFactor*float(BottomMostRow-Row)) + 0.0001
+        Col2 = ScalingFactor*float(Col - CenterCol)
+        PositiveCoordinatesFile.write(str(Col2) + " " + str(Row2) + "\n")
+        ScaledPositiveEdgePoints.append((Col2, Row2))
+    PositiveCoordinatesFile.close()
+
+
+    # Draw the detected edge points of the droplet.
+    Image2 = copy.deepcopy(Image)
+    for Row in range(0, NumOfRow):
+        for Col in range(0, NumOfCol):
+            Image[(Row,Col)] = 0
+            EdgeImage[(Row,Col)] = 0
+    for Point in PositiveEdgePoints:
+        Image[Point] = (0, 0, 255)
+        EdgeImage[Point] = 255
+    for Point in NegativeEdgePoints:
+        Image[Point] = (0, 0, 255)
+        EdgeImage[Point] = 255
+
+    # Draw the center column of the drop
+    cv2.line(Image, (CenterCol, TransitionRow), (CenterCol, BottomMostRow), (0, 255, 0), 1) # image, start, end, color(BGR), thickness
+
+    MaxWidthRatio = 0.0    
+    for Row in range(BottomMostRow, TransitionRow-1 ,-1):
+        RightCol = 99999
+        LeftCol  = -1
+        for Col in range(LeftMostCol, CenterCol + 1, 1):
+           if EdgeImage[Row, Col] == 255:
+                LeftCol = Col
+                break
+        for Col in range(RightMostCol, CenterCol, -1):
+            if EdgeImage[Row, Col] == 255:
+                RightCol = Col
+                break
+        WidthRatio = float(RightCol - LeftCol)/float(RightMostCol-LeftMostCol)
+        if WidthRatio < 1.0 and WidthRatio > MaxWidthRatio:
+            MaxWidthRatio = WidthRatio
+
+    RowWithMaxWidth = []
+    for Row in range(BottomMostRow, TransitionRow-1 ,-1):
+        RightCol = 99999
+        LeftCol  = -1
+        for Col in range(LeftMostCol, CenterCol + 1, 1):
+           if EdgeImage[Row, Col] == 255:
+                LeftCol = Col
+                break
+        for Col in range(RightMostCol, CenterCol, -1):
+            if EdgeImage[Row, Col] == 255:
+                RightCol = Col
+                break
+        WidthRatio = float(RightCol - LeftCol)/float(RightMostCol-LeftMostCol)
+        if WidthRatio == MaxWidthRatio:
+            RowWithMaxWidth.append((Row, LeftCol, RightCol))
+
+    # Draw the main diameter
+    n = len(RowWithMaxWidth)
+    n = int(n/2)
+    Row = RowWithMaxWidth[n][0]
+    LeftCol = RowWithMaxWidth[n][1]
+    RightCol = RowWithMaxWidth[n][2]
+    cv2.line(Image, (LeftCol, Row), (RightCol, Row), (0, 255, 0), 1)
+
+    # Measure and draw the ten diameters
+    Diameters = []
+    MaxWidth = RightMostCol - LeftMostCol
+    for i in range(1, 13, 1):
+        for Col in range(LeftMostCol, CenterCol + 1, 1):
+            if EdgeImage[BottomMostRow-int(i*MaxWidth/10.0), Col] == 255:
+                LeftCol = Col
+                break
+        for Col in range(RightMostCol, CenterCol, -1):
+            if EdgeImage[BottomMostRow-int(i*MaxWidth/10.0), Col] == 255:
+                RightCol = Col
+                break
+        Diameters.append(RightCol-LeftCol)
+        cv2.line(Image, (LeftCol, BottomMostRow-int(i*MaxWidth/10.0)), (RightCol, BottomMostRow-int(i*MaxWidth/10.0)), (255, 0, 0), 1)
+
+    #DELETE THIS
+    #cv2.imwrite("1.jpg", Image)
+    #sys.exit()
+
+
+    # Scale the 12 drop diameters
+    for i in range(12):
+        Diameters[i] *= ScalingFactor
+
+    ScaledMaxWidth = ScalingFactor*float(MaxWidth)
+    ScaledUpWidth = ScalingFactor*float(RightCol - LeftCol)
+    return ScaledPositiveEdgePoints, ScaledNegativeEdgePoints, ScaledMaxWidth, Diameters
+
+
+
+# ========== RK4 for BASHFORTH-ADAMS FORMULATION  ==========
+
+def BashforthAdamsRK4(_afRK4Table, _fApexCurvature, _fShapeFactor, _fSign):
+    A    = _fApexCurvature
+    A2   = 2.0/A
+    B    = _fShapeFactor
+    KX0  = 1.0
+    KT0  = 1.0
+    Inv6 = 1.0/6.0
+    fTotalDiffSquared = 0.0
+    n = 1
+    while n < len(_afRK4Table):
+        x   = _afRK4Table[n-1][3] # predicted x
+        y   = _afRK4Table[n-1][1] # actual y
+        t   = _afRK4Table[n-1][4] # predicted angle
+        dy  = _afRK4Table[n][2]   # actual y diff
+        AG  =  1.0 #AG: Added 
+        ydy = y + 0.5 * dy
+        KX1   = dy * (1.0 / math.tan(t))
+        KT1   = dy * (1.0 / math.sin(t)) * (A2 - (B * y) - (math.sin(t) / (AG * x))) # A -> AG
+        KX2   = dy * (1.0 / math.tan(t + 0.5 * KT1))
+        STKT1 = math.sin(t + 0.5 * KT1)
+        KT2   = dy * (1.0 / STKT1) * (A2 - (B * ydy) - (STKT1 / (AG * (x + 0.5 * KX1)))) # A -> AG
+        KX3   = dy * (1.0 / math.tan(t + 0.5 * KT2))
+        STKT2 = math.sin(t + 0.5 * KT2)
+        KT3   = dy * (1.0 / STKT2) * (A2 - (B * ydy) - (STKT2 / (AG * (x + 0.5 * KX2)))) # A -> AG
+        KX4   = dy * (1.0 / math.tan(t + KT3))
+        STKT3 = math.sin(t + KT3)
+        KT4   = dy * (1.0 / STKT3) * (A2 - (B * (y + dy)) - (STKT3 / (AG * (x + KX3)))) # A -> AG
+        KX  = (KX1 + 2.0 * (KX2 + KX3) + KX4) * Inv6
+        KT  = (KT1 + 2.0 * (KT2 + KT3) + KT4) * Inv6
+        _afRK4Table[n][3] = x + KX
+        _afRK4Table[n][4] = t + KT
+        fTotalDiffSquared += (_afRK4Table[n][0] - (_fSign * _afRK4Table[n][3])) ** 2
+        n += 1
+    return fTotalDiffSquared
+
+def MakeRK4table(_edgePoints):
+    InitialValues = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0]
+
+    rk4table = []
+    rk4table.append(InitialValues)
+    yPrev = 0.0
+    for x, y in _edgePoints:
+        EntryValues = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+        EntryValues[0] = x
+        EntryValues[1] = y
+        EntryValues[2] = y - yPrev
+        yPrev = y 
+        rk4table.append(EntryValues)
+
+    return rk4table
+    """
+    RK4NegTable = []
+    RK4NegTable.append(InitialValues)
+    yPrev = 0.0
+    for x, y in _NegEdgePoints:
+        EntryValues = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+        EntryValues[0] = x
+        EntryValues[1] = y
+        EntryValues[2] = y - yPrev
+        yPrev = y 
+        RK4NegTable.append(EntryValues)
+
+    return RK4NegTable
+    """
+
+# ========== FINDING OPTIMAL PARAMETERS for BASHFORTH-ADAMS SOLUTION ==========
+def FindOptimalParameters(_PosEdgePoints, _NegEdgePoints, _ARange_radCurv, _BRange_shapeFact, _XRange, _TRange_angle, _Params, _Ticks):
+    
+    RK4PosTable = MakeRK4table(_PosEdgePoints)
+    RK4NegTable = MakeRK4table(_NegEdgePoints)
+
+    MinimumRMSD = 999999.0
+    BestParameters = [0, 0, 0, 0]
+    for A_radCurv in _ARange_radCurv:
+        for B_shapeFact in _BRange_shapeFact:
+            for X in _XRange:
+                for T_angle in _TRange_angle:
+                    # x, y, dy, x*, t*, KX1, KT1, KX2, KT2, KX3, KT3, KX4, KT4
+                    fTotalDiffSquared = 0.0
+                    RK4PosTable[0][3] = X
+                    RK4PosTable[0][4] = T_angle
+                    RK4NegTable[0][3] = X
+                    RK4NegTable[0][4] = T_angle
+                    fTotalDiffSquared += BashforthAdamsRK4(RK4PosTable, A_radCurv, B_shapeFact, 1.0)
+                    fTotalDiffSquared += BashforthAdamsRK4(RK4NegTable, A_radCurv, B_shapeFact, -1.0)
+
+                    CurrentRMSD =  (fTotalDiffSquared/(len(_PosEdgePoints) + len(_NegEdgePoints)))**0.5
+                    if CurrentRMSD < MinimumRMSD:
+                        MinimumRMSD = CurrentRMSD
+                        BestParameters = [A_radCurv, B_shapeFact, X, T_angle]
+        _Ticks.put("#")
+
+    A_radCurv = BestParameters[0]
+    B_shapeFact = BestParameters[1]
+    X = BestParameters[2]
+    T_angle = BestParameters[3]
+    ST = (9.8 * A_radCurv) / B_shapeFact
+    _Params.put((MinimumRMSD, A_radCurv, B_shapeFact, X, T_angle))
+
+
+# ========== FINDING OPTIMAL PARAMETERS USING MINIMZATION ==========
+def OptimizeParameters(_PosEdgePoints, _NegEdgePoints, _AGuess_radCurv, _BGuess_shapeFact, _XGuess, _TGuess_angle):
+    
+    RK4PosTable = MakeRK4table(_PosEdgePoints)
+    RK4NegTable = MakeRK4table(_NegEdgePoints)
+    """
+    ARG_RAD = 0
+    ARG_SHAPE = 1
+    ARG_X = 2
+    ARG_ANGLE = 3
+    """
+
+    def msd(args):
+        A_radCurv = args[0]
+        B_shapeFact = args[1]
+        X = args[2]
+        T_angle = args[3]
+
+        RK4PosTable[0][3] = X
+        RK4PosTable[0][4] = T_angle
+        RK4NegTable[0][3] = X
+        RK4NegTable[0][4] = T_angle
+        fTotalDiffSquared = BashforthAdamsRK4(RK4PosTable, A_radCurv, B_shapeFact, 1.0) + BashforthAdamsRK4(RK4NegTable, A_radCurv, B_shapeFact, -1.0)
+
+        return  (fTotalDiffSquared/(len(_PosEdgePoints) + len(_NegEdgePoints)))**0.5
+
+
+    optResult = scipy.optimize.minimize(msd, [_AGuess_radCurv, _BGuess_shapeFact, _XGuess, _TGuess_angle])
+    if optResult.success:
+        print("minimization success")
+        #print(optResult.x)
+        #print(optResult.fun)
+        return [float(optResult.fun)] + optResult.x.tolist()
+    else:
+        return [9999999,0,0,0,0]
+
+
+# ========== Juza's equation for 1/H ==========
+
+def HJuza(_S_diamRatio, _K):
+    # LowerS, UpperS, Ke, Kex, Kep, K3, K2, K1, K0
+
+    # 0.82 - 0.999
+    Coefficient8 = [[  0.82,  0.83,  1791452.8,  533.85850,   170.55837, -81676.15812, 202187.89690, -166836.27680, 45888.22973],
+                    [  0.83,  0.84,  189.07578,  272.52455,   72.730022, -19963.60152,  50019.79936,  -41775.38186, 11629.85610],
+                    [  0.84,  0.85,  7.1549709,  165.45945,   35.285687,  -6944.66848,  17609.43832,  -14883.84379, 4193.34232],
+                    [  0.85,  0.87,  1.1496269,  95.066407,   12.600013,  -2158.91585,   5571.60176,   -4792.82331, 1374.26272],
+                    [  0.87, 0.895, 0.47873040,  50.357240, 0.089787883,   -567.76534,   1503.51828,   -1327.11835, 390.45562],
+                    [ 0.895,  0.93, 0.35255000,  25.498893,  -5.4176608,   -165.99710,    454.58851,    -414.93772, 126.23908],
+                    [  0.93,  0.97, 0.32002037,  6.8474560,  -8.0901766,   -102.84970,    293.25377,    -278.69176, 88.27639],
+                    [  0.97,  0.99, 0.30845061, -32.343947,  -10.455428,   -475.69091,   1398.86173,   -1371.17931, 448.00538],
+                    [  0.99, 0.999, 0.30110729, -333.50440,  -15.711260, -11334.69334,  33822.93507,  -33642.61426, 11154.37157]]
+
+    # 0.635 - 0.997
+    Coefficient9 = [[ 0.635, 0.645,   58249804,  119.64583,   89.483167, -28072.11478, 53918.28040, -34519.94034, 7366.77050],
+                    [ 0.645,  0.66,  5100.2910,  70.920100,   46.811007,  -9051.10879, 17726.62108, -15572.21470, 2518.10214],
+                    [  0.66, 0.685,  19.518159,  38.509198,   19.951285,  -2338.00251,  4719.64936,  -3175.58038, 712.17229],
+                    [ 0.685,  0.72,  1.3823760,  20.055606,   5.9746092,   -522.67397,  1102.26575,   -774.75596, 181.49582],
+                    [  0.72,  0.77, 0.49074291,  10.484929, -0.31885445,   -111.99730,   250.54286,   -186.78287, 46.40581],
+                    [  0.77,  0.84, 0.34607161,  5.4063548,  -2.9788620,    -24.21100,    58.53312,    -47.15244, 12.65668],
+                    [  0.84,  0.93, 0.31342828,  2.1140055,  -4.1151543,     -9.16969,    24.37544,    -21.58758, 6.36954],
+                    [  0.93,  0.98, 0.30397966, -3.6334200,  -4.9395699,    -29.80626,    85.43510,    -81.61766, 25.98669],
+                    [  0.98, 0.997, 0.30007321, -34.095653,  -6.1531194,   -434.11439,  1287.65238,  -1273.10762, 419.56923]]
+
+    # 0.17 - 0.983
+    Coefficient10 = [[ 0.17,  0.30, 0.31081678, -0.086278355, -2.7023254, -13.95071, 10.30398,  -2.49619, 0.19805],
+                     [ 0.30,  0.45, 0.30636442, -0.094871613, -2.7246428,   0.38766, -0.44128,   0.16613, -0.02068],
+                     [ 0.45,  0.68, 0.31156188, -0.063734909, -2.6789763,   0.41537, -0.71168,   0.40321, -0.07551],
+                     [ 0.68,  0.90, 0.31195754, -0.092720991, -2.6863859,  -0.44813,  1.06637,  -0.84260, 0.22106],
+                     [ 0.90, 0.983, 0.30712046,   -1.5619311, -2.9809169,  -5.74538, 16.23781, -15.29128, 4.79808]]
+
+    # 0.06 - 0.953
+    Coefficient11 = [[ 0.06,  0.08,  1.6030433,  0.043380701, -0.15208454, -1341.32950, 282.27311, -19.71010, 0.45664],
+                     [ 0.08,  0.13, 0.85491410, -0.056761738, -0.65372414,  -160.97221,  50.59168,  -5.23625, 0.17842],
+                     [ 0.13,  0.20, 0.57401485,  -0.15265815,  -1.0443069,   -42.79943,  21.22139,  -3.47357, 0.18765],
+                     [ 0.20,  0.30, 0.41622542,  -0.27871823,  -1.4464670,   -14.08741,  10.58863,  -2.63159, 0.21621],
+                     [ 0.30,  0.44, 0.33587066,  -0.42674255,  -1.8022482,    -3.22540,   3.58964,  -1.32194, 0.16106],
+                     [ 0.44,  0.75, 0.31504207,  -0.51197565,  -1.9499037,     0.07609,  -0.13681,   0.08090, -0.01572],
+                     [ 0.75, 0.953, 0.31658938,  -0.49808609,  -1.9290368,    -0.24018,   0.61450,  -0.52258, 0.14771]]
+ 
+    # 0.10 - 0.902
+    Coefficient12 = [[ 0.10,  0.12,  103.56308,   1.2019976,   4.4869062, -6625.95443, 2292.46751, -264.28560, 10.15218],
+                     [ 0.12,  0.14,  2.1585254,  0.34129627,  0.83653215,  -742.15388,  289.52312,  -37.59979, 1.62555],
+                     [ 0.14,  0.19, 0.65654048, 0.031877859, -0.37693028,   -66.92134,   33.18430,   -5.45788, 0.29773],
+                     [ 0.19,  0.27, 0.45076908, -0.10378254, -0.82836350,   -10.66154,    7.36263,   -1.68453, 0.12768],
+                     [ 0.27,  0.40, 0.37085833, -0.21965481,  -1.1287016,    -2.87493,    2.88810,   -0.95966, 0.10546],
+                     [ 0.40,  0.55, 0.33605594, -0.33317467,  -1.3397591,    -0.70394,    1.00402,   -0.47492, 0.07450],
+                     [ 0.55, 0.902, 0.32790337, -0.39597877,  -1.4180887,     0.00490,   -0.01070,    0.00769, -0.00182]]
+    
+    if ( _K == 0.8):
+        Coeff = Coefficient8
+    if ( _K == 0.9):
+        Coeff = Coefficient9
+    if ( _K == 1.0):
+        Coeff = Coefficient10
+    if ( _K == 1.1):
+        Coeff = Coefficient11
+    if ( _K == 1.2):
+        Coeff = Coefficient12
+
+    # Juza 1996/1997 Equation: 8
+    for Entry_k in Coeff:
+        if (Entry_k[0] <= _S_diamRatio) and (_S_diamRatio <= Entry_k[1]):
+            HInv = Entry_k[2] * _S_diamRatio**(Entry_k[3] * math.log(_S_diamRatio) + Entry_k[4]) + Entry_k[5] * (_S_diamRatio**3.0) + Entry_k[6] * (_S_diamRatio **2.0) + Entry_k[7] * _S_diamRatio + Entry_k[8]
+            return HInv
+            break
+
+    return 0
+
+
+
+# ========== USAGE PRINTER ==========
+
+def PrintCorrectUsage():
+    print("\nDESCRIPTION:\n")
+    print("This program will take an image or a set of files (coordinate points) representing")
+    print("a droplet and will process the data to calculate the surface tension of the droplet.")
+    print("When an image file is set, the program will extract the coordinate of the points")
+    print("representing the edge of the droplet. When the files are set, it is assume that they")
+    print("will already contain the points representing the edge of the droplet. RK4 will be")
+    print("use to solve the Bashforth-Adams set of equations to get the parameters for surface")
+    print("tension calculation. parameters: A (apex radius curvature) and B (shape factor)")
+    print("\nUSAGE:\n")
+    print("Syntax 1: ./img.py -option1 value1 -option2 value2")
+    print("Syntax 2: python img.py -option1 value1 -option2 value2\n")
+    print("Options:")
+    print("-help  : Prints this help message. ")
+    print("-out   : Reference name for all the output files (coordinate files, RK4 dump, etc.).")
+    print("       : This should always be set. ")
+    print("-img   : Image file to be processed. ")
+    print("       : When this is set, the file name inputs (-filep, -filen) should not be set.")
+    print("-filep : File containing the positive(x) point coordinates to be processed.")
+    print("       : If this is set, -filen should also be set and -img should not be set.")
+    print("-filen : File containing the negative(x) point coordinates to be processed.")
+    print("       : If this is set, -filep should also be set and -img should not be set.")
+    print("-proc  : The number of processor to use.")
+    print("       : If not specified the default value is 2.")
+    print("-syrg  : This is the syringe width in millimeters.")
+    print("       : If not specified the default value is 0.805 mm.")
+    print("-a     : RK4 Parameter: minimum value for alpha (radius of curvature at apex).")
+    print("       : If not specified the default value is 0.0001")
+    print("-A     : RK4 Parameter: maximum value for alpha (radius of curvature at apex).")
+    print("       : If not specified the default value is 2.0001")
+    print("-b     : RK4 Parameter: minimum value for beta (shape factor).")
+    print("       : If not specified the default value is 0.0001")
+    print("-B     : RK4 Parameter: minimum value for beta (shape factor).")
+    print("       : If not specified the default value is 0.5001.")
+    print("-x     : RK4 Parameter: minimum value for x (initial guessed x coordinate).")
+    print("       : If not specified the default value is 0.0001.")
+    print("-X     : RK4 Parameter: maximum value for x (initial guessed x coordinate).")
+    print("       : If not specified the default value is 0.5001.")
+    print("-t     : RK4 Parameter: minimum value for t (initial guessed angle).")
+    print("       : If not specified the default value is 0.0001.")
+    print("-T     : RK4 Parameter: maximum value for t (initial guessed angle).")
+    print("       : If not specified the default value is 0.5001.")
+    print("-ai    : RK4 Parameter: alpha interval - the number of values to consider between min alpha and max alpha.")
+    print("       : If not specified the default value is 20.")
+    print("-bi    : RK4 Parameter: beta interval - the number of values to consider between min beta and max beta.")
+    print("       : If not specified the default value is 20.")
+    print("-xi    : RK4 Parameter: x interval - the number of values to consider between min x and max x.")
+    print("       : If not specified the default value is 5.")
+    print("-ti    : RK4 Parameter: angle interval - the number of values to consider between min angle and max angle.")
+    print("       : If not specified the default value is 5.")
+    print("-solver    : 1 for divide and conquer scanning.")
+    print("       : If not specified, optimization will be used to solve the parameters.")
+    print("\nSAMPLE USAGE:\n")
+    print("1. Calculate surface tension of a drop using default values.")
+    print("./img.py -img water-drop.jpg -out water-drop")
+    print("python img.py -img water-drop.jpg -out water-drop\n")
+    print("2. Uses 4 processors for calculation.")
+    print("./img.py -img water-drop.jpg -out water-drop -proc 4\n")
+    print("3. Setting interval sizes for A and B parameters (search for 30 possible values for A and B).")
+    print("./img.py -img water-drop.jpg -out water-drop -ai 30 -bi 30\n")
+    print("4. Setting min (0.00001) and max (1.5) values for parameter.")
+    print("./img.py -img water-drop.jpg -out water-drop -a 0.00001 -A 1.5\n")
+    
+
+
+# ========== MAIN  ==========
+
+if __name__ == '__main__':
+
+    ImageFilePath = ""
+    OutputFileName = ""
+    PosPointsFileName = ""
+    NegPointsFileName = ""
+    ProcessCount = 2
+    SyringeWidth = 0.70 * 1.15
+    MinA_radCurv = 0.0001
+    MaxA_radCurv = 2.0001
+    MinB_shapeFact = 0.0001
+    MaxB_shapeFact = 1.0001
+    MinX = 0.0001
+    MaxX = 0.5001
+    MinT_angle = 0.0001
+    MaxT_angle = 0.5001
+    AStep = 20
+    BStep = 20
+    XStep = 5
+    TStep = 5
+
+    if (len(sys.argv) <= 1):
+        PrintCorrectUsage()
+        sys.exit()
+
+    ImageFlag = 0
+    PosFileFlag = 0
+    NegFileFlag = 0
+    OutFlag = 0
+    Counter = 1
+    SolveMethod = 0
+
+    while (Counter <= len(sys.argv)-1):
+
+        CurrentOption = sys.argv[Counter]
+        try:
+            CurrentValue  = sys.argv[Counter+1]
+        except:
+           PrintCorrectUsage()
+           sys.exit()
+
+        if CurrentOption == "-help":
+            PrintCorrectUsage()
+            sys.exit()
+        elif CurrentOption == "-img":
+            ImageFilePath = CurrentValue
+            ImageFlag = 1
+        elif CurrentOption == "-filep":
+            PosPointsFileName = CurrentValue
+            PosFileFlag = 1
+        elif CurrentOption == "-filen":
+            NegPointsFileName = CurrentValue
+            NegFileFlag = 1
+        elif CurrentOption == "-out":
+            OutputFileName = CurrentValue
+            OutFlag = 1
+        elif CurrentOption == "-proc":
+            ProcessCount = int(CurrentValue)
+        elif CurrentOption == "-syrg":
+            SyringeWidth = float(CurrentValue)
+        elif CurrentOption == "-a":
+            MinA_radCurv = float(CurrentValue)
+        elif CurrentOption == "-A":
+            MaxA_radCurv = float(CurrentValue)
+        elif CurrentOption == "-b":
+            MinB_shapeFact = float(CurrentValue)
+        elif CurrentOption == "-B":
+            MaxB_shapeFact = float(CurrentValue)
+        elif CurrentOption == "-x":
+            MinX = float(CurrentValue)
+        elif CurrentOption == "-X":
+            MaxX = float(CurrentValue)
+        elif CurrentOption == "-t":
+            MinT_angle = float(CurrentValue)
+        elif CurrentOption == "-T":
+            MaxT_angle = float(CurrentValue)
+        elif CurrentOption == "-ai":
+            AStep = int(CurrentValue)
+        elif CurrentOption == "-bi":
+            BStep = int(CurrentValue)
+        elif CurrentOption == "-xi":
+            XStep = int(CurrentValue)
+        elif CurrentOption == "-ti":
+            TStep = int(CurrentValue)
+        elif CurrentOption == "-solver":
+            SolveMethod = int(CurrentValue)
+        else:
+            PrintCorrectUsage()
+            sys.exit()
+        Counter = Counter + 2
+
+    if (OutFlag == 0 and ImageFlag == 1):
+        print("Output file name not set. (-out)")
+        PrintCorrectUsage()
+        sys.exit()
+    if (ImageFlag == 1 and ((PosFileFlag == 1) or (NegFileFlag == 1))):
+        print("Image(-img) can not be set with files option (-filep, -filen).")
+        print("Either set image only or files only.")
+        PrintCorrectUsage()
+        sys.exit()
+    if (ImageFlag == 0 and ((PosFileFlag == 1 and NegFileFlag == 0) or (PosFileFlag == 0 and NegFileFlag == 1))):
+        print("File inputs (-filep, -filen) should both be set if image input is not set.")
+        PrintCorrectUsage()
+        sys.exit()
+
+    ARange_radCurv = []
+    a = MinA_radCurv
+    ahop = float(MaxA_radCurv - MinA_radCurv)/float(AStep-1)
+    while (a <= MaxA_radCurv):
+        ARange_radCurv.append(a)
+        a += ahop
+        if ahop == 0.0:
+            break
+    if(np.abs(MaxA_radCurv - ARange_radCurv[len(ARange_radCurv)-1] - ahop) < 0.000001 and ahop != 0.0):
+        ARange_radCurv.append(MaxA_radCurv)
+
+    BRange_shapeFact = []
+    b = MinB_shapeFact
+    bhop = float(MaxB_shapeFact - MinB_shapeFact)/float(BStep-1)
+    while (b <= MaxB_shapeFact):
+        BRange_shapeFact.append(b)
+        b += bhop
+        if bhop == 0:
+            break
+    if(np.abs(MaxB_shapeFact - BRange_shapeFact[len(BRange_shapeFact)-1] - bhop) < 0.000001 and bhop != 0.0):
+        BRange_shapeFact.append(MaxB_shapeFact)
+    
+    XRange = []
+    x = MinX
+    xhop = float(MaxX - MinX)/float(XStep-1)
+    while (x <= MaxX):
+        XRange.append(x)
+        x += xhop
+        if xhop == 0:
+            break
+    if(np.abs(MaxX - XRange[len(XRange)-1] - xhop) < 0.000001 and xhop != 0.0):
+        XRange.append(MaxX)
+
+    TRange_angle = []
+    t = MinT_angle
+    thop = float(MaxT_angle - MinT_angle)/float(TStep-1)
+    while (t <= MaxT_angle):
+        TRange_angle.append(t)
+        t += thop
+        if thop == 0.0:
+            break
+    if(np.abs(MaxT_angle - TRange_angle[len(TRange_angle)-1] - thop) < 0.000001 and thop != 0.0):
+        TRange_angle.append(MaxT_angle)
+
+
+    print("\n")
+    if (ImageFlag == 1):
+        print("Image File                : " + ImageFilePath)
+        print("Output Name               : " + OutputFileName)
+        print("Negative Cooridnate File  : " + OutputFileName + "_Negative.dat")
+        print("Positive Cooridnate File  : " + OutputFileName + "_Positive.dat")
+        print("Syringe Width (millimeter): " + str(SyringeWidth))
+    else:
+        print("Negative Cooridnate File  : " + NegPointsFileName)
+        print("Positive Cooridnate File  : " + PosPointsFileName)
+    print("Radius of Curvature Range : " + str(MinA_radCurv) + "-" + str(MaxA_radCurv) + " (interval: "+str(len(ARange_radCurv))+")")
+    print("Shape Factor Range        : " + str(MinB_shapeFact) + "-" + str(MaxB_shapeFact) + " (interval: "+str(len(BRange_shapeFact))+")")
+    print("Initial X Coordinate Range: " + str(MinX) + "-" + str(MaxX) + " (interval: "+str(len(XRange))+")")
+    print("Initial Angle Range       : " + str(MinT_angle) + "-" + str(MaxT_angle) + " (interval: "+str(len(TRange_angle))+")")
+    print("Parameter Combinations    : " + str(len(ARange_radCurv) * len(BRange_shapeFact) * len(XRange) * len(TRange_angle)))
+    print("Number of Process to Use  : " + str(ProcessCount))
+
+    if (ImageFlag == 1):
+        Pos_edgePts, Neg_edgePts, De_scaledMaxWidth, Dms_diamters = ExtractEdgeCoordinate(ImageFilePath, OutputFileName, SyringeWidth)
+        HInv1  = HJuza(Dms_diamters[7]/De_scaledMaxWidth, 0.8)
+        HInv2  = HJuza(Dms_diamters[8]/De_scaledMaxWidth, 0.9)
+        HInv3  = HJuza(Dms_diamters[9]/De_scaledMaxWidth, 1.0)
+        HInv4  = HJuza(Dms_diamters[10]/De_scaledMaxWidth, 1.1)
+        HInv5  = HJuza(Dms_diamters[11]/De_scaledMaxWidth, 1.2)
+        HInvM  = (0.20)*(HInv1 + HInv2 + HInv3 + HInv4 + HInv5)
+        HInvSD = math.sqrt((0.20)*( (HInv1-HInvM)**2.0 + (HInv2-HInvM)**2.0 + (HInv3-HInvM)**2.0 + (HInv4-HInvM)**2.0 + (HInv5-HInvM)**2.0))
+        print("Juza 5-Plane (1/H) Std.Dev: " + str(HInvSD))
+    else:
+        Pos_edgePts = []
+        PositivePointFile = open(PosPointsFileName,'r')
+        for Line in PositivePointFile:
+            Coordinate = Line.split()
+            #print(Coordinate)
+            Pos_edgePts.append((float(Coordinate[0]), float(Coordinate[1])))
+        PositivePointFile.close()
+        Neg_edgePts = []
+        NegativePointFile = open(NegPointsFileName,'r')
+        for Line in NegativePointFile:
+            Coordinate = Line.split()
+            #print(Coordinate)
+            Neg_edgePts.append((float(Coordinate[0]), float(Coordinate[1])))
+        NegativePointFile.close()
+
+    def BruteForce():
+        PosList = []
+        NegList = []
+        for ProcessNo in range(ProcessCount):
+            PosList.append(copy.deepcopy(Pos_edgePts))
+            NegList.append(copy.deepcopy(Neg_edgePts))
+            #print(ProcessNo)
+
+        ARanges = []
+        for ProcessNo in range(ProcessCount):
+            ARanges.append([])
+
+        i = 0
+        for A in ARange_radCurv:
+            ARanges[i%ProcessCount].append(A)
+            i += 1
+
+        BestParams = multiprocessing.Queue()
+        TicksQueue = multiprocessing.Queue()
+        Processes = []
+        
+        for ProcessNo in range(ProcessCount):
+            Processes.append(multiprocessing.Process(name='Search ' + str(ProcessNo), target=FindOptimalParameters, args=(PosList[ProcessNo], NegList[ProcessNo], ARanges[ProcessNo], BRange_shapeFact, XRange, TRange_angle, BestParams, TicksQueue))) 
+
+        for aProcess in Processes:
+            aProcess.start()
+    
+        sys.stdout.write("\rParameter Search Progress : 0%")
+        sys.stdout.flush()
+        Count = 0
+        while(Count < len(ARange_radCurv)):
+            t = TicksQueue.get()
+            Count += 1
+            sys.stdout.write("\rParameter Search Progress : " + str(int(100*float(Count)/float(len(ARange_radCurv)))) + "%")
+            sys.stdout.flush()
+
+        for aProcess in Processes:
+            aProcess.join()
+
+        BestOutput = (999999999, 1, 1, 1 ,1)
+        while not BestParams.empty():
+            Output = BestParams.get()
+            if Output[0] < BestOutput[0]:
+                BestOutput = Output
+        return BestOutput
+
+    def Optimize():
+        return OptimizeParameters(Pos_edgePts, Neg_edgePts, 0.95, 0.3, 0.1, 0.2)
+        
+    starttime = time.time()
+
+    BestOutput = Optimize() if 1 != SolveMethod else BruteForce()
+
+    print("best output: " + str(BestOutput))
+    
+    print("\nLowest RMSD               : " + str(BestOutput[0]))
+    print("Computed Surface Tension  : " + str(9.8*BestOutput[1]/BestOutput[2]))
+    print("Best Radius of Curvature  : " + str(BestOutput[1]))
+    print("Best Shape Factor         : " + str(BestOutput[2]))
+    print("Best Initial X Coordinate : " + str(BestOutput[3]))
+    print("Best Initial Angle        : " + str(BestOutput[4]))
+    print("Lapsed Time in Seconds    : " + str(time.time() -starttime))

lib/scripts/juszas_equation.dart

@@ -0,0 +1,466 @@
+// ========== Juza's equation for 1/H ==========
+import 'dart:math';
+
+double HJuza(double _S_diamRatio, double _K) {
+  // LowerS, UpperS, Ke, Kex, Kep, K3, K2, K1, K0
+
+  // 0.82 - 0.999
+  List<List<double>> Coefficient8 = [
+    [
+      0.82,
+      0.83,
+      1791452.8,
+      533.85850,
+      170.55837,
+      -81676.15812,
+      202187.89690,
+      -166836.27680,
+      45888.22973,
+    ],
+    [
+      0.83,
+      0.84,
+      189.07578,
+      272.52455,
+      72.730022,
+      -19963.60152,
+      50019.79936,
+      -41775.38186,
+      11629.85610,
+    ],
+    [
+      0.84,
+      0.85,
+      7.1549709,
+      165.45945,
+      35.285687,
+      -6944.66848,
+      17609.43832,
+      -14883.84379,
+      4193.34232,
+    ],
+    [
+      0.85,
+      0.87,
+      1.1496269,
+      95.066407,
+      12.600013,
+      -2158.91585,
+      5571.60176,
+      -4792.82331,
+      1374.26272,
+    ],
+    [
+      0.87,
+      0.895,
+      0.47873040,
+      50.357240,
+      0.089787883,
+      -567.76534,
+      1503.51828,
+      -1327.11835,
+      390.45562,
+    ],
+    [
+      0.895,
+      0.93,
+      0.35255000,
+      25.498893,
+      -5.4176608,
+      -165.99710,
+      454.58851,
+      -414.93772,
+      126.23908,
+    ],
+    [
+      0.93,
+      0.97,
+      0.32002037,
+      6.8474560,
+      -8.0901766,
+      -102.84970,
+      293.25377,
+      -278.69176,
+      88.27639,
+    ],
+    [
+      0.97,
+      0.99,
+      0.30845061,
+      -32.343947,
+      -10.455428,
+      -475.69091,
+      1398.86173,
+      -1371.17931,
+      448.00538,
+    ],
+    [
+      0.99,
+      0.999,
+      0.30110729,
+      -333.50440,
+      -15.711260,
+      -11334.69334,
+      33822.93507,
+      -33642.61426,
+      11154.37157,
+    ],
+  ];
+
+  // 0.635 - 0.997
+  List<List<double>> Coefficient9 = [
+    [
+      0.635,
+      0.645,
+      58249804,
+      119.64583,
+      89.483167,
+      -28072.11478,
+      53918.28040,
+      -34519.94034,
+      7366.77050,
+    ],
+    [
+      0.645,
+      0.66,
+      5100.2910,
+      70.920100,
+      46.811007,
+      -9051.10879,
+      17726.62108,
+      -15572.21470,
+      2518.10214,
+    ],
+    [
+      0.66,
+      0.685,
+      19.518159,
+      38.509198,
+      19.951285,
+      -2338.00251,
+      4719.64936,
+      -3175.58038,
+      712.17229,
+    ],
+    [
+      0.685,
+      0.72,
+      1.3823760,
+      20.055606,
+      5.9746092,
+      -522.67397,
+      1102.26575,
+      -774.75596,
+      181.49582,
+    ],
+    [
+      0.72,
+      0.77,
+      0.49074291,
+      10.484929,
+      -0.31885445,
+      -111.99730,
+      250.54286,
+      -186.78287,
+      46.40581,
+    ],
+    [
+      0.77,
+      0.84,
+      0.34607161,
+      5.4063548,
+      -2.9788620,
+      -24.21100,
+      58.53312,
+      -47.15244,
+      12.65668,
+    ],
+    [
+      0.84,
+      0.93,
+      0.31342828,
+      2.1140055,
+      -4.1151543,
+      -9.16969,
+      24.37544,
+      -21.58758,
+      6.36954,
+    ],
+    [
+      0.93,
+      0.98,
+      0.30397966,
+      -3.6334200,
+      -4.9395699,
+      -29.80626,
+      85.43510,
+      -81.61766,
+      25.98669,
+    ],
+    [
+      0.98,
+      0.997,
+      0.30007321,
+      -34.095653,
+      -6.1531194,
+      -434.11439,
+      1287.65238,
+      -1273.10762,
+      419.56923,
+    ],
+  ];
+
+  // 0.17 - 0.983
+  List<List<double>> Coefficient10 = [
+    [
+      0.17,
+      0.30,
+      0.31081678,
+      -0.086278355,
+      -2.7023254,
+      -13.95071,
+      10.30398,
+      -2.49619,
+      0.19805,
+    ],
+    [
+      0.30,
+      0.45,
+      0.30636442,
+      -0.094871613,
+      -2.7246428,
+      0.38766,
+      -0.44128,
+      0.16613,
+      -0.02068,
+    ],
+    [
+      0.45,
+      0.68,
+      0.31156188,
+      -0.063734909,
+      -2.6789763,
+      0.41537,
+      -0.71168,
+      0.40321,
+      -0.07551,
+    ],
+    [
+      0.68,
+      0.90,
+      0.31195754,
+      -0.092720991,
+      -2.6863859,
+      -0.44813,
+      1.06637,
+      -0.84260,
+      0.22106,
+    ],
+    [
+      0.90,
+      0.983,
+      0.30712046,
+      -1.5619311,
+      -2.9809169,
+      -5.74538,
+      16.23781,
+      -15.29128,
+      4.79808,
+    ],
+  ];
+
+  // 0.06 - 0.953
+  List<List<double>> Coefficient11 = [
+    [
+      0.06,
+      0.08,
+      1.6030433,
+      0.043380701,
+      -0.15208454,
+      -1341.32950,
+      282.27311,
+      -19.71010,
+      0.45664,
+    ],
+    [
+      0.08,
+      0.13,
+      0.85491410,
+      -0.056761738,
+      -0.65372414,
+      -160.97221,
+      50.59168,
+      -5.23625,
+      0.17842,
+    ],
+    [
+      0.13,
+      0.20,
+      0.57401485,
+      -0.15265815,
+      -1.0443069,
+      -42.79943,
+      21.22139,
+      -3.47357,
+      0.18765,
+    ],
+    [
+      0.20,
+      0.30,
+      0.41622542,
+      -0.27871823,
+      -1.4464670,
+      -14.08741,
+      10.58863,
+      -2.63159,
+      0.21621,
+    ],
+    [
+      0.30,
+      0.44,
+      0.33587066,
+      -0.42674255,
+      -1.8022482,
+      -3.22540,
+      3.58964,
+      -1.32194,
+      0.16106,
+    ],
+    [
+      0.44,
+      0.75,
+      0.31504207,
+      -0.51197565,
+      -1.9499037,
+      0.07609,
+      -0.13681,
+      0.08090,
+      -0.01572,
+    ],
+    [
+      0.75,
+      0.953,
+      0.31658938,
+      -0.49808609,
+      -1.9290368,
+      -0.24018,
+      0.61450,
+      -0.52258,
+      0.14771,
+    ],
+  ];
+
+  // 0.10 - 0.902
+  List<List<double>> Coefficient12 = [
+    [
+      0.10,
+      0.12,
+      103.56308,
+      1.2019976,
+      4.4869062,
+      -6625.95443,
+      2292.46751,
+      -264.28560,
+      10.15218,
+    ],
+    [
+      0.12,
+      0.14,
+      2.1585254,
+      0.34129627,
+      0.83653215,
+      -742.15388,
+      289.52312,
+      -37.59979,
+      1.62555,
+    ],
+    [
+      0.14,
+      0.19,
+      0.65654048,
+      0.031877859,
+      -0.37693028,
+      -66.92134,
+      33.18430,
+      -5.45788,
+      0.29773,
+    ],
+    [
+      0.19,
+      0.27,
+      0.45076908,
+      -0.10378254,
+      -0.82836350,
+      -10.66154,
+      7.36263,
+      -1.68453,
+      0.12768,
+    ],
+    [
+      0.27,
+      0.40,
+      0.37085833,
+      -0.21965481,
+      -1.1287016,
+      -2.87493,
+      2.88810,
+      -0.95966,
+      0.10546,
+    ],
+    [
+      0.40,
+      0.55,
+      0.33605594,
+      -0.33317467,
+      -1.3397591,
+      -0.70394,
+      1.00402,
+      -0.47492,
+      0.07450,
+    ],
+    [
+      0.55,
+      0.902,
+      0.32790337,
+      -0.39597877,
+      -1.4180887,
+      0.00490,
+      -0.01070,
+      0.00769,
+      -0.00182,
+    ],
+  ];
+
+  List<List<double>> Coeff = [];
+  if (_K == 0.8) {
+    Coeff = Coefficient8;
+  }
+  if (_K == 0.9) {
+    Coeff = Coefficient9;
+  }
+  if (_K == 1.0) {
+    Coeff = Coefficient10;
+  }
+  if (_K == 1.1) {
+    Coeff = Coefficient11;
+  }
+  if (_K == 1.2) {
+    Coeff = Coefficient12;
+  }
+
+  // Juza 1996/1997 Equation: 8
+  for (var Entry_k in Coeff) {
+    if (Entry_k[0] <= _S_diamRatio && _S_diamRatio <= Entry_k[1]) {
+      double HInv =
+          Entry_k[2] *
+              pow(_S_diamRatio, (Entry_k[3] * log(_S_diamRatio) + Entry_k[4])) +
+          Entry_k[5] * pow(_S_diamRatio, 3.0) +
+          Entry_k[6] * pow(_S_diamRatio, 2.0) +
+          Entry_k[7] * _S_diamRatio +
+          Entry_k[8];
+      return HInv;
+    }
+  }
+
+  return 0;
+}

lib/scripts/minimize_params_optimization.dart

@@ -0,0 +1,48 @@
+import 'dart:math';
+
+import 'package:surface_tension_calculator/scripts/rk4.dart';
+
+/// ========== FINDING OPTIMAL PARAMETERS USING MINIMZATION ==========
+List<double> optimizeParameters(
+  List<double> posEdgePoints,
+  List<double> negEdgePoints,
+  double aGuessRadCurv,
+  double bGuessShapeFact,
+  double xGuess,
+  double tGuessAngle,
+) {
+  var rk4PosTable = makeRK4Table(posEdgePoints);
+  var rk4NegTable = makeRK4Table(negEdgePoints);
+
+  double msd(List<double> args) {
+    double aRadCurv = args[0];
+    double bShapeFact = args[1];
+    double x = args[2];
+    double tAngle = args[3];
+
+    rk4PosTable[0][3] = x;
+    rk4PosTable[0][4] = tAngle;
+    rk4NegTable[0][3] = x;
+    rk4NegTable[0][4] = tAngle;
+    double fTotalDiffSquared =
+        bashforthAdamsRK4(rk4PosTable, aRadCurv, bShapeFact, 1.0) +
+        bashforthAdamsRK4(rk4NegTable, aRadCurv, bShapeFact, -1.0);
+
+    return sqrt(
+      fTotalDiffSquared / (posEdgePoints.length + negEdgePoints.length),
+    );
+  }
+
+  var optResult = minimize(msd, [
+    aGuessRadCurv,
+    bGuessShapeFact,
+    xGuess,
+    tGuessAngle,
+  ]);
+  if (optResult.success) {
+    print("minimization success");
+    return [optResult.fun.toDouble()] + optResult.x;
+  } else {
+    return [9999999, 0, 0, 0, 0];
+  }
+}