Habe eigene Vektor-Implementationen hinzugefügt

src/JuicyGraphics.csproj

@@ -51,7 +51,13 @@
     <Reference Include="System.Xml" />
   </ItemGroup>
   <ItemGroup>
+    <Compile Include="JuicyGraphics\math\doubleExtentions.cs" />
+    <Compile Include="JuicyGraphics\math\normalizeVectorException.cs" />
+    <Compile Include="JuicyGraphics\math\vec2.cs" />
+    <Compile Include="JuicyGraphics\math\vec3.cs" />
     <Compile Include="JuicyGraphics\renderer\graphicalObjects\gridBackground.cs" />
+    <Compile Include="JuicyGraphics\renderer\stain.cs" />
+    <Compile Include="JuicyGraphics\renderer\stainGraphicTexture.cs" />
     <Compile Include="SharpGL\Matrix.cs" />
     <Compile Include="JuicyGraphics\renderer\camera2D.cs" />
     <Compile Include="JuicyGraphics\renderer\iGraphicalObject.cs" />
@@ -66,7 +72,7 @@
     <Compile Include="JuicyGraphics\ui\mainForm.Designer.cs">
       <DependentUpon>mainForm.cs</DependentUpon>
     </Compile>
-    <Compile Include="JuicyGraphics\Program.cs" />
+    <Compile Include="JuicyGraphics\app.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
     <Compile Include="SharpGL\DIBSection.cs" />
     <Compile Include="SharpGL\Enumerations\OpenGLEnumerations.cs" />
@@ -124,8 +130,6 @@
   <ItemGroup>
     <None Include="App.config" />
   </ItemGroup>
-  <ItemGroup>
-    <Folder Include="JuicyGraphics\math\" />
-  </ItemGroup>
+  <ItemGroup />
   <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
 </Project>

src/JuicyGraphics/App.cs

@@ -1,11 +1,8 @@
 using System;
-using System.Collections.Generic;
-using System.Linq;
-using System.Threading.Tasks;
 using System.Windows.Forms;
 
 namespace JuicyGraphics {
-    static class Program {
+    static class app {
         /// <summary>
         /// The main entry point for the application.
         /// </summary>

src/JuicyGraphics/math/doubleExtentions.cs

@@ -0,0 +1,58 @@
+using System;
+
+namespace JuicyGraphics.Mathematics {
+
+    public static class doubleExtension {
+        public static bool almostEqualsWithAbsTolerance(this double a, double b, double maxAbsoluteError) {
+            double diff = Math.Abs(a - b);
+
+            if (a.Equals(b)) {
+                return true;
+            }
+
+            return diff <= maxAbsoluteError;
+        }
+
+        public static bool almostEqualsWithAbsOrRelativeTolerance(
+                this double a,
+                double b,
+                double maxAbsoluteError,
+                double maxRelativeError) {
+            if (almostEqualsWithAbsTolerance(a, b, maxAbsoluteError)) {
+                return true;
+            }
+
+            double absA = Math.Abs(a);
+            double absB = Math.Abs(b);
+
+            double relativeError;
+            if (absB > absA) {
+                relativeError = Math.Abs((a - b) / b);
+            }
+            else {
+                relativeError = Math.Abs((a - b) / a);
+            }
+
+            return relativeError <= maxRelativeError;
+        }
+
+        public static bool almostEqualsWithAbsOrUlpsTolerance(
+                this double a,
+                double b,
+                double maxAbsoluteError,
+                long maxUlps) {
+            if (almostEqualsWithAbsTolerance(a, b, maxAbsoluteError)) {
+                return true;
+            }
+
+            long longA = BitConverter.DoubleToInt64Bits(a);
+            longA = longA < 0 ? (long)(0x8000000000000000 - (ulong)longA) : longA;
+
+            long longB = BitConverter.DoubleToInt64Bits(b);
+            longB = longB < 0 ? (long)(0x8000000000000000 - (ulong)longB) : longB;
+
+            long diff = Math.Abs(longA - longB);
+            return diff <= maxUlps;
+        }
+    }
+}

src/JuicyGraphics/math/normalizeVectorException.cs

@@ -0,0 +1,23 @@
+using System;
+using System.Runtime.Serialization;
+
+namespace JuicyGraphics.Exceptions {
+
+    [Serializable]
+    public class normalizeVectorException : Exception {
+        public normalizeVectorException() {
+        }
+
+        public normalizeVectorException(string message)
+            : base(message) {
+        }
+
+        public normalizeVectorException(string message, Exception innerException)
+            : base(message, innerException) {
+        }
+
+        protected normalizeVectorException(SerializationInfo info, StreamingContext context)
+            : base(info, context) {
+        }
+    }
+}

src/JuicyGraphics/math/vec2.cs

@@ -0,0 +1,637 @@
+using System;
+using System.ComponentModel;
+using System.Xml.Serialization;
+
+namespace JuicyGraphics.Mathematics {
+    using Exceptions;
+
+    [ImmutableObject(true), Serializable]
+    public struct vec2
+        : IComparable, IComparable<vec2>, IEquatable<vec2>, IFormattable {
+
+        private readonly double _x;
+        private readonly double _y;
+
+        public vec2(double x, double y) {
+            this._x = x;
+            this._y = y;
+        }
+
+        public vec2(double[] xy) {
+            if (xy.Length == 2) {
+                this._x = xy[0];
+                this._y = xy[1];
+            }
+            else {
+                throw new ArgumentException(TWO_COMPONENTS);
+            }
+        }
+
+        public vec2(vec2 v1) {
+            this._x = v1.x;
+            this._y = v1.y;
+        }
+
+        public double x {
+            get {
+                return _x;
+            }
+        }
+
+        public double y {
+            get {
+                return _y;
+            }
+        }
+
+        public vec2 xx {
+            get {
+                return new vec2(_x, _x);
+            }
+        }
+
+        public vec2 xy {
+            get {
+                return this;
+            }
+        }
+
+        public vec2 yx {
+            get {
+                return new vec2(_y, _x);
+            }
+        }
+
+        public vec2 yy {
+            get {
+                return new vec2(_y, _y);
+            }
+        }
+
+        public vec2 normal {
+            get {
+                return this.normalize();
+            }
+        }
+
+        public double magnitude {
+            get {
+                return Math.Sqrt(this.sumComponentSqrs());
+            }
+        }
+
+        [XmlIgnore]
+        public double[] array {
+            get {
+                return new[] { this.x, this.y };
+            }
+        }
+
+        public double this[int index] {
+            get {
+                switch (index) {
+                    case 0:
+                        return this._x;
+                    case 1:
+                        return this._y;
+                    default:
+                        throw new ArgumentException(TWO_COMPONENTS, "index");
+                }
+            }
+        }
+
+        public static vec2 operator +(vec2 v1, vec2 v2) {
+            return new vec2(
+                v1.x + v2.x,
+                v1.y + v2.y);
+        }
+
+        public static vec2 operator -(vec2 v1, vec2 v2) {
+            return new vec2(
+                v1.x - v2.x,
+                v1.y - v2.y);
+        }
+
+        public static vec2 operator *(vec2 v1, double s2) {
+            return
+                new vec2(
+                        v1.x * s2,
+                        v1.y * s2);
+        }
+
+        public static vec2 operator *(double s1, vec2 v2) {
+            return v2 * s1;
+        }
+
+        public static vec2 operator /(vec2 v1, double s2) {
+            return new vec2(
+                        v1.x / s2,
+                        v1.y / s2);
+        }
+
+        public static vec2 operator -(vec2 v1) {
+            return new vec2(
+                -v1.x,
+                -v1.y);
+        }
+
+        public static vec2 operator +(vec2 v1) {
+            return new vec2(
+                +v1.x,
+                +v1.y);
+        }
+
+        public static bool operator <(vec2 v1, vec2 v2) {
+            return v1.sumComponentSqrs() < v2.sumComponentSqrs();
+        }
+
+        public static bool operator >(vec2 v1, vec2 v2) {
+            return v1.sumComponentSqrs() > v2.sumComponentSqrs();
+        }
+
+        public static bool operator <=(vec2 v1, vec2 v2) {
+            return v1.sumComponentSqrs() <= v2.sumComponentSqrs();
+        }
+
+        public static bool operator >=(vec2 v1, vec2 v2) {
+            return v1.sumComponentSqrs() >= v2.sumComponentSqrs();
+        }
+
+        public static bool operator ==(vec2 v1, vec2 v2) {
+            return
+                v1.x == v2.x &&
+                v1.y == v2.y;
+        }
+
+        public static bool operator !=(vec2 v1, vec2 v2) {
+            return !(v1 == v2);
+        }
+
+        public static vec2 scale(vec2 vector, double magnitude) {
+            if (magnitude < 0) {
+                throw new ArgumentOutOfRangeException("magnitude", magnitude, NEGATIVE_magnitude);
+            }
+
+            if (vector == new vec2(0, 0)) {
+                throw new ArgumentException(ORIGIN_VECTOR_magnitude, "vector");
+            }
+
+            return vector * (magnitude / vector.magnitude);
+        }
+
+        public vec2 scale(double magnitude) {
+            return vec2.scale(this, magnitude);
+        }
+
+        public static double dotProduct(vec2 v1, vec2 v2) {
+            return
+                v1.x * v2.x +
+                v1.y * v2.y;
+        }
+
+        public double dotProduct(vec2 other) {
+            return dotProduct(this, other);
+        }
+
+        public static vec2 normalize(vec2 v1) {
+            if (double.IsInfinity(v1.magnitude)) {
+                v1 = normalizeSpecialCasesOrOrigional(v1);
+
+                if (v1.isNaN()) {
+                    throw new normalizeVectorException(NORMALIZE_Inf);
+                }
+            }
+
+            if (v1.magnitude == 0) {
+                throw new normalizeVectorException(NORMALIZE_0);
+            }
+
+            if (v1.isNaN()) {
+                throw new normalizeVectorException(NORMALIZE_NaN);
+            }
+
+            return normalizeOrNaN(v1);
+        }
+
+        public static vec2 normalizeOrDefault(vec2 v1) {
+            v1 = normalizeSpecialCasesOrOrigional(v1);
+
+            if (v1.magnitude == 0) {
+                return origin;
+            }
+
+            if (v1.isNaN()) {
+                return NaN;
+            }
+
+            return normalizeOrNaN(v1);
+        }
+
+        public vec2 normalize() {
+            return normalize(this);
+        }
+
+        public vec2 normalizeOrDefault() {
+            return normalizeOrDefault(this);
+        }
+
+        private static vec2 normalizeOrNaN(vec2 v1) {
+            double inverse = 1 / v1.magnitude;
+
+            return new vec2(
+                v1.x * inverse,
+                v1.y * inverse);
+        }
+
+        private static vec2 normalizeSpecialCasesOrOrigional(vec2 v1) {
+            if (double.IsInfinity(v1.magnitude)) {
+                var x = v1.x == 0 ? 0 : v1.x == -0 ? -0 : double.IsPositiveInfinity(v1.x) ? 1 : double.IsNegativeInfinity(v1.x) ? -1 : double.NaN;
+                var y = v1.y == 0 ? 0 : v1.y == -0 ? -0 : double.IsPositiveInfinity(v1.y) ? 1 : double.IsNegativeInfinity(v1.y) ? -1 : double.NaN;
+
+                return new vec2(x, y);
+            }
+
+            return v1;
+        }
+
+        public static vec2 interpolate(vec2 v1, vec2 v2, double control, bool allowExtrapolation) {
+            if (!allowExtrapolation && (control > 1 || control < 0)) {
+                throw new ArgumentOutOfRangeException(
+                    "control",
+                    control,
+                    INTERPOLATION_RANGE + "\n" + ARGUMENT_VALUE + control);
+            }
+
+            return new vec2(
+                v1.x * (1 - control) + v2.x * control,
+                v1.y * (1 - control) + v2.y * control);
+        }
+
+        public static vec2 interpolate(vec2 v1, vec2 v2, double control) {
+            return interpolate(v1, v2, control, false);
+        }
+
+        public vec2 interpolate(vec2 other, double control) {
+            return interpolate(this, other, control);
+        }
+
+        public vec2 interpolate(vec2 other, double control, bool allowExtrapolation) {
+            return interpolate(this, other, control);
+        }
+
+        public static double distance(vec2 v1, vec2 v2) {
+            return Math.Sqrt(
+                (v1.x - v2.x) * (v1.x - v2.x) +
+                (v1.y - v2.y) * (v1.y - v2.y));
+        }
+
+        public double distance(vec2 other) {
+            return distance(this, other);
+        }
+
+        public static double angle(vec2 v1, vec2 v2) {
+            if (v1 == v2) {
+                return 0;
+            }
+
+            return
+                Math.Acos(
+                    Math.Min(1.0f, normalizeOrDefault(v1).dotProduct(normalizeOrDefault(v2))));
+        }
+
+        public double angle(vec2 other) {
+            return angle(this, other);
+        }
+
+        public static vec2 max(vec2 v1, vec2 v2) {
+            return v1 >= v2 ? v1 : v2;
+        }
+
+        public vec2 max(vec2 other) {
+            return max(this, other);
+        }
+
+        public static vec2 min(vec2 v1, vec2 v2) {
+            return v1 <= v2 ? v1 : v2;
+        }
+
+        public vec2 min(vec2 other) {
+            return min(this, other);
+        }
+
+        public static vec2 rotate(vec2 v1, double rad) {
+            double x = (v1.x * Math.Cos(rad)) - (v1.y * Math.Sin(rad));
+            double y = (v1.x * Math.Sin(rad)) + (v1.y * Math.Cos(rad));
+            return new vec2(x, y);
+        }
+
+        public vec2 rotate(double rad) {
+            return rotate(this, rad);
+        }
+
+        public static vec2 rotate(vec2 v1, double xOff, double yOff, double rad) {
+            double x = (v1.x * Math.Cos(rad)) - (v1.y * Math.Sin(rad)) + (xOff * (1 - Math.Cos(rad)) + yOff * Math.Sin(rad));
+            double y = (v1.x * Math.Sin(rad)) + (v1.y * Math.Cos(rad)) + (yOff * (1 - Math.Cos(rad)) - xOff * Math.Sin(rad));
+            return new vec2(x, y);
+        }
+
+        public vec2 rotate(double xOff, double yOff, double rad) {
+            return rotate(this, xOff, yOff, rad);
+        }
+
+        public static vec2 projection(vec2 v1, vec2 v2) {
+            return new vec2(v2 * (v1.dotProduct(v2) / Math.Pow(v2.magnitude, 2)));
+        }
+
+        public vec2 projection(vec2 direction) {
+            return projection(this, direction);
+        }
+
+        public static vec2 rejection(vec2 v1, vec2 v2) {
+            return v1 - v1.projection(v2);
+        }
+
+        public vec2 rejection(vec2 direction) {
+            return rejection(this, direction);
+        }
+
+        public vec2 reflection(vec2 reflector) {
+            this = vec2.reflection(this, reflector);
+            return this;
+        }
+
+        public static vec2 reflection(vec2 v1, vec2 v2) {
+            if (Math.Abs(Math.Abs(v1.angle(v2)) - Math.PI / 2) < Double.Epsilon) {
+                return -v1;
+            }
+
+            vec2 retval = new vec2(2 * v1.projection(v2) - v1);
+            return retval.scale(v1.magnitude);
+        }
+
+        public static Double abs(vec2 v1) {
+            return v1.magnitude;
+        }
+
+        public double abs() {
+            return this.magnitude;
+        }
+
+        public static double sumComponents(vec2 v1) {
+            return v1.x + v1.y;
+        }
+
+        public double sumComponents() {
+            return sumComponents(this);
+        }
+
+        public static double sumComponentSqrs(vec2 v1) {
+            vec2 v2 = sqrComponents(v1);
+            return v2.sumComponents();
+        }
+
+        public double sumComponentSqrs() {
+            return sumComponentSqrs(this);
+        }
+
+        public static vec2 powComponents(vec2 v1, double power) {
+            return new vec2(
+                Math.Pow(v1.x, power),
+                Math.Pow(v1.y, power));
+        }
+
+        public vec2 powComponents(double power) {
+            return powComponents(this, power);
+        }
+
+        public static vec2 sqrtComponents(vec2 v1) {
+            return new vec2(
+                Math.Sqrt(v1.x),
+                Math.Sqrt(v1.y));
+        }
+
+        public vec2 sqrtComponents() {
+            return sqrtComponents(this);
+        }
+
+        public static vec2 sqrComponents(vec2 v1) {
+            return new vec2(
+                v1.x * v1.x,
+                v1.y * v1.y);
+        }
+
+        public vec2 sqrComponents() {
+            return sqrComponents(this);
+        }
+
+        public static vec2 round(vec2 v1) {
+            return new vec2(Math.Round(v1.x), Math.Round(v1.y));
+        }
+
+        public static vec2 round(vec2 v1, int digits) {
+            return new vec2(Math.Round(v1.x, digits), Math.Round(v1.y, digits));
+        }
+
+        public static vec2 round(vec2 v1, MidpointRounding mode) {
+            return new vec2(Math.Round(v1.x, mode), Math.Round(v1.y, mode));
+        }
+
+        public static vec2 round(vec2 v1, int digits, MidpointRounding mode) {
+            return new vec2(Math.Round(v1.x, digits, mode), Math.Round(v1.y, digits, mode));
+        }
+
+        public vec2 round() {
+            return new vec2(Math.Round(this.x), Math.Round(this.y));
+        }
+
+        public vec2 round(int digits) {
+            return new vec2(Math.Round(this.x, digits), Math.Round(this.y, digits));
+        }
+
+        public vec2 round(MidpointRounding mode) {
+            return new vec2(Math.Round(this.x, mode), Math.Round(this.y, mode));
+        }
+
+        public vec2 round(int digits, MidpointRounding mode) {
+            return new vec2(Math.Round(this.x, digits, mode), Math.Round(this.y, digits, mode));
+        }
+
+        public override string ToString() {
+            return this.ToString(null, null);
+        }
+
+        public string ToVerbString() {
+            string output = null;
+
+            if (this.isUnitVector()) {
+                output += UNIT_VECTOR;
+            }
+            else {
+                output += POSITIONAL_VECTOR;
+            }
+
+            output += string.Format("( x={0}, y={1} )", this.x, this.y);
+            output += magnitude + this.magnitude;
+
+            return output;
+        }
+
+        public string ToString(string format, IFormatProvider formatProvider) {
+            if (format == null || format == "") {
+                return string.Format("({0}, {1})", this.x, this.y);
+            }
+
+            char firstChar = format[0];
+            string remainder = null;
+
+            if (format.Length > 1) {
+                remainder = format.Substring(1);
+            }
+
+            switch (firstChar) {
+                case 'x': return this.x.ToString(remainder, formatProvider);
+                case 'y': return this.y.ToString(remainder, formatProvider);
+                default:
+                    return String.Format(
+                        "({0}, {1})",
+                        this.x.ToString(format, formatProvider),
+                        this.y.ToString(format, formatProvider));
+            }
+        }
+
+        public override int GetHashCode() {
+            unchecked {
+                var hashCode = this.x.GetHashCode();
+                hashCode = (hashCode * 397) ^ this.y.GetHashCode();
+                return hashCode;
+            }
+        }
+
+        public override bool Equals(object other) {
+            if (other is vec2) {
+                return other.Equals(this);
+            }
+            else {
+                return false;
+            }
+        }
+
+        public bool Equals(object other, double tolerance) {
+            if (other is vec2) {
+                return this.Equals((vec2)other, tolerance);
+            }
+            return false;
+        }
+
+        public bool Equals(vec2 other) {
+            return
+               this.x.Equals(other.x) &&
+               this.y.Equals(other.y);
+        }
+
+        public bool Equals(vec2 other, double tolerance) {
+            return
+                this.x.almostEqualsWithAbsTolerance(other.x, tolerance) &&
+                this.y.almostEqualsWithAbsTolerance(other.y, tolerance);
+        }
+
+        public int CompareTo(vec2 other) {
+            if (this < other) {
+                return -1;
+            }
+
+            if (this > other) {
+                return 1;
+            }
+
+            return 0;
+        }
+
+        public int CompareTo(object other) {
+            if (other is vec2) {
+                return this.CompareTo((vec2)other);
+            }
+
+            throw new ArgumentException(
+                NON_VECTOR_COMPARISON + "\n" + ARGUMENT_TYPE + other.GetType().ToString(),
+                "other");
+        }
+
+        public int CompareTo(vec2 other, double tolerance) {
+            var bothInfinite = double.IsInfinity(this.sumComponentSqrs()) && double.IsInfinity(other.sumComponentSqrs());
+
+            if (this.Equals(other, tolerance) || bothInfinite) {
+                return 0;
+            }
+
+            if (this < other) {
+                return -1;
+            }
+
+            return 1;
+        }
+
+        public int CompareTo(object other, double tolerance) {
+            if (other is vec2) {
+                return this.CompareTo((vec2)other, tolerance);
+            }
+
+            throw new ArgumentException(
+                NON_VECTOR_COMPARISON + "\n" + ARGUMENT_TYPE + other.GetType().ToString(),
+                "other");
+        }
+
+        public static bool isUnitVector(vec2 v1, double tolerance) {
+            return v1.magnitude.almostEqualsWithAbsTolerance(1, tolerance);
+        }
+
+        public static bool isUnitVector(vec2 v1) {
+            return v1.magnitude == 1;
+        }
+
+        public bool isUnitVector() {
+            return isUnitVector(this);
+        }
+
+        public bool isUnitVector(double tolerance) {
+            return isUnitVector(this, tolerance);
+        }
+                
+        public static bool isNaN(vec2 v1) {
+            return double.IsNaN(v1.x) || double.IsNaN(v1.y);
+        }
+
+        public bool isNaN() {
+            return isNaN(this);
+        }
+
+        public static readonly vec2 origin = new vec2(0, 0);
+        public static readonly vec2 right = new vec2(1, 0);
+        public static readonly vec2 left = new vec2(-1, 0);
+        public static readonly vec2 down = new vec2(0, 1);
+        public static readonly vec2 up = new vec2(0, -1);
+
+
+        private const string NORMALIZE_NaN = "Cannot normalize a vector when it's magnitude is NaN";
+        private const string NORMALIZE_0 = "Cannot normalize a vector when it's magnitude is zero";
+        private const string NORMALIZE_Inf = "Cannot normalize a vector when it's magnitude is infinite except under special conditions";
+        private const string TWO_COMPONENTS = "Array must contain exactly two components (x, y)";
+        private const string INTERPOLATION_RANGE = "Control parameter must be a value between 0 & 1";
+        private const string NON_VECTOR_COMPARISON = "Cannot compare a vec2 to a non-vec2";
+        private const string ARGUMENT_TYPE = "The argument provided is a type of ";
+        private const string ARGUMENT_VALUE = "The argument provided has a value of ";
+        private const string ARGUMENT_LENGTH = "The argument provided has a length of ";
+        private const string NEGATIVE_magnitude = "The magnitude of a vec2 must be a positive value, (i.e. greater than 0)";
+        private const string ORIGIN_VECTOR_magnitude = "Cannot change the magnitude of vec2(0, 0)";
+
+        private const string UNIT_VECTOR = "Unit vector composing of ";
+        private const string POSITIONAL_VECTOR = "Positional vector composing of ";
+        private const string MAGNITUDE = " of magnitude ";
+
+        public static readonly vec2 minValue = new vec2(Double.MinValue, Double.MinValue);
+        public static readonly vec2 maxValue = new vec2(Double.MaxValue, Double.MaxValue);
+        public static readonly vec2 epsilon = new vec2(Double.Epsilon, Double.Epsilon);
+        public static readonly vec2 zero = origin;
+        public static readonly vec2 NaN = new vec2(double.NaN, double.NaN);
+    }
+}

src/JuicyGraphics/math/vec3.cs

@@ -0,0 +1,956 @@
+using System;
+using System.ComponentModel;
+using System.Xml.Serialization;
+
+namespace JuicyGraphics.Mathematics {
+    using Exceptions;
+
+    [ImmutableObject(true), Serializable]
+    public struct vec3
+        : IComparable, IComparable<vec3>, IEquatable<vec3>, IFormattable {
+
+        private readonly double _x;
+        private readonly double _y;
+        private readonly double _z;
+
+        public vec3(double x, double y, double z) {
+            _x = x;
+            _y = y;
+            _z = z;
+        }
+
+        public vec3(double[] xyz) {
+            if (xyz.Length == 3) {
+                _x = xyz[0];
+                _y = xyz[1];
+                _z = xyz[2];
+            }
+            else {
+                throw new ArgumentException(THREE_COMPONENTS);
+            }
+        }
+
+        public vec3(vec3 v1) {
+            _x = v1.x;
+            _y = v1.y;
+            _z = v1.z;
+        }
+
+        public double x {
+            get {
+                return _x;
+            }
+        }
+
+        public double y {
+            get {
+                return _y;
+            }
+        }
+
+        public double z {
+            get {
+                return _z;
+            }
+        }
+
+        public vec2 xx {
+            get {
+                return new vec2(_x, _x);
+            }
+        }
+
+        public vec2 xy {
+            get {
+                return new vec2(_x, _y);
+            }
+        }
+
+        public vec2 yx {
+            get {
+                return new vec2(_y, _x);
+            }
+        }
+
+        public vec2 yy {
+            get {
+                return new vec2(_y, _y);
+            }
+        }
+
+        public vec3 xxx {
+            get {
+                return new vec3(_x, _x, _x);
+            }
+        }
+
+        public vec3 xxy {
+            get {
+                return new vec3(_x, _x, _y);
+            }
+        }
+
+        public vec3 xxz {
+            get {
+                return new vec3(_x, _x, _z);
+            }
+        }
+
+        public vec3 xyx {
+            get {
+                return new vec3(_x, _y, _x);
+            }
+        }
+
+        public vec3 xyy {
+            get {
+                return new vec3(_x, _y, _y);
+            }
+        }
+
+        public vec3 xyz {
+            get {
+                return new vec3(_x, _y, _z);
+            }
+        }
+
+        public vec3 xzx {
+            get {
+                return new vec3(_x, _z, _x);
+            }
+        }
+
+        public vec3 xzy {
+            get {
+                return new vec3(_x, _z, _y);
+            }
+        }
+
+        public vec3 xzz {
+            get {
+                return new vec3(_x, _z, _z);
+            }
+        }
+
+        public vec3 yxx {
+            get {
+                return new vec3(_y, _x, _x);
+            }
+        }
+
+        public vec3 yxy {
+            get {
+                return new vec3(_y, _x, _y);
+            }
+        }
+
+        public vec3 yxz {
+            get {
+                return new vec3(_y, _x, _z);
+            }
+        }
+
+        public vec3 yyx {
+            get {
+                return new vec3(_y, _y, _x);
+            }
+        }
+
+        public vec3 yyy {
+            get {
+                return new vec3(_y, _y, _y);
+            }
+        }
+
+        public vec3 yyz {
+            get {
+                return new vec3(_y, _y, _z);
+            }
+        }
+
+        public vec3 yzx {
+            get {
+                return new vec3(_y, _z, _x);
+            }
+        }
+
+        public vec3 yzy {
+            get {
+                return new vec3(_y, _z, _y);
+            }
+        }
+
+        public vec3 yzz {
+            get {
+                return new vec3(_y, _z, _z);
+            }
+        }
+
+        public vec3 zxx {
+            get {
+                return new vec3(_z, _x, _x);
+            }
+        }
+
+        public vec3 zxy {
+            get {
+                return new vec3(_z, _x, _y);
+            }
+        }
+
+        public vec3 zxz {
+            get {
+                return new vec3(_z, _x, _z);
+            }
+        }
+
+        public vec3 zyx {
+            get {
+                return new vec3(_z, _y, _x);
+            }
+        }
+
+        public vec3 zyy {
+            get {
+                return new vec3(_z, _y, _y);
+            }
+        }
+
+        public vec3 zyz {
+            get {
+                return new vec3(_z, _y, _z);
+            }
+        }
+
+        public vec3 zzx {
+            get {
+                return new vec3(_z, _z, _x);
+            }
+        }
+
+        public vec3 zzy {
+            get {
+                return new vec3(_z, _z, _y);
+            }
+        }
+
+        public vec3 zzz {
+            get {
+                return new vec3(_z, _z, _z);
+            }
+        }
+
+        public vec3 normal {
+            get {
+                return normalize();
+            }
+        }
+
+        public double magnitude {
+            get {
+                return Math.Sqrt(sumComponentSqrs());
+            }
+        }
+
+        [XmlIgnore]
+        public double[] array {
+            get {
+                return new[] { _x, _y, _z };
+            }
+        }
+
+        public double this[int index] {
+            get {
+                switch (index) {
+                    case 0:
+                        return x;
+                    case 1:
+                        return y;
+                    case 2:
+                        return z;
+                    default:
+                        throw new ArgumentException(THREE_COMPONENTS, "index");
+                }
+            }
+        }
+
+        public static vec3 operator +(vec3 v1, vec3 v2) {
+            return new vec3(
+                v1.x + v2.x,
+                v1.y + v2.y,
+                v1.z + v2.z);
+        }
+
+        public static vec3 operator -(vec3 v1, vec3 v2) {
+            return new vec3(
+                v1.x - v2.x,
+                v1.y - v2.y,
+                v1.z - v2.z);
+        }
+
+        public static vec3 operator *(vec3 v1, double s2) {
+            return
+                new vec3(
+                        v1.x * s2,
+                        v1.y * s2,
+                        v1.z * s2);
+        }
+
+        public static vec3 operator *(double s1, vec3 v2) {
+            return v2 * s1;
+        }
+
+        public static vec3 operator /(vec3 v1, double s2) {
+            return new vec3(
+                        v1.x / s2,
+                        v1.y / s2,
+                        v1.z / s2);
+        }
+
+        public static vec3 operator -(vec3 v1) {
+            return new vec3(
+                -v1.x,
+                -v1.y,
+                -v1.z);
+        }
+
+        public static vec3 operator +(vec3 v1) {
+            return new vec3(
+                +v1.x,
+                +v1.y,
+                +v1.z);
+        }
+
+        public static bool operator <(vec3 v1, vec3 v2) {
+            return v1.sumComponentSqrs() < v2.sumComponentSqrs();
+        }
+
+        public static bool operator >(vec3 v1, vec3 v2) {
+            return v1.sumComponentSqrs() > v2.sumComponentSqrs();
+        }
+
+        public static bool operator <=(vec3 v1, vec3 v2) {
+            return v1.sumComponentSqrs() <= v2.sumComponentSqrs();
+        }
+
+        public static bool operator >=(vec3 v1, vec3 v2) {
+            return v1.sumComponentSqrs() >= v2.sumComponentSqrs();
+        }
+
+        public static bool operator ==(vec3 v1, vec3 v2) {
+            return
+                v1.x == v2.x &&
+                v1.y == v2.y &&
+                v1.z == v2.z;
+        }
+
+        public static bool operator !=(vec3 v1, vec3 v2) {
+            return !(v1 == v2);
+        }
+
+        public static vec3 scale(vec3 vector, double magnitude) {
+            if (magnitude < 0) {
+                throw new ArgumentOutOfRangeException("magnitude", magnitude, NEGATIVE_magnitude);
+            }
+
+            if (vector == new vec3(0, 0, 0)) {
+                throw new ArgumentException(ORIGIN_VECTOR_magnitude, "vector");
+            }
+
+            return vector * (magnitude / vector.magnitude);
+        }
+
+        public vec3 scale(double magnitude) {
+            return vec3.scale(this, magnitude);
+        }
+
+        public static vec3 crossProduct(vec3 v1, vec3 v2) {
+            return
+                new vec3(
+                        v1.y * v2.z - v1.z * v2.y,
+                        v1.z * v2.x - v1.x * v2.z,
+                        v1.x * v2.y - v1.y * v2.x);
+        }
+
+        public vec3 crossProduct(vec3 other) {
+            return crossProduct(this, other);
+        }
+
+        public static double dotProduct(vec3 v1, vec3 v2) {
+            return
+                v1.x * v2.x +
+                v1.y * v2.y +
+                v1.z * v2.z;
+        }
+
+        public double dotProduct(vec3 other) {
+            return dotProduct(this, other);
+        }
+
+        public static double mixedProduct(vec3 v1, vec3 v2, vec3 v3) {
+            return dotProduct(crossProduct(v1, v2), v3);
+        }
+
+        public double mixedProduct(vec3 other_v1, vec3 other_v2) {
+            return dotProduct(crossProduct(this, other_v1), other_v2);
+        }
+
+        public static vec3 normalize(vec3 v1) {
+            if (double.IsInfinity(v1.magnitude)) {
+                v1 = normalizeSpecialCasesOrOrigional(v1);
+
+                if (v1.isNaN()) {
+                    throw new normalizeVectorException(NORMALIZE_Inf);
+                }
+            }
+
+            if (v1.magnitude == 0) {
+                throw new normalizeVectorException(NORMALIZE_0);
+            }
+
+            if (v1.isNaN()) {
+                throw new normalizeVectorException(NORMALIZE_NaN);
+            }
+
+            return normalizeOrNaN(v1);
+        }
+
+        public static vec3 normalizeOrDefault(vec3 v1) {
+            v1 = normalizeSpecialCasesOrOrigional(v1);
+
+            if (v1.magnitude == 0) {
+                return origin;
+            }
+
+            if (v1.isNaN()) {
+                return NaN;
+            }
+
+            return normalizeOrNaN(v1);
+        }
+
+        public vec3 normalize() {
+            return normalize(this);
+        }
+
+        public vec3 normalizeOrDefault() {
+            return normalizeOrDefault(this);
+        }
+
+        private static vec3 normalizeOrNaN(vec3 v1) {
+            double inverse = 1 / v1.magnitude;
+
+            return new vec3(
+                v1.x * inverse,
+                v1.y * inverse,
+                v1.z * inverse);
+        }
+
+        private static vec3 normalizeSpecialCasesOrOrigional(vec3 v1) {
+            if (double.IsInfinity(v1.magnitude)) {
+                var x = v1.x == 0 ? 0 : v1.x == -0 ? -0 : double.IsPositiveInfinity(v1.x) ? 1 : double.IsNegativeInfinity(v1.x) ? -1 : double.NaN;
+                var y = v1.y == 0 ? 0 : v1.y == -0 ? -0 : double.IsPositiveInfinity(v1.y) ? 1 : double.IsNegativeInfinity(v1.y) ? -1 : double.NaN;
+                var z = v1.z == 0 ? 0 : v1.z == -0 ? -0 : double.IsPositiveInfinity(v1.z) ? 1 : double.IsNegativeInfinity(v1.z) ? -1 : double.NaN;
+
+                return new vec3(x, y, z);
+            }
+
+            return v1;
+        }
+
+        public static vec3 interpolate(vec3 v1, vec3 v2, double control, bool allowExtrapolation) {
+            if (!allowExtrapolation && (control > 1 || control < 0)) {
+                throw new ArgumentOutOfRangeException(
+                    "control",
+                    control,
+                    INTERPOLATION_RANGE + "\n" + ARGUMENT_VALUE + control);
+            }
+
+            return new vec3(
+                v1.x * (1 - control) + v2.x * control,
+                v1.y * (1 - control) + v2.y * control,
+                v1.z * (1 - control) + v2.z * control);
+        }
+
+        public static vec3 interpolate(vec3 v1, vec3 v2, double control) {
+            return interpolate(v1, v2, control, false);
+        }
+
+        public vec3 interpolate(vec3 other, double control) {
+            return interpolate(this, other, control);
+        }
+
+        public vec3 interpolate(vec3 other, double control, bool allowExtrapolation) {
+            return interpolate(this, other, control);
+        }
+
+        public static double distance(vec3 v1, vec3 v2) {
+            return Math.Sqrt(
+                (v1.x - v2.x) * (v1.x - v2.x) +
+                (v1.y - v2.y) * (v1.y - v2.y) +
+                (v1.z - v2.z) * (v1.z - v2.z));
+        }
+
+        public double distance(vec3 other) {
+            return distance(this, other);
+        }
+
+        public static double angle(vec3 v1, vec3 v2) {
+            if (v1 == v2) {
+                return 0;
+            }
+
+            return
+                Math.Acos(
+                    Math.Min(1.0f, normalizeOrDefault(v1).dotProduct(normalizeOrDefault(v2))));
+        }
+
+        public double angle(vec3 other) {
+            return angle(this, other);
+        }
+
+        public static vec3 max(vec3 v1, vec3 v2) {
+            return v1 >= v2 ? v1 : v2;
+        }
+
+        public vec3 max(vec3 other) {
+            return max(this, other);
+        }
+
+        public static vec3 min(vec3 v1, vec3 v2) {
+            return v1 <= v2 ? v1 : v2;
+        }
+
+        public vec3 min(vec3 other) {
+            return min(this, other);
+        }
+
+        public static vec3 yaw(vec3 v1, double rad) {
+            return rotateY(v1, rad);
+        }
+
+        public vec3 yaw(double rad) {
+            return yaw(this, rad);
+        }
+
+        public static vec3 pitch(vec3 v1, double rad) {
+            return rotateX(v1, rad);
+        }
+
+        public vec3 pitch(double rad) {
+            return pitch(this, rad);
+        }
+
+        public static vec3 roll(vec3 v1, double rad) {
+            return rotateZ(v1, rad);
+        }
+
+        public vec3 roll(double rad) {
+            return roll(this, rad);
+        }
+
+        public static vec3 rotateX(vec3 v1, double rad) {
+            double x = v1.x;
+            double y = (v1.y * Math.Cos(rad)) - (v1.z * Math.Sin(rad));
+            double z = (v1.y * Math.Sin(rad)) + (v1.z * Math.Cos(rad));
+            return new vec3(x, y, z);
+        }
+
+        public vec3 rotateX(double rad) {
+            return rotateX(this, rad);
+        }
+
+        public static vec3 rotateY(vec3 v1, double rad) {
+            double x = (v1.z * Math.Sin(rad)) + (v1.x * Math.Cos(rad));
+            double y = v1.y;
+            double z = (v1.z * Math.Cos(rad)) - (v1.x * Math.Sin(rad));
+            return new vec3(x, y, z);
+        }
+
+        public vec3 rotateY(double rad) {
+            return rotateY(this, rad);
+        }
+
+        public static vec3 rotateZ(vec3 v1, double rad) {
+            double x = (v1.x * Math.Cos(rad)) - (v1.y * Math.Sin(rad));
+            double y = (v1.x * Math.Sin(rad)) + (v1.y * Math.Cos(rad));
+            double z = v1.z;
+            return new vec3(x, y, z);
+        }
+
+        public vec3 rotateZ(double rad) {
+            return rotateZ(this, rad);
+        }
+
+        public static vec3 rotateX(vec3 v1, double yOff, double zOff, double rad) {
+            double x = v1.x;
+            double y = (v1.y * Math.Cos(rad)) - (v1.z * Math.Sin(rad)) + (yOff * (1 - Math.Cos(rad)) + zOff * Math.Sin(rad));
+            double z = (v1.y * Math.Sin(rad)) + (v1.z * Math.Cos(rad)) + (zOff * (1 - Math.Cos(rad)) - yOff * Math.Sin(rad));
+            return new vec3(x, y, z);
+        }
+
+        public vec3 rotateX(double yOff, double zOff, double rad) {
+            return rotateX(this, yOff, zOff, rad);
+        }
+
+        public static vec3 rotateY(vec3 v1, double xOff, double zOff, double rad) {
+            double x = (v1.z * Math.Sin(rad)) + (v1.x * Math.Cos(rad)) + (xOff * (1 - Math.Cos(rad)) - zOff * Math.Sin(rad));
+            double y = v1.y;
+            double z = (v1.z * Math.Cos(rad)) - (v1.x * Math.Sin(rad)) + (zOff * (1 - Math.Cos(rad)) + xOff * Math.Sin(rad));
+            return new vec3(x, y, z);
+        }
+
+        public vec3 rotateY(double xOff, double zOff, double rad) {
+            return rotateY(this, xOff, zOff, rad);
+        }
+
+        public static vec3 rotateZ(vec3 v1, double xOff, double yOff, double rad) {
+            double x = (v1.x * Math.Cos(rad)) - (v1.y * Math.Sin(rad)) + (xOff * (1 - Math.Cos(rad)) + yOff * Math.Sin(rad));
+            double y = (v1.x * Math.Sin(rad)) + (v1.y * Math.Cos(rad)) + (yOff * (1 - Math.Cos(rad)) - xOff * Math.Sin(rad));
+            double z = v1.z;
+            return new vec3(x, y, z);
+        }
+
+        public vec3 rotateZ(double xOff, double yOff, double rad) {
+            return rotateZ(this, xOff, yOff, rad);
+        }
+
+        public static vec3 projection(vec3 v1, vec3 v2) {
+            return new vec3(v2 * (v1.dotProduct(v2) / Math.Pow(v2.magnitude, 2)));
+        }
+
+        public vec3 projection(vec3 direction) {
+            return projection(this, direction);
+        }
+
+        public static vec3 rejection(vec3 v1, vec3 v2) {
+            return v1 - v1.projection(v2);
+        }
+
+        public vec3 rejection(vec3 direction) {
+            return rejection(this, direction);
+        }
+
+        public vec3 reflection(vec3 reflector) {
+            this = vec3.reflection(this, reflector);
+            return this;
+        }
+
+        public static vec3 reflection(vec3 v1, vec3 v2) {
+            if (Math.Abs(Math.Abs(v1.angle(v2)) - Math.PI / 2) < Double.Epsilon) {
+                return -v1;
+            }
+
+            vec3 retval = new vec3(2 * v1.projection(v2) - v1);
+            return retval.scale(v1.magnitude);
+        }
+
+        public static Double abs(vec3 v1) {
+            return v1.magnitude;
+        }
+
+        public double abs() {
+            return magnitude;
+        }
+
+        public static double sumComponents(vec3 v1) {
+            return v1.x + v1.y + v1.z;
+        }
+
+        public double sumComponents() {
+            return sumComponents(this);
+        }
+
+        public static double sumComponentSqrs(vec3 v1) {
+            vec3 v2 = sqrComponents(v1);
+            return v2.sumComponents();
+        }
+
+        public double sumComponentSqrs() {
+            return sumComponentSqrs(this);
+        }
+
+        public static vec3 powComponents(vec3 v1, double power) {
+            return new vec3(
+                Math.Pow(v1.x, power),
+                Math.Pow(v1.y, power),
+                Math.Pow(v1.z, power));
+        }
+
+        public vec3 powComponents(double power) {
+            return powComponents(this, power);
+        }
+
+        public static vec3 sqrtComponents(vec3 v1) {
+            return new vec3(
+                Math.Sqrt(v1.x),
+                Math.Sqrt(v1.y),
+                Math.Sqrt(v1.z));
+        }
+
+        public vec3 sqrtComponents() {
+            return sqrtComponents(this);
+        }
+
+        public static vec3 sqrComponents(vec3 v1) {
+            return new vec3(
+                v1.x * v1.x,
+                v1.y * v1.y,
+                v1.z * v1.z);
+        }
+
+        public vec3 sqrComponents() {
+            return sqrComponents(this);
+        }
+
+        public static vec3 round(vec3 v1) {
+            return new vec3(Math.Round(v1.x), Math.Round(v1.y), Math.Round(v1.z));
+        }
+
+        public static vec3 round(vec3 v1, int digits) {
+            return new vec3(Math.Round(v1.x, digits), Math.Round(v1.y, digits), Math.Round(v1.z, digits));
+        }
+
+        public static vec3 round(vec3 v1, MidpointRounding mode) {
+            return new vec3(Math.Round(v1.x, mode), Math.Round(v1.y, mode), Math.Round(v1.z, mode));
+        }
+
+        public static vec3 round(vec3 v1, int digits, MidpointRounding mode) {
+            return new vec3(Math.Round(v1.x, digits, mode), Math.Round(v1.y, digits, mode), Math.Round(v1.z, digits, mode));
+        }
+
+        public vec3 round() {
+            return new vec3(Math.Round(x), Math.Round(y), Math.Round(z));
+        }
+