#region --- License --- /* Copyright (c) 2006 - 2008 The Open Toolkit library. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #endregion using System; using System.Runtime.InteropServices; using System.Xml.Serialization; namespace OpenTK { /// /// Represents a 3D vector using three double-precision floating-point numbers. /// [Serializable] [StructLayout(LayoutKind.Sequential)] public struct Vector3d : IEquatable { #region Fields /// /// The X component of the Vector3. /// public double X; /// /// The Y component of the Vector3. /// public double Y; /// /// The Z component of the Vector3. /// public double Z; #endregion #region Constructors /// /// Constructs a new Vector3. /// /// The x component of the Vector3. /// The y component of the Vector3. /// The z component of the Vector3. public Vector3d(double x, double y, double z) { X = x; Y = y; Z = z; } /// /// Constructs a new instance from the given Vector2d. /// /// The Vector2d to copy components from. public Vector3d(Vector2d v) { X = v.X; Y = v.Y; Z = 0.0f; } /// /// Constructs a new instance from the given Vector3d. /// /// The Vector3d to copy components from. public Vector3d(Vector3d v) { X = v.X; Y = v.Y; Z = v.Z; } /// /// Constructs a new instance from the given Vector4d. /// /// The Vector4d to copy components from. public Vector3d(Vector4d v) { X = v.X; Y = v.Y; Z = v.Z; } #endregion #region Public Members #region Instance #region public void Add() /// Add the Vector passed as parameter to this instance. /// Right operand. This parameter is only read from. [Obsolete("Use static Add() method instead.")] public void Add(Vector3d right) { this.X += right.X; this.Y += right.Y; this.Z += right.Z; } /// Add the Vector passed as parameter to this instance. /// Right operand. This parameter is only read from. [CLSCompliant(false)] [Obsolete("Use static Add() method instead.")] public void Add(ref Vector3d right) { this.X += right.X; this.Y += right.Y; this.Z += right.Z; } #endregion public void Add() #region public void Sub() /// Subtract the Vector passed as parameter from this instance. /// Right operand. This parameter is only read from. [Obsolete("Use static Subtract() method instead.")] public void Sub(Vector3d right) { this.X -= right.X; this.Y -= right.Y; this.Z -= right.Z; } /// Subtract the Vector passed as parameter from this instance. /// Right operand. This parameter is only read from. [CLSCompliant(false)] [Obsolete("Use static Subtract() method instead.")] public void Sub(ref Vector3d right) { this.X -= right.X; this.Y -= right.Y; this.Z -= right.Z; } #endregion public void Sub() #region public void Mult() /// Multiply this instance by a scalar. /// Scalar operand. [Obsolete("Use static Multiply() method instead.")] public void Mult(double f) { this.X *= f; this.Y *= f; this.Z *= f; } #endregion public void Mult() #region public void Div() /// Divide this instance by a scalar. /// Scalar operand. [Obsolete("Use static Divide() method instead.")] public void Div(double f) { double mult = 1.0 / f; this.X *= mult; this.Y *= mult; this.Z *= mult; } #endregion public void Div() #region public double Length /// /// Gets the length (magnitude) of the vector. /// /// /// public double Length { get { return (float)System.Math.Sqrt(X * X + Y * Y + Z * Z); } } #endregion #region public double LengthFast /// /// Gets an approximation of the vector length (magnitude). /// /// /// This property uses an approximation of the square root function to calculate vector magnitude, with /// an upper error bound of 0.001. /// /// /// public double LengthFast { get { return 1.0f / MathHelper.InverseSqrtFast(X * X + Y * Y + Z * Z); } } #endregion #region public double LengthSquared /// /// Gets the square of the vector length (magnitude). /// /// /// This property avoids the costly square root operation required by the Length property. This makes it more suitable /// for comparisons. /// /// /// public double LengthSquared { get { return X * X + Y * Y + Z * Z; } } #endregion #region public void Normalize() /// /// Scales the Vector3d to unit length. /// public void Normalize() { double scale = 1.0f / this.Length; X *= scale; Y *= scale; Z *= scale; } #endregion #region public void NormalizeFast() /// /// Scales the Vector3d to approximately unit length. /// public void NormalizeFast() { double scale = MathHelper.InverseSqrtFast(X * X + Y * Y + Z * Z); X *= scale; Y *= scale; Z *= scale; } #endregion #region public void Scale() /// /// Scales the current Vector3d by the given amounts. /// /// The scale of the X component. /// The scale of the Y component. /// The scale of the Z component. [Obsolete("Use static Multiply() method instead.")] public void Scale(double sx, double sy, double sz) { this.X = X * sx; this.Y = Y * sy; this.Z = Z * sz; } /// Scales this instance by the given parameter. /// The scaling of the individual components. [Obsolete("Use static Multiply() method instead.")] public void Scale(Vector3d scale) { this.X *= scale.X; this.Y *= scale.Y; this.Z *= scale.Z; } /// Scales this instance by the given parameter. /// The scaling of the individual components. [CLSCompliant(false)] [Obsolete("Use static Multiply() method instead.")] public void Scale(ref Vector3d scale) { this.X *= scale.X; this.Y *= scale.Y; this.Z *= scale.Z; } #endregion public void Scale() #endregion #region Static #region Fields /// /// Defines a unit-length Vector3d that points towards the X-axis. /// public static readonly Vector3d UnitX = new Vector3d(1, 0, 0); /// /// Defines a unit-length Vector3d that points towards the Y-axis. /// public static readonly Vector3d UnitY = new Vector3d(0, 1, 0); /// /// /// Defines a unit-length Vector3d that points towards the Z-axis. /// public static readonly Vector3d UnitZ = new Vector3d(0, 0, 1); /// /// Defines a zero-length Vector3. /// public static readonly Vector3d Zero = new Vector3d(0, 0, 0); /// /// Defines an instance with all components set to 1. /// public static readonly Vector3d One = new Vector3d(1, 1, 1); /// /// Defines the size of the Vector3d struct in bytes. /// public static readonly int SizeInBytes = Marshal.SizeOf(new Vector3d()); #endregion #region Obsolete #region Sub /// /// Subtract one Vector from another /// /// First operand /// Second operand /// Result of subtraction [Obsolete("Use static Subtract() method instead.")] public static Vector3d Sub(Vector3d a, Vector3d b) { a.X -= b.X; a.Y -= b.Y; a.Z -= b.Z; return a; } /// /// Subtract one Vector from another /// /// First operand /// Second operand /// Result of subtraction [Obsolete("Use static Subtract() method instead.")] public static void Sub(ref Vector3d a, ref Vector3d b, out Vector3d result) { result.X = a.X - b.X; result.Y = a.Y - b.Y; result.Z = a.Z - b.Z; } #endregion #region Mult /// /// Multiply a vector and a scalar /// /// Vector operand /// Scalar operand /// Result of the multiplication [Obsolete("Use static Multiply() method instead.")] public static Vector3d Mult(Vector3d a, double f) { a.X *= f; a.Y *= f; a.Z *= f; return a; } /// /// Multiply a vector and a scalar /// /// Vector operand /// Scalar operand /// Result of the multiplication [Obsolete("Use static Multiply() method instead.")] public static void Mult(ref Vector3d a, double f, out Vector3d result) { result.X = a.X * f; result.Y = a.Y * f; result.Z = a.Z * f; } #endregion #region Div /// /// Divide a vector by a scalar /// /// Vector operand /// Scalar operand /// Result of the division [Obsolete("Use static Divide() method instead.")] public static Vector3d Div(Vector3d a, double f) { double mult = 1.0f / f; a.X *= mult; a.Y *= mult; a.Z *= mult; return a; } /// /// Divide a vector by a scalar /// /// Vector operand /// Scalar operand /// Result of the division [Obsolete("Use static Divide() method instead.")] public static void Div(ref Vector3d a, double f, out Vector3d result) { double mult = 1.0f / f; result.X = a.X * mult; result.Y = a.Y * mult; result.Z = a.Z * mult; } #endregion #endregion #region Add /// /// Adds two vectors. /// /// Left operand. /// Right operand. /// Result of operation. public static Vector3d Add(Vector3d a, Vector3d b) { Add(ref a, ref b, out a); return a; } /// /// Adds two vectors. /// /// Left operand. /// Right operand. /// Result of operation. public static void Add(ref Vector3d a, ref Vector3d b, out Vector3d result) { result = new Vector3d(a.X + b.X, a.Y + b.Y, a.Z + b.Z); } #endregion #region Subtract /// /// Subtract one Vector from another /// /// First operand /// Second operand /// Result of subtraction public static Vector3d Subtract(Vector3d a, Vector3d b) { Subtract(ref a, ref b, out a); return a; } /// /// Subtract one Vector from another /// /// First operand /// Second operand /// Result of subtraction public static void Subtract(ref Vector3d a, ref Vector3d b, out Vector3d result) { result = new Vector3d(a.X - b.X, a.Y - b.Y, a.Z - b.Z); } #endregion #region Multiply /// /// Multiplies a vector by a scalar. /// /// Left operand. /// Right operand. /// Result of the operation. public static Vector3d Multiply(Vector3d vector, double scale) { Multiply(ref vector, scale, out vector); return vector; } /// /// Multiplies a vector by a scalar. /// /// Left operand. /// Right operand. /// Result of the operation. public static void Multiply(ref Vector3d vector, double scale, out Vector3d result) { result = new Vector3d(vector.X * scale, vector.Y * scale, vector.Z * scale); } /// /// Multiplies a vector by the components a vector (scale). /// /// Left operand. /// Right operand. /// Result of the operation. public static Vector3d Multiply(Vector3d vector, Vector3d scale) { Multiply(ref vector, ref scale, out vector); return vector; } /// /// Multiplies a vector by the components of a vector (scale). /// /// Left operand. /// Right operand. /// Result of the operation. public static void Multiply(ref Vector3d vector, ref Vector3d scale, out Vector3d result) { result = new Vector3d(vector.X * scale.X, vector.Y * scale.Y, vector.Z * scale.Z); } #endregion #region Divide /// /// Divides a vector by a scalar. /// /// Left operand. /// Right operand. /// Result of the operation. public static Vector3d Divide(Vector3d vector, double scale) { Divide(ref vector, scale, out vector); return vector; } /// /// Divides a vector by a scalar. /// /// Left operand. /// Right operand. /// Result of the operation. public static void Divide(ref Vector3d vector, double scale, out Vector3d result) { Multiply(ref vector, 1 / scale, out result); } /// /// Divides a vector by the components of a vector (scale). /// /// Left operand. /// Right operand. /// Result of the operation. public static Vector3d Divide(Vector3d vector, Vector3d scale) { Divide(ref vector, ref scale, out vector); return vector; } /// /// Divide a vector by the components of a vector (scale). /// /// Left operand. /// Right operand. /// Result of the operation. public static void Divide(ref Vector3d vector, ref Vector3d scale, out Vector3d result) { result = new Vector3d(vector.X / scale.X, vector.Y / scale.Y, vector.Z / scale.Z); } #endregion #region ComponentMin /// /// Calculate the component-wise minimum of two vectors /// /// First operand /// Second operand /// The component-wise minimum public static Vector3d ComponentMin(Vector3d a, Vector3d b) { a.X = a.X < b.X ? a.X : b.X; a.Y = a.Y < b.Y ? a.Y : b.Y; a.Z = a.Z < b.Z ? a.Z : b.Z; return a; } /// /// Calculate the component-wise minimum of two vectors /// /// First operand /// Second operand /// The component-wise minimum public static void ComponentMin(ref Vector3d a, ref Vector3d b, out Vector3d result) { result.X = a.X < b.X ? a.X : b.X; result.Y = a.Y < b.Y ? a.Y : b.Y; result.Z = a.Z < b.Z ? a.Z : b.Z; } #endregion #region ComponentMax /// /// Calculate the component-wise maximum of two vectors /// /// First operand /// Second operand /// The component-wise maximum public static Vector3d ComponentMax(Vector3d a, Vector3d b) { a.X = a.X > b.X ? a.X : b.X; a.Y = a.Y > b.Y ? a.Y : b.Y; a.Z = a.Z > b.Z ? a.Z : b.Z; return a; } /// /// Calculate the component-wise maximum of two vectors /// /// First operand /// Second operand /// The component-wise maximum public static void ComponentMax(ref Vector3d a, ref Vector3d b, out Vector3d result) { result.X = a.X > b.X ? a.X : b.X; result.Y = a.Y > b.Y ? a.Y : b.Y; result.Z = a.Z > b.Z ? a.Z : b.Z; } #endregion #region Min /// /// Returns the Vector3d with the minimum magnitude /// /// Left operand /// Right operand /// The minimum Vector3 public static Vector3d Min(Vector3d left, Vector3d right) { return left.LengthSquared < right.LengthSquared ? left : right; } #endregion #region Max /// /// Returns the Vector3d with the minimum magnitude /// /// Left operand /// Right operand /// The minimum Vector3 public static Vector3d Max(Vector3d left, Vector3d right) { return left.LengthSquared >= right.LengthSquared ? left : right; } #endregion #region Clamp /// /// Clamp a vector to the given minimum and maximum vectors /// /// Input vector /// Minimum vector /// Maximum vector /// The clamped vector public static Vector3d Clamp(Vector3d vec, Vector3d min, Vector3d max) { vec.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X; vec.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y; vec.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z; return vec; } /// /// Clamp a vector to the given minimum and maximum vectors /// /// Input vector /// Minimum vector /// Maximum vector /// The clamped vector public static void Clamp(ref Vector3d vec, ref Vector3d min, ref Vector3d max, out Vector3d result) { result.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X; result.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y; result.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z; } #endregion #region Normalize /// /// Scale a vector to unit length /// /// The input vector /// The normalized vector public static Vector3d Normalize(Vector3d vec) { double scale = 1.0f / vec.Length; vec.X *= scale; vec.Y *= scale; vec.Z *= scale; return vec; } /// /// Scale a vector to unit length /// /// The input vector /// The normalized vector public static void Normalize(ref Vector3d vec, out Vector3d result) { double scale = 1.0f / vec.Length; result.X = vec.X * scale; result.Y = vec.Y * scale; result.Z = vec.Z * scale; } #endregion #region NormalizeFast /// /// Scale a vector to approximately unit length /// /// The input vector /// The normalized vector public static Vector3d NormalizeFast(Vector3d vec) { double scale = MathHelper.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z); vec.X *= scale; vec.Y *= scale; vec.Z *= scale; return vec; } /// /// Scale a vector to approximately unit length /// /// The input vector /// The normalized vector public static void NormalizeFast(ref Vector3d vec, out Vector3d result) { double scale = MathHelper.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z); result.X = vec.X * scale; result.Y = vec.Y * scale; result.Z = vec.Z * scale; } #endregion #region Dot /// /// Calculate the dot (scalar) product of two vectors /// /// First operand /// Second operand /// The dot product of the two inputs public static double Dot(Vector3d left, Vector3d right) { return left.X * right.X + left.Y * right.Y + left.Z * right.Z; } /// /// Calculate the dot (scalar) product of two vectors /// /// First operand /// Second operand /// The dot product of the two inputs public static void Dot(ref Vector3d left, ref Vector3d right, out double result) { result = left.X * right.X + left.Y * right.Y + left.Z * right.Z; } #endregion #region Cross /// /// Caclulate the cross (vector) product of two vectors /// /// First operand /// Second operand /// The cross product of the two inputs public static Vector3d Cross(Vector3d left, Vector3d right) { return new Vector3d(left.Y * right.Z - left.Z * right.Y, left.Z * right.X - left.X * right.Z, left.X * right.Y - left.Y * right.X); } /// /// Caclulate the cross (vector) product of two vectors /// /// First operand /// Second operand /// The cross product of the two inputs /// The cross product of the two inputs public static void Cross(ref Vector3d left, ref Vector3d right, out Vector3d result) { result.X = left.Y * right.Z - left.Z * right.Y; result.Y = left.Z * right.X - left.X * right.Z; result.Z = left.X * right.Y - left.Y * right.X; } #endregion #region Lerp /// /// Returns a new Vector that is the linear blend of the 2 given Vectors /// /// First input vector /// Second input vector /// The blend factor. a when blend=0, b when blend=1. /// a when blend=0, b when blend=1, and a linear combination otherwise public static Vector3d Lerp(Vector3d a, Vector3d b, double blend) { a.X = blend * (b.X - a.X) + a.X; a.Y = blend * (b.Y - a.Y) + a.Y; a.Z = blend * (b.Z - a.Z) + a.Z; return a; } /// /// Returns a new Vector that is the linear blend of the 2 given Vectors /// /// First input vector /// Second input vector /// The blend factor. a when blend=0, b when blend=1. /// a when blend=0, b when blend=1, and a linear combination otherwise public static void Lerp(ref Vector3d a, ref Vector3d b, double blend, out Vector3d result) { result.X = blend * (b.X - a.X) + a.X; result.Y = blend * (b.Y - a.Y) + a.Y; result.Z = blend * (b.Z - a.Z) + a.Z; } #endregion #region Barycentric /// /// Interpolate 3 Vectors using Barycentric coordinates /// /// First input Vector /// Second input Vector /// Third input Vector /// First Barycentric Coordinate /// Second Barycentric Coordinate /// a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise public static Vector3d BaryCentric(Vector3d a, Vector3d b, Vector3d c, double u, double v) { return a + u * (b - a) + v * (c - a); } /// Interpolate 3 Vectors using Barycentric coordinates /// First input Vector. /// Second input Vector. /// Third input Vector. /// First Barycentric Coordinate. /// Second Barycentric Coordinate. /// Output Vector. a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise public static void BaryCentric(ref Vector3d a, ref Vector3d b, ref Vector3d c, double u, double v, out Vector3d result) { result = a; // copy Vector3d temp = b; // copy Subtract(ref temp, ref a, out temp); Multiply(ref temp, u, out temp); Add(ref result, ref temp, out result); temp = c; // copy Subtract(ref temp, ref a, out temp); Multiply(ref temp, v, out temp); Add(ref result, ref temp, out result); } #endregion #region Transform /// Transform a direction vector by the given Matrix /// Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored. /// /// The vector to transform /// The desired transformation /// The transformed vector public static Vector3d TransformVector(Vector3d vec, Matrix4d mat) { return new Vector3d( Vector3d.Dot(vec, new Vector3d(mat.Column0)), Vector3d.Dot(vec, new Vector3d(mat.Column1)), Vector3d.Dot(vec, new Vector3d(mat.Column2))); } /// Transform a direction vector by the given Matrix /// Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored. /// /// The vector to transform /// The desired transformation /// The transformed vector public static void TransformVector(ref Vector3d vec, ref Matrix4d mat, out Vector3d result) { result.X = vec.X * mat.Row0.X + vec.Y * mat.Row1.X + vec.Z * mat.Row2.X; result.Y = vec.X * mat.Row0.Y + vec.Y * mat.Row1.Y + vec.Z * mat.Row2.Y; result.Z = vec.X * mat.Row0.Z + vec.Y * mat.Row1.Z + vec.Z * mat.Row2.Z; } /// Transform a Normal by the given Matrix /// /// This calculates the inverse of the given matrix, use TransformNormalInverse if you /// already have the inverse to avoid this extra calculation /// /// The normal to transform /// The desired transformation /// The transformed normal public static Vector3d TransformNormal(Vector3d norm, Matrix4d mat) { mat.Invert(); return TransformNormalInverse(norm, mat); } /// Transform a Normal by the given Matrix /// /// This calculates the inverse of the given matrix, use TransformNormalInverse if you /// already have the inverse to avoid this extra calculation /// /// The normal to transform /// The desired transformation /// The transformed normal public static void TransformNormal(ref Vector3d norm, ref Matrix4d mat, out Vector3d result) { Matrix4d Inverse = Matrix4d.Invert(mat); Vector3d.TransformNormalInverse(ref norm, ref Inverse, out result); } /// Transform a Normal by the (transpose of the) given Matrix /// /// This version doesn't calculate the inverse matrix. /// Use this version if you already have the inverse of the desired transform to hand /// /// The normal to transform /// The inverse of the desired transformation /// The transformed normal public static Vector3d TransformNormalInverse(Vector3d norm, Matrix4d invMat) { return new Vector3d( Vector3d.Dot(norm, new Vector3d(invMat.Row0)), Vector3d.Dot(norm, new Vector3d(invMat.Row1)), Vector3d.Dot(norm, new Vector3d(invMat.Row2))); } /// Transform a Normal by the (transpose of the) given Matrix /// /// This version doesn't calculate the inverse matrix. /// Use this version if you already have the inverse of the desired transform to hand /// /// The normal to transform /// The inverse of the desired transformation /// The transformed normal public static void TransformNormalInverse(ref Vector3d norm, ref Matrix4d invMat, out Vector3d result) { result.X = norm.X * invMat.Row0.X + norm.Y * invMat.Row0.Y + norm.Z * invMat.Row0.Z; result.Y = norm.X * invMat.Row1.X + norm.Y * invMat.Row1.Y + norm.Z * invMat.Row1.Z; result.Z = norm.X * invMat.Row2.X + norm.Y * invMat.Row2.Y + norm.Z * invMat.Row2.Z; } /// Transform a Position by the given Matrix /// The position to transform /// The desired transformation /// The transformed position public static Vector3d TransformPosition(Vector3d pos, Matrix4d mat) { return new Vector3d( Vector3d.Dot(pos, new Vector3d(mat.Column0)) + mat.Row3.X, Vector3d.Dot(pos, new Vector3d(mat.Column1)) + mat.Row3.Y, Vector3d.Dot(pos, new Vector3d(mat.Column2)) + mat.Row3.Z); } /// Transform a Position by the given Matrix /// The position to transform /// The desired transformation /// The transformed position public static void TransformPosition(ref Vector3d pos, ref Matrix4d mat, out Vector3d result) { result.X = pos.X * mat.Row0.X + pos.Y * mat.Row1.X + pos.Z * mat.Row2.X + mat.Row3.X; result.Y = pos.X * mat.Row0.Y + pos.Y * mat.Row1.Y + pos.Z * mat.Row2.Y + mat.Row3.Y; result.Z = pos.X * mat.Row0.Z + pos.Y * mat.Row1.Z + pos.Z * mat.Row2.Z + mat.Row3.Z; } /// Transform a Vector by the given Matrix /// The vector to transform /// The desired transformation /// The transformed vector public static Vector3d Transform(Vector3d vec, Matrix4d mat) { Vector3d result; Transform(ref vec, ref mat, out result); return result; } /// Transform a Vector by the given Matrix /// The vector to transform /// The desired transformation /// The transformed vector public static void Transform(ref Vector3d vec, ref Matrix4d mat, out Vector3d result) { Vector4d v4 = new Vector4d(vec.X, vec.Y, vec.Z, 1.0f); Vector4d.Transform(ref v4, ref mat, out v4); result = v4.Xyz; } /// /// Transform a Vector3d by the given Matrix, and project the resulting Vector4 back to a Vector3 /// /// The vector to transform /// The desired transformation /// The transformed vector public static Vector3d TransformPerspective(Vector3d vec, Matrix4d mat) { Vector3d result; TransformPerspective(ref vec, ref mat, out result); return result; } /// Transform a Vector3d by the given Matrix, and project the resulting Vector4d back to a Vector3d /// The vector to transform /// The desired transformation /// The transformed vector public static void TransformPerspective(ref Vector3d vec, ref Matrix4d mat, out Vector3d result) { Vector4d v = new Vector4d(vec); Vector4d.Transform(ref v, ref mat, out v); result.X = v.X / v.W; result.Y = v.Y / v.W; result.Z = v.Z / v.W; } #endregion #region CalculateAngle /// /// Calculates the angle (in radians) between two vectors. /// /// The first vector. /// The second vector. /// Angle (in radians) between the vectors. /// Note that the returned angle is never bigger than the constant Pi. public static double CalculateAngle(Vector3d first, Vector3d second) { return System.Math.Acos((Vector3d.Dot(first, second)) / (first.Length * second.Length)); } /// Calculates the angle (in radians) between two vectors. /// The first vector. /// The second vector. /// Angle (in radians) between the vectors. /// Note that the returned angle is never bigger than the constant Pi. public static void CalculateAngle(ref Vector3d first, ref Vector3d second, out double result) { double temp; Vector3d.Dot(ref first, ref second, out temp); result = System.Math.Acos(temp / (first.Length * second.Length)); } #endregion #endregion #region Swizzle /// /// Gets or sets an OpenTK.Vector2d with the X and Y components of this instance. /// [XmlIgnore] public Vector2d Xy { get { return new Vector2d(X, Y); } set { X = value.X; Y = value.Y; } } #endregion #region Operators /// /// Adds two instances. /// /// The first instance. /// The second instance. /// The result of the calculation. public static Vector3d operator +(Vector3d left, Vector3d right) { left.X += right.X; left.Y += right.Y; left.Z += right.Z; return left; } /// /// Subtracts two instances. /// /// The first instance. /// The second instance. /// The result of the calculation. public static Vector3d operator -(Vector3d left, Vector3d right) { left.X -= right.X; left.Y -= right.Y; left.Z -= right.Z; return left; } /// /// Negates an instance. /// /// The instance. /// The result of the calculation. public static Vector3d operator -(Vector3d vec) { vec.X = -vec.X; vec.Y = -vec.Y; vec.Z = -vec.Z; return vec; } /// /// Multiplies an instance by a scalar. /// /// The instance. /// The scalar. /// The result of the calculation. public static Vector3d operator *(Vector3d vec, double scale) { vec.X *= scale; vec.Y *= scale; vec.Z *= scale; return vec; } /// /// Multiplies an instance by a scalar. /// /// The scalar. /// The instance. /// The result of the calculation. public static Vector3d operator *(double scale, Vector3d vec) { vec.X *= scale; vec.Y *= scale; vec.Z *= scale; return vec; } /// /// Divides an instance by a scalar. /// /// The instance. /// The scalar. /// The result of the calculation. public static Vector3d operator /(Vector3d vec, double scale) { double mult = 1 / scale; vec.X *= mult; vec.Y *= mult; vec.Z *= mult; return vec; } /// /// Compares two instances for equality. /// /// The first instance. /// The second instance. /// True, if left equals right; false otherwise. public static bool operator ==(Vector3d left, Vector3d right) { return left.Equals(right); } /// /// Compares two instances for inequality. /// /// The first instance. /// The second instance. /// True, if left does not equa lright; false otherwise. public static bool operator !=(Vector3d left, Vector3d right) { return !left.Equals(right); } /// Converts OpenTK.Vector3 to OpenTK.Vector3d. /// The Vector3 to convert. /// The resulting Vector3d. public static explicit operator Vector3d(Vector3 v3) { return new Vector3d(v3.X, v3.Y, v3.Z); } /// Converts OpenTK.Vector3d to OpenTK.Vector3. /// The Vector3d to convert. /// The resulting Vector3. public static explicit operator Vector3(Vector3d v3d) { return new Vector3((float)v3d.X, (float)v3d.Y, (float)v3d.Z); } #endregion #region Overrides #region public override string ToString() /// /// Returns a System.String that represents the current Vector3. /// /// public override string ToString() { return String.Format("({0}, {1}, {2})", X, Y, Z); } #endregion #region public override int GetHashCode() /// /// Returns the hashcode for this instance. /// /// A System.Int32 containing the unique hashcode for this instance. public override int GetHashCode() { return X.GetHashCode() ^ Y.GetHashCode() ^ Z.GetHashCode(); } #endregion #region public override bool Equals(object obj) /// /// Indicates whether this instance and a specified object are equal. /// /// The object to compare to. /// True if the instances are equal; false otherwise. public override bool Equals(object obj) { if (!(obj is Vector3)) return false; return this.Equals((Vector3)obj); } #endregion #endregion #endregion #region IEquatable Members /// Indicates whether the current vector is equal to another vector. /// A vector to compare with this vector. /// true if the current vector is equal to the vector parameter; otherwise, false. public bool Equals(Vector3d other) { return X == other.X && Y == other.Y && Z == other.Z; } #endregion } }