#region --- License --- /* Copyright (c) 2006, 2007 Stefanos Apostolopoulos * See license.txt for license info * * Contributions by Andy Gill. */ #endregion using System; using System.Collections.Generic; using System.Text; using System.Runtime.InteropServices; namespace OpenTK.Math { /// <summary> /// Represents a three-dimensional vector. /// </summary> [StructLayout(LayoutKind.Sequential)] public struct Vector3 { #region Fields /// <summary> /// The X component of the Vector3. /// </summary> public float X; /// <summary> /// The Y component of the Vector3. /// </summary> public float Y; /// <summary> /// The Z component of the Vector3. /// </summary> public float Z; public static readonly Vector3 UnitX = new Vector3(1, 0, 0); public static readonly Vector3 UnitY = new Vector3(0, 1, 0); public static readonly Vector3 UnitZ = new Vector3(0, 0, 1); public static readonly Vector3 Zero = new Vector3(0, 0, 0); public static readonly int SizeInBytes = Marshal.SizeOf(new Vector3()); #endregion #region Constructors /// <summary> /// Constructs a new Vector3. /// </summary> /// <param name="x">The x component of the Vector3.</param> /// <param name="y">The y component of the Vector3.</param> /// <param name="z">The z component of the Vector3.</param> public Vector3(float x, float y, float z) { X = x; Y = y; Z = z; } /// <summary> /// Constructs a new Vector3 from the given Vector2. /// </summary> /// <param name="v">The Vector2 to copy components from.</param> public Vector3(Vector2 v) { X = v.X; Y = v.Y; Z = 0.0f; } /// <summary> /// Constructs a new Vector3 from the given Vector3. /// </summary> /// <param name="v">The Vector3 to copy components from.</param> public Vector3(Vector3 v) { X = v.X; Y = v.Y; Z = v.Z; } /// <summary> /// Constructs a new Vector3 from the given Vector4. /// </summary> /// <param name="v">The Vector4 to copy components from.</param> public Vector3(Vector4 v) { X = v.X; Y = v.Y; Z = v.Z; } #endregion #region Functions #region public float Length /// <summary> /// Gets the length (magnitude) of the vector. /// </summary> /// <see cref="FastLength"/> /// <seealso cref="LengthSquared"/> public float Length { get { return (float)System.Math.Sqrt(X * X + Y * Y + Z * Z); } } #endregion #region public float LengthFast /// <summary> /// Gets an approximation of the vector length (magnitude). /// </summary> /// <remarks> /// This property uses an approximation of the square root function to calculate vector magnitude, with /// an upper error bound of 0.001. /// </remarks> /// <see cref="Length"/> /// <seealso cref="LengthSquared"/> /// <seealso cref="OpenTK.Math.FastSqrt"/> public float LengthFast { get { return 1.0f / OpenTK.Math.Functions.InverseSqrtFast(X * X + Y * Y + Z * Z); } } #endregion #region public float LengthSquared /// <summary> /// Gets the square of the vector length (magnitude). /// </summary> /// <remarks> /// This property avoids the costly square root operation required by the Length property. This makes it more suitable /// for comparisons. /// </remarks> /// <see cref="Length"/> /// <seealso cref="FastLength"/> public float LengthSquared { get { return X * X + Y * Y + Z * Z; } } #endregion #region public Vector3 Normalize() /// <summary> /// Scales the Vector3 to unit length. /// </summary> public void Normalize() { float scale = 1.0f / this.Length; X *= scale; Y *= scale; Z *= scale; } #endregion #region public Vector3 NormalizeFast() /// <summary> /// Scales the Vector3 to approximately unit length. /// </summary> public void NormalizeFast() { float scale = Functions.InverseSqrtFast(X * X + Y * Y + Z * Z); X *= scale; Y *= scale; Z *= scale; } #endregion #region public Vector3 Scale(float sx, float sy, float sz) /// <summary> /// Scales the current Vector3 by the given amounts. /// </summary> /// <param name="sx">The scale of the X component.</param> /// <param name="sy">The scale of the Y component.</param> /// <param name="sz">The scale of the Z component.</param> public void Scale(float sx, float sy, float sz) { this.X = X * sx; this.Y = Y * sy; this.Z = Z * sz; } #endregion #endregion #region Operator overloads public static Vector3 operator +(Vector3 left, Vector3 right) { left.X += right.X; left.Y += right.Y; left.Z += right.Z; return left; } public static Vector3 operator -(Vector3 left, Vector3 right) { left.X -= right.X; left.Y -= right.Y; left.Z -= right.Z; return left; } public static Vector3 operator -(Vector3 vec) { vec.X = -vec.X; vec.Y = -vec.Y; vec.Z = -vec.Z; return vec; } public static Vector3 operator *(Vector3 vec, float f) { vec.X *= f; vec.Y *= f; vec.Z *= f; return vec; } public static Vector3 operator *(float f, Vector3 vec) { vec.X *= f; vec.Y *= f; vec.Z *= f; return vec; } public static Vector3 operator /(Vector3 vec, float f) { float mult = 1.0f / f; vec.X *= mult; vec.Y *= mult; vec.Z *= mult; return vec; } public float get(int index) { switch (index) { case 0: return X; case 1: return Y; case 2: return Z; default: throw new ArgumentOutOfRangeException("index", index, "Should be 0, 1 or 2."); } /* unsafe { fixed (float* ptr = &this.X) return *(ptr + index); } */ } #endregion #region Static functions #region Add /// <summary> /// Add two Vectors /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <returns>Result of addition</returns> public static Vector3 Add(Vector3 a, Vector3 b) { a.X += b.X; a.Y += b.Y; a.Z += b.Z; return a; } /// <summary> /// Add two Vectors /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <param name="result">Result of addition</param> public static void Add(ref Vector3 a, ref Vector3 b, out Vector3 result) { result.X = a.X + b.X; result.Y = a.Y + b.Y; result.Z = a.Z + b.Z; } #endregion #region Sub /// <summary> /// Subtract one Vector from another /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <returns>Result of subtraction</returns> public static Vector3 Sub(Vector3 a, Vector3 b) { a.X -= b.X; a.Y -= b.Y; a.Z -= b.Z; return a; } /// <summary> /// Subtract one Vector from another /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <param name="result">Result of subtraction</param> public static void Sub(ref Vector3 a, ref Vector3 b, out Vector3 result) { result.X = a.X - b.X; result.Y = a.Y - b.Y; result.Z = a.Z - b.Z; } #endregion #region Mult /// <summary> /// Multiply a vector and a scalar /// </summary> /// <param name="a">Vector operand</param> /// <param name="f">Scalar operand</param> /// <returns>Result of the multiplication</returns> public static Vector3 Mult(Vector3 a, float f) { a.X *= f; a.Y *= f; a.Z *= f; return a; } /// <summary> /// Multiply a vector and a scalar /// </summary> /// <param name="a">Vector operand</param> /// <param name="f">Scalar operand</param> /// <param name="result">Result of the multiplication</param> public static void Mult(ref Vector3 a, float f, out Vector3 result) { result.X = a.X * f; result.Y = a.Y * f; result.Z = a.Z * f; } #endregion #region Div /// <summary> /// Divide a vector by a scalar /// </summary> /// <param name="a">Vector operand</param> /// <param name="f">Scalar operand</param> /// <returns>Result of the division</returns> public static Vector3 Div(Vector3 a, float f) { float mult = 1.0f / f; a.X *= mult; a.Y *= mult; a.Z *= mult; return a; } /// <summary> /// Divide a vector by a scalar /// </summary> /// <param name="a">Vector operand</param> /// <param name="f">Scalar operand</param> /// <param name="result">Result of the division</param> public static void Div(ref Vector3 a, float f, out Vector3 result) { float mult = 1.0f / f; result.X = a.X * mult; result.Y = a.Y * mult; result.Z = a.Z * mult; } #endregion #region ComponentMin /// <summary> /// Calculate the component-wise minimum of two vectors /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <returns>The component-wise minimum</returns> public static Vector3 ComponentMin(Vector3 a, Vector3 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; } /// <summary> /// Calculate the component-wise minimum of two vectors /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <param name="result">The component-wise minimum</param> public static void ComponentMin(ref Vector3 a, ref Vector3 b, out Vector3 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 /// <summary> /// Calculate the component-wise maximum of two vectors /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <returns>The component-wise maximum</returns> public static Vector3 ComponentMax(Vector3 a, Vector3 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; } /// <summary> /// Calculate the component-wise maximum of two vectors /// </summary> /// <param name="a">First operand</param> /// <param name="b">Second operand</param> /// <param name="result">The component-wise maximum</param> public static void ComponentMax(ref Vector3 a, ref Vector3 b, out Vector3 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 /// <summary> /// Returns the Vector3 with the minimum magnitude /// </summary> /// <param name="left">Left operand</param> /// <param name="right">Right operand</param> /// <returns>The minimum Vector3</returns> public static Vector3 Min(Vector3 left, Vector3 right) { return left.LengthSquared < right.LengthSquared ? left : right; } #endregion #region Max /// <summary> /// Returns the Vector3 with the minimum magnitude /// </summary> /// <param name="left">Left operand</param> /// <param name="right">Right operand</param> /// <returns>The minimum Vector3</returns> public static Vector3 Max(Vector3 left, Vector3 right) { return left.LengthSquared >= right.LengthSquared ? left : right; } #endregion #region Clamp /// <summary> /// Clamp a vector to the given minimum and maximum vectors /// </summary> /// <param name="vec">Input vector</param> /// <param name="min">Minimum vector</param> /// <param name="max">Maximum vector</param> /// <returns>The clamped vector</returns> public static Vector3 Clamp(Vector3 vec, Vector3 min, Vector3 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; } /// <summary> /// Clamp a vector to the given minimum and maximum vectors /// </summary> /// <param name="vec">Input vector</param> /// <param name="min">Minimum vector</param> /// <param name="max">Maximum vector</param> /// <param name="result">The clamped vector</param> public static void Clamp(ref Vector3 vec, ref Vector3 min, ref Vector3 max, out Vector3 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 /// <summary> /// Scale a vector to unit length /// </summary> /// <param name="vec">The input vector</param> /// <returns>The normalized vector</returns> public static Vector3 Normalize(Vector3 vec) { float scale = 1.0f / vec.Length; vec.X *= scale; vec.Y *= scale; vec.Z *= scale; return vec; } /// <summary> /// Scale a vector to unit length /// </summary> /// <param name="vec">The input vector</param> /// <param name="result">The normalized vector</param> public static void Normalize(ref Vector3 vec, out Vector3 result) { float scale = 1.0f / vec.Length; result.X = vec.X * scale; result.Y = vec.Y * scale; result.Z = vec.Z * scale; } #endregion #region NormalizeFast /// <summary> /// Scale a vector to approximately unit length /// </summary> /// <param name="vec">The input vector</param> /// <returns>The normalized vector</returns> public static Vector3 NormalizeFast(Vector3 vec) { float scale = Functions.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z); vec.X *= scale; vec.Y *= scale; vec.Z *= scale; return vec; } /// <summary> /// Scale a vector to approximately unit length /// </summary> /// <param name="vec">The input vector</param> /// <param name="result">The normalized vector</param> public static void NormalizeFast(ref Vector3 vec, out Vector3 result) { float scale = Functions.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 /// <summary> /// Caclulate the dot (scalar) product of two vectors /// </summary> /// <param name="left">First operand</param> /// <param name="right">Second operand</param> /// <returns>The dot product of the two inputs</returns> public static float Dot(Vector3 left, Vector3 right) { return left.X * right.X + left.Y * right.Y + left.Z * right.Z; } #endregion #region Cross /// <summary> /// Caclulate the cross (vector) product of two vectors /// </summary> /// <param name="left">First operand</param> /// <param name="right">Second operand</param> /// <returns>The cross product of the two inputs</returns> public static Vector3 Cross(Vector3 left, Vector3 right) { float x = left.Y * right.Z - left.Z * right.Y, y = left.Z * right.X - left.X * right.Z, z = left.X * right.Y - left.Y * right.X; left.X = x; left.Y = y; left.Z = z; return left; } /// <summary> /// Caclulate the cross (vector) product of two vectors /// </summary> /// <param name="left">First operand</param> /// <param name="right">Second operand</param> /// <returns>The cross product of the two inputs</returns> /// <param name="result">The cross product of the two inputs</param> public static void Cross(ref Vector3 left, ref Vector3 right, out Vector3 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 /// <summary> /// Returns a new Vector that is the linear blend of the 2 given Vectors /// </summary> /// <param name="a">First input vector</param> /// <param name="b">Second input vector</param> /// <param name="blend">The blend factor</param> /// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns> public static Vector3 Lerp(Vector3 a, Vector3 b, float 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; } #endregion #region Barycentric /// <summary> /// Interpolate 3 Vectors using Barycentric coordinates /// </summary> /// <param name="a">First input Vector</param> /// <param name="b">Second input Vector</param> /// <param name="c">Third input Vector</param> /// <param name="u">First Barycentric Coordinate</param> /// <param name="v">Second Barycentric Coordinate</param> /// <returns>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</returns> public static Vector3 BaryCentric(Vector3 a, Vector3 b, Vector3 c, float u, float v) { return a + u * (b - a) + v * (c - a); } #endregion #region Transform /// <summary> /// 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. /// </summary> /// <param name="vec">The vector to transform</param> /// <param name="mat">The desired transformation</param> /// <returns>The transformed vector</returns> public static Vector3 TransformVector(Vector3 vec, Matrix4 mat) { Vector3 v; v.X = Vector3.Dot(vec, new Vector3(mat.Column0)); v.Y = Vector3.Dot(vec, new Vector3(mat.Column1)); v.Z = Vector3.Dot(vec, new Vector3(mat.Column2)); return v; } /// <summary> /// Transform a Normal by the given Matrix /// </summary> /// <remarks> /// This calculates the inverse of the given matrix, use TransformNormalInverse if you /// already have the inverse to avoid this extra calculation /// </remarks> /// <param name="norm">The normal to transform</param> /// <param name="mat">The desired transformation</param> /// <returns>The transformed normal</returns> public static Vector3 TransformNormal(Vector3 norm, Matrix4 mat) { mat.Invert(); return TransformNormalInverse(norm, mat); } /// <summary> /// Transform a Normal by the (transpose of the) given Matrix /// </summary> /// <remarks> /// This version doesn't calculate the inverse matrix. /// Use this version if you already have the inverse of the desired transform to hand /// </remarks> /// <param name="norm">The normal to transform</param> /// <param name="mat">The inverse of the desired transformation</param> /// <returns>The transformed normal</returns> public static Vector3 TransformNormalInverse(Vector3 norm, Matrix4 invMat) { Vector3 n; n.X = Vector3.Dot(norm, new Vector3(invMat.Row0)); n.Y = Vector3.Dot(norm, new Vector3(invMat.Row1)); n.Z = Vector3.Dot(norm, new Vector3(invMat.Row2)); return n; } /// <summary> /// Transform a Position by the given Matrix /// </summary> /// <param name="pos">The position to transform</param> /// <param name="mat">The desired transformation</param> /// <returns>The transformed position</returns> public static Vector3 TransformPosition(Vector3 pos, Matrix4 mat) { Vector3 p; p.X = Vector3.Dot(pos, new Vector3(mat.Column0)) + mat.Row3.X; p.Y = Vector3.Dot(pos, new Vector3(mat.Column1)) + mat.Row3.Y; p.Z = Vector3.Dot(pos, new Vector3(mat.Column2)) + mat.Row3.Z; return p; } /// <summary> /// Transform a Vector by the given Matrix /// </summary> /// <param name="pos">The vector to transform</param> /// <param name="mat">The desired transformation</param> /// <returns>The transformed vector</returns> public static Vector4 Transform(Vector3 vec, Matrix4 mat) { Vector4 v4 = new Vector4(vec.X, vec.Y, vec.Z, 1.0f); Vector4 result; result.X = Vector4.Dot(v4, mat.Column0); result.Y = Vector4.Dot(v4, mat.Column1); result.Z = Vector4.Dot(v4, mat.Column2); result.W = Vector4.Dot(v4, mat.Column3); return result; } /// <summary> /// Transform a Vector3 by the given Matrix, and project the resulting Vector4 back to a Vector3 /// </summary> /// <param name="pos">The vector to transform</param> /// <param name="mat">The desired transformation</param> /// <returns>The transformed vector</returns> public static Vector3 TransformPerspective(Vector3 vec, Matrix4 mat) { Vector4 h = Transform(vec, mat); return new Vector3(h.X / h.W, h.Y / h.W, h.Z / h.W); } #endregion #endregion #region public override string ToString() /// <summary> /// Returns a System.String that represents the current Vector3. /// </summary> /// <returns></returns> public override string ToString() { return String.Format("({0}, {1}, {2})", X, Y, Z); } #endregion } }