814 lines
23 KiB
C#
814 lines
23 KiB
C#
#region --- License ---
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/* Copyright (c) 2006, 2007 Stefanos Apostolopoulos
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* See license.txt for license info
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*
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* Contributions by Andy Gill.
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*/
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#endregion
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using System;
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using System.Collections.Generic;
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using System.Text;
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using System.Runtime.InteropServices;
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namespace OpenTK.Math
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{
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/// <summary>
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/// Represents a three-dimensional vector.
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/// </summary>
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[StructLayout(LayoutKind.Sequential)]
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public struct Vector3
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{
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#region Fields
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/// <summary>
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/// The X component of the Vector3.
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/// </summary>
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public float X;
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/// <summary>
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/// The Y component of the Vector3.
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/// </summary>
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public float Y;
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/// <summary>
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/// The Z component of the Vector3.
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/// </summary>
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public float Z;
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public static readonly Vector3 UnitX = new Vector3(1, 0, 0);
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public static readonly Vector3 UnitY = new Vector3(0, 1, 0);
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public static readonly Vector3 UnitZ = new Vector3(0, 0, 1);
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public static readonly Vector3 Zero = new Vector3(0, 0, 0);
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public static readonly int SizeInBytes = Marshal.SizeOf(new Vector3());
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#endregion
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#region Constructors
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/// <summary>
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/// Constructs a new Vector3.
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/// </summary>
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/// <param name="x">The x component of the Vector3.</param>
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/// <param name="y">The y component of the Vector3.</param>
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/// <param name="z">The z component of the Vector3.</param>
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public Vector3(float x, float y, float z)
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{
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X = x;
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Y = y;
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Z = z;
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}
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/// <summary>
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/// Constructs a new Vector3 from the given Vector2.
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/// </summary>
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/// <param name="v">The Vector2 to copy components from.</param>
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public Vector3(Vector2 v)
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{
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X = v.X;
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Y = v.Y;
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Z = 0.0f;
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}
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/// <summary>
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/// Constructs a new Vector3 from the given Vector3.
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/// </summary>
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/// <param name="v">The Vector3 to copy components from.</param>
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public Vector3(Vector3 v)
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{
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X = v.X;
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Y = v.Y;
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Z = v.Z;
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}
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/// <summary>
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/// Constructs a new Vector3 from the given Vector4.
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/// </summary>
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/// <param name="v">The Vector4 to copy components from.</param>
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public Vector3(Vector4 v)
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{
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X = v.X;
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Y = v.Y;
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Z = v.Z;
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}
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#endregion
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#region Functions
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#region public float Length
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/// <summary>
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/// Gets the length (magnitude) of the vector.
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/// </summary>
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/// <see cref="FastLength"/>
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/// <seealso cref="LengthSquared"/>
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public float Length
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{
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get
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{
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return (float)System.Math.Sqrt(X * X + Y * Y + Z * Z);
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}
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}
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#endregion
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#region public float LengthFast
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/// <summary>
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/// Gets an approximation of the vector length (magnitude).
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/// </summary>
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/// <remarks>
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/// This property uses an approximation of the square root function to calculate vector magnitude, with
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/// an upper error bound of 0.001.
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/// </remarks>
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/// <see cref="Length"/>
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/// <seealso cref="LengthSquared"/>
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/// <seealso cref="OpenTK.Math.FastSqrt"/>
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public float LengthFast
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{
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get
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{
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return 1.0f / OpenTK.Math.Functions.InverseSqrtFast(X * X + Y * Y + Z * Z);
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}
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}
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#endregion
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#region public float LengthSquared
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/// <summary>
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/// Gets the square of the vector length (magnitude).
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/// </summary>
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/// <remarks>
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/// This property avoids the costly square root operation required by the Length property. This makes it more suitable
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/// for comparisons.
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/// </remarks>
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/// <see cref="Length"/>
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/// <seealso cref="FastLength"/>
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public float LengthSquared
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{
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get
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{
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return X * X + Y * Y + Z * Z;
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}
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}
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#endregion
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#region public void Normalize()
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/// <summary>
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/// Scales the Vector3 to unit length.
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/// </summary>
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public void Normalize()
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{
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float scale = 1.0f / this.Length;
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X *= scale;
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Y *= scale;
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Z *= scale;
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}
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#endregion
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#region public void NormalizeFast()
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/// <summary>
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/// Scales the Vector3 to approximately unit length.
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/// </summary>
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public void NormalizeFast()
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{
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float scale = Functions.InverseSqrtFast(X * X + Y * Y + Z * Z);
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X *= scale;
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Y *= scale;
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Z *= scale;
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}
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#endregion
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#region public void Scale(float sx, float sy, float sz)
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/// <summary>
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/// Scales the current Vector3 by the given amounts.
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/// </summary>
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/// <param name="sx">The scale of the X component.</param>
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/// <param name="sy">The scale of the Y component.</param>
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/// <param name="sz">The scale of the Z component.</param>
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public void Scale(float sx, float sy, float sz)
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{
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this.X = X * sx;
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this.Y = Y * sy;
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this.Z = Z * sz;
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}
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#endregion
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#endregion
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#region Operator overloads
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public static Vector3 operator +(Vector3 left, Vector3 right)
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{
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left.X += right.X;
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left.Y += right.Y;
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left.Z += right.Z;
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return left;
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}
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public static Vector3 operator -(Vector3 left, Vector3 right)
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{
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left.X -= right.X;
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left.Y -= right.Y;
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left.Z -= right.Z;
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return left;
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}
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public static Vector3 operator -(Vector3 vec)
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{
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vec.X = -vec.X;
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vec.Y = -vec.Y;
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vec.Z = -vec.Z;
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return vec;
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}
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public static Vector3 operator *(Vector3 vec, float f)
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{
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vec.X *= f;
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vec.Y *= f;
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vec.Z *= f;
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return vec;
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}
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public static Vector3 operator *(float f, Vector3 vec)
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{
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vec.X *= f;
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vec.Y *= f;
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vec.Z *= f;
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return vec;
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}
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public static Vector3 operator /(Vector3 vec, float f)
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{
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float mult = 1.0f / f;
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vec.X *= mult;
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vec.Y *= mult;
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vec.Z *= mult;
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return vec;
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}
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public float get(int index)
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{
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switch (index)
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{
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case 0: return X;
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case 1: return Y;
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case 2: return Z;
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default: throw new ArgumentOutOfRangeException("index", index, "Should be 0, 1 or 2.");
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}
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/*
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unsafe
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{
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fixed (float* ptr = &this.X)
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return *(ptr + index);
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}
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*/
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}
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#endregion
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#region Static functions
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#region Add
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/// <summary>
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/// Add two Vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>Result of addition</returns>
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public static Vector3 Add(Vector3 a, Vector3 b)
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{
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a.X += b.X;
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a.Y += b.Y;
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a.Z += b.Z;
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return a;
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}
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/// <summary>
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/// Add two Vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">Result of addition</param>
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public static void Add(ref Vector3 a, ref Vector3 b, out Vector3 result)
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{
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result.X = a.X + b.X;
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result.Y = a.Y + b.Y;
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result.Z = a.Z + b.Z;
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}
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#endregion
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#region Sub
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/// <summary>
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/// Subtract one Vector from another
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>Result of subtraction</returns>
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public static Vector3 Sub(Vector3 a, Vector3 b)
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{
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a.X -= b.X;
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a.Y -= b.Y;
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a.Z -= b.Z;
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return a;
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}
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/// <summary>
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/// Subtract one Vector from another
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">Result of subtraction</param>
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public static void Sub(ref Vector3 a, ref Vector3 b, out Vector3 result)
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{
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result.X = a.X - b.X;
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result.Y = a.Y - b.Y;
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result.Z = a.Z - b.Z;
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}
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#endregion
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#region Mult
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/// <summary>
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/// Multiply a vector and a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <returns>Result of the multiplication</returns>
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public static Vector3 Mult(Vector3 a, float f)
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{
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a.X *= f;
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a.Y *= f;
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a.Z *= f;
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return a;
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}
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/// <summary>
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/// Multiply a vector and a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <param name="result">Result of the multiplication</param>
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public static void Mult(ref Vector3 a, float f, out Vector3 result)
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{
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result.X = a.X * f;
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result.Y = a.Y * f;
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result.Z = a.Z * f;
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}
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#endregion
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#region Div
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/// <summary>
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/// Divide a vector by a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <returns>Result of the division</returns>
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public static Vector3 Div(Vector3 a, float f)
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{
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float mult = 1.0f / f;
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a.X *= mult;
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a.Y *= mult;
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a.Z *= mult;
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return a;
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}
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/// <summary>
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/// Divide a vector by a scalar
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/// </summary>
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/// <param name="a">Vector operand</param>
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/// <param name="f">Scalar operand</param>
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/// <param name="result">Result of the division</param>
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public static void Div(ref Vector3 a, float f, out Vector3 result)
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{
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float mult = 1.0f / f;
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result.X = a.X * mult;
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result.Y = a.Y * mult;
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result.Z = a.Z * mult;
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}
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#endregion
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#region ComponentMin
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/// <summary>
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/// Calculate the component-wise minimum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>The component-wise minimum</returns>
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public static Vector3 ComponentMin(Vector3 a, Vector3 b)
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{
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a.X = a.X < b.X ? a.X : b.X;
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a.Y = a.Y < b.Y ? a.Y : b.Y;
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a.Z = a.Z < b.Z ? a.Z : b.Z;
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return a;
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}
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/// <summary>
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/// Calculate the component-wise minimum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">The component-wise minimum</param>
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public static void ComponentMin(ref Vector3 a, ref Vector3 b, out Vector3 result)
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{
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result.X = a.X < b.X ? a.X : b.X;
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result.Y = a.Y < b.Y ? a.Y : b.Y;
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result.Z = a.Z < b.Z ? a.Z : b.Z;
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}
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#endregion
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#region ComponentMax
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/// <summary>
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/// Calculate the component-wise maximum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <returns>The component-wise maximum</returns>
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public static Vector3 ComponentMax(Vector3 a, Vector3 b)
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{
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a.X = a.X > b.X ? a.X : b.X;
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a.Y = a.Y > b.Y ? a.Y : b.Y;
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a.Z = a.Z > b.Z ? a.Z : b.Z;
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return a;
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}
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/// <summary>
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/// Calculate the component-wise maximum of two vectors
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/// </summary>
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/// <param name="a">First operand</param>
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/// <param name="b">Second operand</param>
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/// <param name="result">The component-wise maximum</param>
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public static void ComponentMax(ref Vector3 a, ref Vector3 b, out Vector3 result)
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{
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result.X = a.X > b.X ? a.X : b.X;
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result.Y = a.Y > b.Y ? a.Y : b.Y;
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result.Z = a.Z > b.Z ? a.Z : b.Z;
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}
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#endregion
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#region Min
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/// <summary>
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/// Returns the Vector3 with the minimum magnitude
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/// </summary>
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/// <param name="left">Left operand</param>
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/// <param name="right">Right operand</param>
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/// <returns>The minimum Vector3</returns>
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public static Vector3 Min(Vector3 left, Vector3 right)
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{
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return left.LengthSquared < right.LengthSquared ? left : right;
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}
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#endregion
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#region Max
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/// <summary>
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/// Returns the Vector3 with the minimum magnitude
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/// </summary>
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/// <param name="left">Left operand</param>
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/// <param name="right">Right operand</param>
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/// <returns>The minimum Vector3</returns>
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public static Vector3 Max(Vector3 left, Vector3 right)
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{
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return left.LengthSquared >= right.LengthSquared ? left : right;
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}
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#endregion
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#region Clamp
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/// <summary>
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/// Clamp a vector to the given minimum and maximum vectors
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/// </summary>
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/// <param name="vec">Input vector</param>
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/// <param name="min">Minimum vector</param>
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/// <param name="max">Maximum vector</param>
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/// <returns>The clamped vector</returns>
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public static Vector3 Clamp(Vector3 vec, Vector3 min, Vector3 max)
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{
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vec.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
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vec.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
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vec.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
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return vec;
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}
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/// <summary>
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/// Clamp a vector to the given minimum and maximum vectors
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/// </summary>
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/// <param name="vec">Input vector</param>
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/// <param name="min">Minimum vector</param>
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/// <param name="max">Maximum vector</param>
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/// <param name="result">The clamped vector</param>
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public static void Clamp(ref Vector3 vec, ref Vector3 min, ref Vector3 max, out Vector3 result)
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{
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result.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
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result.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
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result.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
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}
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#endregion
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#region Normalize
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/// <summary>
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/// Scale a vector to unit length
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/// </summary>
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/// <param name="vec">The input vector</param>
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/// <returns>The normalized vector</returns>
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public static Vector3 Normalize(Vector3 vec)
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{
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float scale = 1.0f / vec.Length;
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vec.X *= scale;
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vec.Y *= scale;
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vec.Z *= scale;
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return vec;
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}
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/// <summary>
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/// Scale a vector to unit length
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/// </summary>
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/// <param name="vec">The input vector</param>
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/// <param name="result">The normalized vector</param>
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public static void Normalize(ref Vector3 vec, out Vector3 result)
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{
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float scale = 1.0f / vec.Length;
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result.X = vec.X * scale;
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result.Y = vec.Y * scale;
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result.Z = vec.Z * scale;
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}
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#endregion
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#region NormalizeFast
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/// <summary>
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/// Scale a vector to approximately unit length
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/// </summary>
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/// <param name="vec">The input vector</param>
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/// <returns>The normalized vector</returns>
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public static Vector3 NormalizeFast(Vector3 vec)
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{
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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
|
|
|
|
#region CalculateAngle
|
|
|
|
/// <summary>
|
|
/// Calculates the angle (in radians) between two vectors.
|
|
/// </summary>
|
|
/// <param name="first">The first vector.</param>
|
|
/// <param name="second">The second vector.</param>
|
|
/// <returns>Angle (in radians) between the vectors.</returns>
|
|
/// <remarks>Note that the returned angle is never bigger than the constant Pi.</remarks>
|
|
public static float CalculateAngle(Vector3 first, Vector3 second)
|
|
{
|
|
return (float)System.Math.Acos((Vector3.Dot(first, second)) / (first.Length * second.Length));
|
|
}
|
|
|
|
#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
|
|
}
|
|
}
|