459 lines
11 KiB
C#
459 lines
11 KiB
C#
#region --- License ---
|
|
/* Copyright (c) 2006, 2007 the OpenTK team
|
|
* See license.txt for license info
|
|
*
|
|
* Implemented by Andy Gill
|
|
*/
|
|
#endregion
|
|
|
|
using System;
|
|
using System.Collections.Generic;
|
|
using System.Text;
|
|
using System.Runtime.InteropServices;
|
|
|
|
namespace OpenTK.Math
|
|
{
|
|
/// <summary>
|
|
/// Represents a Quaternion
|
|
/// </summary>
|
|
[StructLayout(LayoutKind.Sequential)]
|
|
public struct Quaternion
|
|
{
|
|
#region Fields
|
|
|
|
/// <summary>
|
|
/// The vector part of the quaternion
|
|
/// </summary>
|
|
public Vector3 XYZ;
|
|
/// <summary>
|
|
/// The w component of the quaternion
|
|
/// </summary>
|
|
public float W;
|
|
|
|
public static Quaternion Identity = new Quaternion(0, 0, 0, 1);
|
|
|
|
#endregion
|
|
|
|
#region Constructors
|
|
|
|
/// <summary>
|
|
/// Construct a new Quaternion from vector and w components
|
|
/// </summary>
|
|
/// <param name="v">The vector part</param>
|
|
/// <param name="w">The w part</param>
|
|
public Quaternion(Vector3 v, float w)
|
|
{
|
|
XYZ = v;
|
|
W = w;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Construct a new Quaternion
|
|
/// </summary>
|
|
/// <param name="x">The x component</param>
|
|
/// <param name="y">The y component</param>
|
|
/// <param name="z">The z component</param>
|
|
/// <param name="w">The w component</param>
|
|
public Quaternion(float x, float y, float z, float w)
|
|
{
|
|
XYZ = new Vector3(x, y, z);
|
|
W = w;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Functions
|
|
|
|
#region pubilc void ToAxisAngle(out Vector3 axis, out float angle)
|
|
|
|
/// <summary>
|
|
/// Convert the current quaternion to axis angle representation
|
|
/// </summary>
|
|
/// <param name="axis">The resultant axis</param>
|
|
/// <param name="angle">The resultant angle</param>
|
|
public void ToAxisAngle(out Vector3 axis, out float angle)
|
|
{
|
|
Quaternion q = this;
|
|
if (q.W > 1.0f)
|
|
q.Normalize();
|
|
|
|
angle = 2.0f * (float)System.Math.Acos(q.W);
|
|
float den = (float)System.Math.Sqrt(1.0 - q.W * q.W);
|
|
axis = q.XYZ;
|
|
if (den > 0.0001f)
|
|
{
|
|
axis = q.XYZ / den;
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public float Length
|
|
|
|
/// <summary>
|
|
/// Gets the length (magnitude) of the quaternion.
|
|
/// </summary>
|
|
/// <seealso cref="LengthSquared"/>
|
|
public float Length
|
|
{
|
|
get
|
|
{
|
|
return (float)System.Math.Sqrt(W * W + XYZ.LengthSquared);
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public float LengthSquared
|
|
|
|
/// <summary>
|
|
/// Gets the square of the quaternion length (magnitude).
|
|
/// </summary>
|
|
public float LengthSquared
|
|
{
|
|
get
|
|
{
|
|
return W * W + XYZ.LengthSquared;
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public void Normalize()
|
|
|
|
/// <summary>
|
|
/// Scales the Quaternion to unit length.
|
|
/// </summary>
|
|
public void Normalize()
|
|
{
|
|
float scale = 1.0f / this.Length;
|
|
XYZ *= scale;
|
|
W *= scale;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public void Conjugate()
|
|
|
|
/// <summary>
|
|
/// Convert this quaternion to its conjugate
|
|
/// </summary>
|
|
public void Conjugate()
|
|
{
|
|
XYZ = -XYZ;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Operator overloads
|
|
|
|
public static Quaternion operator +(Quaternion left, Quaternion right)
|
|
{
|
|
left.XYZ += right.XYZ;
|
|
left.W += right.W;
|
|
return left;
|
|
}
|
|
|
|
public static Quaternion operator -(Quaternion left, Quaternion right)
|
|
{
|
|
left.XYZ -= right.XYZ;
|
|
left.W -= right.W;
|
|
return left;
|
|
}
|
|
|
|
public static Quaternion operator *(Quaternion left, Quaternion right)
|
|
{
|
|
float w = left.W * right.W - Vector3.Dot(left.XYZ, right.XYZ);
|
|
left.XYZ = right.W * left.XYZ + left.W * right.XYZ + Vector3.Cross(left.XYZ, right.XYZ);
|
|
left.W = w;
|
|
return left;
|
|
}
|
|
|
|
[CLSCompliant(false)]
|
|
unsafe public static explicit operator float*(Quaternion q)
|
|
{
|
|
return &q.XYZ.X;
|
|
}
|
|
|
|
public static explicit operator IntPtr(Quaternion q)
|
|
{
|
|
unsafe
|
|
{
|
|
return (IntPtr)(&q.XYZ.X);
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Static functions
|
|
|
|
#region Add
|
|
|
|
/// <summary>
|
|
/// Add two quaternions
|
|
/// </summary>
|
|
/// <param name="left">The first operand</param>
|
|
/// <param name="right">The second operand</param>
|
|
/// <returns>The result of the addition</returns>
|
|
public static Quaternion Add(Quaternion left, Quaternion right)
|
|
{
|
|
left.XYZ += right.XYZ;
|
|
left.W += right.W;
|
|
return left;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Add two quaternions
|
|
/// </summary>
|
|
/// <param name="left">The first operand</param>
|
|
/// <param name="right">The second operand</param>
|
|
/// <param name="result">The result of the addition</param>
|
|
public static void Add(ref Quaternion left, ref Quaternion right, out Quaternion result)
|
|
{
|
|
result.XYZ = left.XYZ + right.XYZ;
|
|
result.W = left.W + right.W;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Sub
|
|
|
|
public static Quaternion Sub(Quaternion left, Quaternion right)
|
|
{
|
|
left.XYZ -= right.XYZ;
|
|
left.W -= right.W;
|
|
return left;
|
|
}
|
|
|
|
public static void Sub(ref Quaternion left, ref Quaternion right, out Quaternion result)
|
|
{
|
|
result.XYZ = left.XYZ - right.XYZ;
|
|
result.W = left.W - right.W;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Mult
|
|
|
|
public static Quaternion Mult(Quaternion left, Quaternion right)
|
|
{
|
|
float w = left.W * right.W - Vector3.Dot(left.XYZ, right.XYZ);
|
|
left.XYZ = right.W * left.XYZ + left.W * right.XYZ + Vector3.Cross(left.XYZ, right.XYZ);
|
|
left.W = w;
|
|
return left;
|
|
}
|
|
|
|
public static void Mult(ref Quaternion left, ref Quaternion right, out Quaternion result)
|
|
{
|
|
result.W = left.W * right.W - Vector3.Dot(left.XYZ, right.XYZ);
|
|
result.XYZ = right.W * left.XYZ + left.W * right.XYZ + Vector3.Cross(left.XYZ, right.XYZ);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Conjugate
|
|
|
|
/// <summary>
|
|
/// Get the conjugate of the given quaternion
|
|
/// </summary>
|
|
/// <param name="q">The quaternion</param>
|
|
/// <returns>The conjugate of the given quaternion</returns>
|
|
public static Quaternion Conjugate(Quaternion q)
|
|
{
|
|
q.XYZ = -q.XYZ;
|
|
return q;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Get the conjugate of the given quaternion
|
|
/// </summary>
|
|
/// <param name="q">The quaternion</param>
|
|
/// <param name="result">The conjugate of the given quaternion</param>
|
|
public static void Conjugate(ref Quaternion q, out Quaternion result)
|
|
{
|
|
result.XYZ = -q.XYZ;
|
|
result.W = q.W;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Invert
|
|
|
|
/// <summary>
|
|
/// Get the inverse of the given quaternion
|
|
/// </summary>
|
|
/// <param name="q">The quaternion to invert</param>
|
|
/// <returns>The inverse of the given quaternion</returns>
|
|
public static Quaternion Invert(Quaternion q)
|
|
{
|
|
float lengthSq = q.LengthSquared;
|
|
if (lengthSq != 0.0)
|
|
{
|
|
float i = 1.0f / lengthSq;
|
|
q.XYZ *= -i;
|
|
q.W *= i;
|
|
}
|
|
return q;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Get the inverse of the given quaternion
|
|
/// </summary>
|
|
/// <param name="q">The quaternion to invert</param>
|
|
/// <param name="result">The inverse of the given quaternion</param>
|
|
public static void Invert(ref Quaternion q, out Quaternion result)
|
|
{
|
|
float lengthSq = q.LengthSquared;
|
|
if (lengthSq != 0.0)
|
|
{
|
|
float i = 1.0f / lengthSq;
|
|
result.XYZ = q.XYZ * -i;
|
|
result.W = q.W * i;
|
|
}
|
|
else
|
|
{
|
|
result = q;
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Normalize
|
|
|
|
/// <summary>
|
|
/// Scale the given quaternion to unit length
|
|
/// </summary>
|
|
/// <param name="q">The quaternion to normalize</param>
|
|
/// <returns>The normalized quaternion</returns>
|
|
public static Quaternion Normalize(Quaternion q)
|
|
{
|
|
float scale = 1.0f / q.Length;
|
|
q.XYZ *= scale;
|
|
q.W *= scale;
|
|
return q;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scale the given quaternion to unit length
|
|
/// </summary>
|
|
/// <param name="q">The quaternion to normalize</param>
|
|
/// <param name="result">The normalized quaternion</param>
|
|
public static void Normalize(ref Quaternion q, out Quaternion result)
|
|
{
|
|
float scale = 1.0f / q.Length;
|
|
result.XYZ = q.XYZ * scale;
|
|
result.W = q.W * scale;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region FromAxisAngle
|
|
|
|
/// <summary>
|
|
/// Build a quaternion from the given axis and angle
|
|
/// </summary>
|
|
/// <param name="axis">The axis to rotate about</param>
|
|
/// <param name="angle">The rotation angle in radians</param>
|
|
/// <returns></returns>
|
|
public static Quaternion FromAxisAngle(Vector3 axis, float angle)
|
|
{
|
|
if (axis.LengthSquared == 0.0f)
|
|
return Identity;
|
|
|
|
Quaternion result = Identity;
|
|
|
|
angle *= 0.5f;
|
|
axis.Normalize();
|
|
result.XYZ = axis * (float)System.Math.Sin(angle);
|
|
result.W = (float)System.Math.Cos(angle);
|
|
|
|
return Normalize(result);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Slerp
|
|
|
|
/// <summary>
|
|
/// Do Spherical linear interpolation between two quaternions
|
|
/// </summary>
|
|
/// <param name="q1">The first quaternion</param>
|
|
/// <param name="q2">The second quaternion</param>
|
|
/// <param name="blend">The blend factor</param>
|
|
/// <returns>A smooth blend between the given quaternions</returns>
|
|
public static Quaternion Slerp(Quaternion q1, Quaternion q2, float blend)
|
|
{
|
|
// if either input is zero, return the other.
|
|
if (q1.LengthSquared == 0.0f)
|
|
{
|
|
if (q2.LengthSquared == 0.0f)
|
|
{
|
|
return Identity;
|
|
}
|
|
return q2;
|
|
}
|
|
else if (q2.LengthSquared == 0.0f)
|
|
{
|
|
return q1;
|
|
}
|
|
|
|
|
|
float cosHalfAngle = q1.W * q2.W + Vector3.Dot(q1.XYZ, q2.XYZ);
|
|
|
|
if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
|
|
{
|
|
// angle = 0.0f, so just return one input.
|
|
return q1;
|
|
}
|
|
else if (cosHalfAngle < 0.0f)
|
|
{
|
|
q2.XYZ = -q2.XYZ;
|
|
q2.W = -q2.W;
|
|
cosHalfAngle = -cosHalfAngle;
|
|
}
|
|
|
|
float blendA;
|
|
float blendB;
|
|
if (cosHalfAngle < 0.99f)
|
|
{
|
|
// do proper slerp for big angles
|
|
float halfAngle = (float)System.Math.Acos(cosHalfAngle);
|
|
float sinHalfAngle = (float)System.Math.Sin(halfAngle);
|
|
float oneOverSinHalfAngle = 1.0f / sinHalfAngle;
|
|
blendA = (float)System.Math.Sin(halfAngle * (1.0f - blend)) * oneOverSinHalfAngle;
|
|
blendB = (float)System.Math.Sin(halfAngle * blend) * oneOverSinHalfAngle;
|
|
}
|
|
else
|
|
{
|
|
// do lerp if angle is really small.
|
|
blendA = 1.0f - blend;
|
|
blendB = blend;
|
|
}
|
|
|
|
Quaternion result = new Quaternion(blendA * q1.XYZ + blendB * q2.XYZ, blendA * q1.W + blendB * q2.W);
|
|
if (result.LengthSquared > 0.0f)
|
|
return Normalize(result);
|
|
else
|
|
return Identity;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Quaternion.
|
|
/// </summary>
|
|
/// <returns></returns>
|
|
public override string ToString()
|
|
{
|
|
return String.Format("V: {0}, W: {1}", XYZ, W);
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
}
|