opensim – Rev 1
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/* The MIT License
*
* Copyright (c) 2010 Intel Corporation.
* All rights reserved.
*
* Based on the convexdecomposition library from
* <http://codesuppository.googlecode.com> by John W. Ratcliff and Stan Melax.
*
* 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.
*/
using System;
namespace OpenSim.Region.Physics.ConvexDecompositionDotNet
{
public class Quaternion : float4
{
public Quaternion()
{
x = y = z = 0.0f;
w = 1.0f;
}
public Quaternion(float3 v, float t)
{
v = float3.normalize(v);
w = (float)Math.Cos(t / 2.0f);
v = v * (float)Math.Sin(t / 2.0f);
x = v.x;
y = v.y;
z = v.z;
}
public Quaternion(float _x, float _y, float _z, float _w)
{
x = _x;
y = _y;
z = _z;
w = _w;
}
public float angle()
{
return (float)Math.Acos(w) * 2.0f;
}
public float3 axis()
{
float3 a = new float3(x, y, z);
if (Math.Abs(angle()) < 0.0000001f)
return new float3(1f, 0f, 0f);
return a * (1 / (float)Math.Sin(angle() / 2.0f));
}
public float3 xdir()
{
return new float3(1 - 2 * (y * y + z * z), 2 * (x * y + w * z), 2 * (x * z - w * y));
}
public float3 ydir()
{
return new float3(2 * (x * y - w * z), 1 - 2 * (x * x + z * z), 2 * (y * z + w * x));
}
public float3 zdir()
{
return new float3(2 * (x * z + w * y), 2 * (y * z - w * x), 1 - 2 * (x * x + y * y));
}
public float3x3 getmatrix()
{
return new float3x3(xdir(), ydir(), zdir());
}
public static implicit operator float3x3(Quaternion q)
{
return q.getmatrix();
}
public static Quaternion operator *(Quaternion a, Quaternion b)
{
Quaternion c = new Quaternion();
c.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z;
c.x = a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y;
c.y = a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x;
c.z = a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w;
return c;
}
public static float3 operator *(Quaternion q, float3 v)
{
// The following is equivalent to:
//return (q.getmatrix() * v);
float qx2 = q.x * q.x;
float qy2 = q.y * q.y;
float qz2 = q.z * q.z;
float qxqy = q.x * q.y;
float qxqz = q.x * q.z;
float qxqw = q.x * q.w;
float qyqz = q.y * q.z;
float qyqw = q.y * q.w;
float qzqw = q.z * q.w;
return new float3((1 - 2 * (qy2 + qz2)) * v.x + (2 * (qxqy - qzqw)) * v.y + (2 * (qxqz + qyqw)) * v.z, (2 * (qxqy + qzqw)) * v.x + (1 - 2 * (qx2 + qz2)) * v.y + (2 * (qyqz - qxqw)) * v.z, (2 * (qxqz - qyqw)) * v.x + (2 * (qyqz + qxqw)) * v.y + (1 - 2 * (qx2 + qy2)) * v.z);
}
public static Quaternion operator +(Quaternion a, Quaternion b)
{
return new Quaternion(a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w);
}
public static Quaternion operator *(Quaternion a, float b)
{
return new Quaternion(a.x *b, a.y *b, a.z *b, a.w *b);
}
public static Quaternion normalize(Quaternion a)
{
float m = (float)Math.Sqrt(a.w * a.w + a.x * a.x + a.y * a.y + a.z * a.z);
if (m < 0.000000001f)
{
a.w = 1;
a.x = a.y = a.z = 0;
return a;
}
return a * (1f / m);
}
public static float dot(Quaternion a, Quaternion b)
{
return (a.w * b.w + a.x * b.x + a.y * b.y + a.z * b.z);
}
public static Quaternion slerp(Quaternion a, Quaternion b, float interp)
{
if (dot(a, b) < 0.0)
{
a.w = -a.w;
a.x = -a.x;
a.y = -a.y;
a.z = -a.z;
}
float d = dot(a, b);
if (d >= 1.0)
{
return a;
}
float theta = (float)Math.Acos(d);
if (theta == 0.0f)
{
return (a);
}
return a * ((float)Math.Sin(theta - interp * theta) / (float)Math.Sin(theta)) + b * ((float)Math.Sin(interp * theta) / (float)Math.Sin(theta));
}
public static Quaternion Interpolate(Quaternion q0, Quaternion q1, float alpha)
{
return slerp(q0, q1, alpha);
}
public static Quaternion Inverse(Quaternion q)
{
return new Quaternion(-q.x, -q.y, -q.z, q.w);
}
public static Quaternion YawPitchRoll(float yaw, float pitch, float roll)
{
roll *= (3.14159264f / 180.0f);
yaw *= (3.14159264f / 180.0f);
pitch *= (3.14159264f / 180.0f);
return new Quaternion(new float3(0.0f, 0.0f, 1.0f), yaw) * new Quaternion(new float3(1.0f, 0.0f, 0.0f), pitch) * new Quaternion(new float3(0.0f, 1.0f, 0.0f), roll);
}
public static float Yaw(Quaternion q)
{
float3 v = q.ydir();
return (v.y == 0.0 && v.x == 0.0) ? 0.0f : (float)Math.Atan2(-v.x, v.y) * (180.0f / 3.14159264f);
}
public static float Pitch(Quaternion q)
{
float3 v = q.ydir();
return (float)Math.Atan2(v.z, Math.Sqrt(v.x * v.x + v.y * v.y)) * (180.0f / 3.14159264f);
}
public static float Roll(Quaternion q)
{
q = new Quaternion(new float3(0.0f, 0.0f, 1.0f), -Yaw(q) * (3.14159264f / 180.0f)) * q;
q = new Quaternion(new float3(1.0f, 0.0f, 0.0f), -Pitch(q) * (3.14159264f / 180.0f)) * q;
return (float)Math.Atan2(-q.xdir().z, q.xdir().x) * (180.0f / 3.14159264f);
}
}
}