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 void Transform(float3 position, Quaternion orientation)
{
// Transforms the plane to the space defined by the
// given position/orientation
float3 newNormal = Quaternion.Inverse(orientation) * normal;
float3 origin = Quaternion.Inverse(orientation) * (-normal * dist - position);
normal = newNormal;
dist = -float3.dot(newNormal, origin);
}
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);
}
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 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 Quaternion Inverse(Quaternion q)
{
return new Quaternion(-q.x, -q.y, -q.z, q.w);
}
public static Quaternion Interpolate(Quaternion q0, Quaternion q1, float alpha)
{
return slerp(q0, q1, alpha);
}
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 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 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 float4x4 MatrixFromQuatVec(Quaternion q, float3 v)
{
// builds a 4x4 transformation matrix based on orientation q and translation 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 float4x4(
1 - 2 * (qy2 + qz2),
2 * (qxqy + qzqw),
2 * (qxqz - qyqw),
0,
2 * (qxqy - qzqw),
1 - 2 * (qx2 + qz2),
2 * (qyqz + qxqw),
0,
2 * (qxqz + qyqw),
2 * (qyqz - qxqw),
1 - 2 * (qx2 + qy2),
0,
v.x,
v.y,
v.z,
1.0f);
}
public static Quaternion operator *(Quaternion a, Quaternion b)
{
Quaternion c = new Quaternion
{
w = a.w*b.w - a.x*b.x - a.y*b.y - a.z*b.z,
x = a.w*b.x + a.x*b.w + a.y*b.z - a.z*b.y,
y = a.w*b.y - a.x*b.z + a.y*b.w + a.z*b.x,
z = a.w*b.z + a.x*b.y - a.y*b.x + a.z*b.w
};
return c;
}