private void testMatrices()
{
var v = new JVertex3D(3, 4, 5, 1);
var vr = new JVertex3D(0, 0, 5, 1);
// trnaslation
var a = new JTranslationMatrix3D(new JVertex3D(1, 0, 0, 0));
var b = new JTranslationMatrix3D(new JVertex3D(0, 1, 0, 0));
var c1 = b * v;
var c2 = a * b * v;
// scale
var s = new JScaleMatrix3D(new JVertex3D(2, 0.5, 1, 0));
var vs = s * v;
// quaternion
var qxz = new JQuaternion3D(new JVertex3D(1, 0, 0, 0), new JVertex3D(0, 0, 1, 0));
var rxz = new JRotationMatrix3D(qxz);
var vrxz = rxz * vr;
// rotate
var qx = new JQuaternion3D(new JVertex3D(1, 0, 0, 0), Math.PI / 2);
var qy = new JQuaternion3D(new JVertex3D(0, 1, 0, 0), Math.PI / 2);
var qz = new JQuaternion3D(new JVertex3D(0, 0, 1, 0), Math.PI / 2);
var rx = new JRotationMatrix3D(qx);
var ry = new JRotationMatrix3D(qy);
var rz = new JRotationMatrix3D(qz);
var vrx = rx * vr;
var vry = ry * vr;
var vrz = rz * vr;
}
public static JVertex3D Cross(JVertex3D a, JVertex3D b)
{
return(new JVertex3D(
a.Y * b.Z - a.Z * b.Y,
a.Z * b.X - a.X * b.Z,
a.X * b.Y - a.Y * b.X,
0));
}
public JQuaternion3D(JVertex3D axis, double angle)
{
axis = axis.Normalized; // this provides that the quaternion is normalized
X = axis.X * Math.Sin(angle / 2);
Y = axis.Y * Math.Sin(angle / 2);
Z = axis.Z * Math.Sin(angle / 2);
W = Math.Cos(angle / 2);
}
public JLine3D(JVertex3D start, JVertex3D stop)
{
Start = start;
Stop = stop;
Start.W = 1;
Stop.W = 1;
if (start == stop)
{
throw new ArgumentException("Start and Stoppoint of line are the same.");
}
}
public JQuaternion3D(JVertex3D a, JVertex3D b) // rotation from a to b
{
double normAB = Math.Sqrt(a.SquaredLength * b.SquaredLength);
double ct = JVertex3D.Dot(a, b) / normAB;
double hc = Math.Sqrt(0.5 * (1.0 + ct));
JVertex3D w = JVertex3D.Cross(a, b) / (normAB * 2.0 * hc);
X = w.X;
Y = w.Y;
Z = w.Z;
W = hc;
Normalize();
/*
* float norm_u_norm_v = sqrt(sqlength(u) * sqlength(v));
* float cos_theta = dot(u, v) / norm_u_norm_v;
* float half_cos = sqrt(0.5f * (1.f + cos_theta));
* vec3 w = cross(u, v) / (norm_u_norm_v * 2.f * half_cos);
* return quat(half_cos, w.x, w.y, w.z);
*/
}
public static double Dot(JVertex3D a, JVertex3D b)
{
return(a.X * b.X + a.Y * b.Y + a.Z * b.Z);
}