public void TransformNormalize(Matrix3 m)
{
float[] result = m.VectorMultiply (new float[4] { X, Y, Z, W });
X = result [0] / result [3];
Y = result [1] / result [3];
Z = result [2];
W = 1;
}
// Multiply two matrices together:
public static Matrix3 operator *(Matrix3 m1, Matrix3 m2)
{
var result = new Matrix3 ();
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
float element = 0;
for (int k = 0; k < 4; k++) {
element += m1.M[i, k] * m2.M[k, j];
}
result.M[i, j] = element;
}
}
return result;
}
// Axonometric projection matrix:
public static Matrix3 Axonometric(float alpha, float beta)
{
var result = new Matrix3();
var sna = (float)Math.Sin (alpha * Math.PI / 180);
var cna = (float)Math.Cos (alpha * Math.PI / 180);
var snb = (float)Math.Sin (beta * Math.PI / 180);
var cnb = (float)Math.Cos (beta * Math.PI / 180);
result.M[0, 0] = cnb;
result.M[0, 2] = snb;
result.M[1, 0] = sna * snb;
result.M[1, 1] = cna;
result.M[1, 2] = -sna * cnb;
result.M[2, 2] = 0;
return result;
}
public Point3[,] SphereCoordinates()
{
Point3[,] pts = new Point3[30, 20];
var m = new Matrix3 ();
var mt = Matrix3.Translate3 (xc, yc, zc);
for (int i = 0; i < pts.GetLength(0); i++) {
for (int j = 0; j < pts.GetLength(1); j++) {
pts[i, j] = m.Spherical(r, i * 180 / (pts.GetLength(0) - 1),
j * 360 / (pts.GetLength(1) - 1));
pts[i, j].Transform(mt);
}
}
return pts;
}
public static Matrix3 Euler(float alpha, float beta, float gamma)
{
var result = new Matrix3 ();
alpha = alpha * (float)Math.PI / 180.0f;
var sna = (float)Math.Sin (alpha);
var cna = (float)Math.Cos (alpha);
beta = beta * (float)Math.PI / 180.0f;
var snb = (float)Math.Sin (beta);
var cnb = (float)Math.Cos (beta);
gamma = gamma * (float)Math.PI / 180.0f;
var sng = (float)Math.Sin (gamma);
var cng = (float)Math.Cos (gamma);
result.M[0, 0] = cna * cng - sna * snb * sng;
result.M[0, 1] = -snb * sng;
result.M[0, 2] = sna * cng - cna * cnb * sng;
result.M[1, 0] = -sna * snb;
result.M[1, 1] = cnb;
result.M[1, 2] = cna * snb;
result.M[2, 0] = -cna * sng - sna * cnb * cng;
result.M[2, 1] = -snb * cng;
result.M[2, 2] = cna * cnb * cng - sna * snb;
return result;
}
// Create a translation matrix
public static Matrix3 Translate3(float dx, float dy, float dz)
{
var result = new Matrix3 ();
result.M[0, 3] = dx;
result.M[1, 3] = dy;
result.M[2, 3] = dz;
return result;
}
// Top view projection matrix:
public static Matrix3 TopView()
{
var result = new Matrix3 ();
result.M[1, 1] = 0;
result.M[2, 2] = 0;
result.M[1, 2] = -1;
return result;
}
// Side view projection matrix:
public static Matrix3 SideView()
{
var result = new Matrix3 ();
result.M[0, 0] = 0;
result.M[2, 2] = 0;
result.M[0, 2] = -1;
return result;
}
// Create a scaling matrix:
public static Matrix3 Scale3(float sx, float sy, float sz)
{
var result = new Matrix3 ();
result.M[0, 0] = sx;
result.M[1, 1] = sy;
result.M[2, 2] = sz;
return result;
}
// Create a rotation matrix around the z axis:
public static Matrix3 Rotate3Z(float theta)
{
theta = theta * (float)Math.PI / 180.0f;
var sn = (float)Math.Sin(theta);
var cn = (float)Math.Cos(theta);
var result = new Matrix3 ();
result.M[0, 0] = cn;
result.M[0, 1] = -sn;
result.M[1, 0] = sn;
result.M[1, 1] = cn;
return result;
}
// Perspective projection matrix:
public static Matrix3 Perspective(float d)
{
var result = new Matrix3 ();
result.M[3, 2] = -1 / d;
return result;
}
// Oblique projection matrix:
public static Matrix3 Oblique(float alpha, float theta)
{
var result = new Matrix3();
var ta = (float)Math.Tan (alpha * Math.PI / 180);
var snt = (float)Math.Sin (theta * Math.PI / 180);
var cnt = (float)Math.Cos (theta * Math.PI / 180);
result.M[0, 2] = -cnt / ta;
result.M[1, 2] = -snt / ta;
result.M[2, 2] = 0;
return result;
}
// Front view projection matrix:
public static Matrix3 FrontView()
{
var result = new Matrix3 ();
result.M[2, 2] = 0;
return result;
}