public Draw3DObject(Panel _panel)
{
panel = _panel;
float oneOverd = oneOverdFactor / (2 * panel.Height / 4);
matrix = Matrix3.AzimuthElevation(elevation, azimuth, oneOverd);
}
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;
}
// Axonometric projection matrix:
public static Matrix3 Axonometric(float alpha, float beta)
{
Matrix3 result = new Matrix3();
float sna = (float)Math.Sin(alpha * Math.PI / 180);
float cna = (float)Math.Cos(alpha * Math.PI / 180);
float snb = (float)Math.Sin(beta * Math.PI / 180);
float 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;
}
// Multiply two matrices together:
public static Matrix3 operator *(Matrix3 m1, Matrix3 m2)
{
Matrix3 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;
}
public static Matrix3 AzimuthElevation(float elevation, float azimuth, float oneOverd)
{
Matrix3 result = new Matrix3();
Matrix3 rotate = new Matrix3();
// make sure elevation in the range of [-90, 90]:
if (elevation > 90)
elevation = 90;
else if (elevation < -90)
elevation = -90;
// Make sure azimuth in the range of [-180, 180]:
if (azimuth > 180)
azimuth = 180;
else if (azimuth < -180)
azimuth = -180;
elevation = elevation * (float)Math.PI / 180.0f;
float sne = (float)Math.Sin(elevation);
float cne = (float)Math.Cos(elevation);
azimuth = azimuth * (float)Math.PI / 180.0f;
float sna = (float)Math.Sin(azimuth);
float cna = (float)Math.Cos(azimuth);
rotate.M[0, 0] = cna;
rotate.M[0, 1] = sna;
rotate.M[0, 2] = 0;
rotate.M[1, 0] = -sne * sna;
rotate.M[1, 1] = sne * cna;
rotate.M[1, 2] = cne;
rotate.M[2, 0] = cne * sna;
rotate.M[2, 1] = -cne * cna;
rotate.M[2, 2] = sne;
if (oneOverd <= 0)
result = rotate;
else if (oneOverd > 0)
{
Matrix3 perspective = Matrix3.Perspective(1 / oneOverd);
result = perspective * rotate;
}
return result;
}
// Create a translation matrix
public static Matrix3 Translate3(float dx, float dy, float dz)
{
Matrix3 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()
{
Matrix3 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()
{
Matrix3 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)
{
Matrix3 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;
float sn = (float)Math.Sin(theta);
float cn = (float)Math.Cos(theta);
Matrix3 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)
{
Matrix3 result = new Matrix3();
result.M[3, 2] = -1 / d;
return result;
}
// Oblique projection matrix:
public static Matrix3 Oblique(float alpha, float theta)
{
Matrix3 result = new Matrix3();
float ta = (float)Math.Tan(alpha * Math.PI / 180);
float snt = (float)Math.Sin(theta * Math.PI / 180);
float 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()
{
Matrix3 result = new Matrix3();
result.M[2, 2] = 0;
return result;
}
public static Matrix3 Euler(float alpha, float beta, float gamma)
{
Matrix3 result = new Matrix3();
alpha = alpha * (float)Math.PI / 180.0f;
float sna = (float)Math.Sin(alpha);
float cna = (float)Math.Cos(alpha);
beta = beta * (float)Math.PI / 180.0f;
float snb = (float)Math.Sin(beta);
float cnb = (float)Math.Cos(beta);
gamma = gamma * (float)Math.PI / 180.0f;
float sng = (float)Math.Sin(gamma);
float 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;
}