// Front view projection matrix
public static Matrix3DHomogeneous FrontView()
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[2, 2] = 0;
return(result);
}
// Create a scaling matrix
public static Matrix3DHomogeneous CreateScale(double sx, double sy, double sz)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[0, 0] = sx;
result.Matrix[1, 1] = sy;
result.Matrix[2, 2] = sz;
return(result);
}
// Side view projection matrix
public static Matrix3DHomogeneous SideView()
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[0, 0] = 0;
result.Matrix[2, 2] = 0;
result.Matrix[0, 2] = -1;
return(result);
}
// Top view projection matrix
public static Matrix3DHomogeneous TopView()
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[1, 1] = 0;
result.Matrix[2, 2] = 0;
result.Matrix[1, 2] = -1;
return(result);
}
////Multiply a matrix with a vector
//public double[] VectorMultiply(double[] vector)
//{
// double[] result = new double[4];
// for (int i = 0; i < 4; i++)
// {
// for (int j = 0; j < 4; j++)
// {
// result[i] += Matrix[i, j] * vector[j];
// }
// }
// return result;
//}
//public double[] VectorMultiply(Vector3DHomogeneous vector)
//{
// double[] _vector= new double[4];
// _vector[0] = vector.X;
// _vector[1] = vector.Y;
// _vector[2] = vector.Z;
// _vector[3] = vector.W;
// return VectorMultiply(_vector);
//}
////Multiply a matrix with a point
//public double[] VectorMultiply(Point3DHomogeneous point)
//{
// double[] _point = new double[4];
// _point[0] = point.X;
// _point[1] = point.Y;
// _point[2] = point.Z;
// _point[3] = point.W;
// return VectorMultiply(_point);
//}
//Create a translation matrix
public static Matrix3DHomogeneous CreateTraslation(double dx, double dy, double dz)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[0, 3] = dx;
result.Matrix[1, 3] = dy;
result.Matrix[2, 3] = dz;
return(result);
}
// Create matrix from azimuth and elevation
public static Matrix3DHomogeneous AzimuthElevation(double elevation, double azimuth, double oneOverd)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
Matrix3DHomogeneous rotate = new Matrix3DHomogeneous();
// 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 * Math.PI / 180.0f;
double sne = Math.Sin(elevation);
double cne = Math.Cos(elevation);
azimuth = azimuth * Math.PI / 180.0f;
double sna = Math.Sin(azimuth);
double cna = Math.Cos(azimuth);
rotate.Matrix[0, 0] = cna;
rotate.Matrix[0, 1] = sna;
rotate.Matrix[0, 2] = 0;
rotate.Matrix[1, 0] = -sne * sna;
rotate.Matrix[1, 1] = sne * cna;
rotate.Matrix[1, 2] = cne;
rotate.Matrix[2, 0] = cne * sna;
rotate.Matrix[2, 1] = -cne * cna;
rotate.Matrix[2, 2] = sne;
if (oneOverd <= 0)
{
result = rotate;
}
else if (oneOverd > 0)
{
//Point3DHomogeneous perspective = Point3DHomogeneous.Perspective(1 / oneOverd);
//result = perspective * rotate;
}
return(result);
}
// Create a rotation matrix around the z axis:
public static Matrix3DHomogeneous RotationAroundZAxis(Angle angle)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double sinAngle = Math.Sin(angle.Radians);
double cosAngle = Math.Cos(angle.Radians);
result.Matrix[0, 0] = cosAngle;
result.Matrix[0, 1] = -sinAngle;
result.Matrix[1, 0] = sinAngle;
result.Matrix[1, 1] = cosAngle;
return(result);
}
// Oblique projection matrix
public static Matrix3DHomogeneous Oblique(Angle alpha, Angle theta)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double tanAlpha = Math.Tan(alpha.Radians);
double sinTheta = Math.Sin(theta.Radians);
double cosTheta = Math.Cos(theta.Radians);
result.Matrix[0, 2] = -cosTheta / tanAlpha;
result.Matrix[1, 2] = -sinTheta / tanAlpha;
result.Matrix[2, 2] = 0;
return(result);
}
// Axonometric projection matrix
public static Matrix3DHomogeneous Axonometric(Angle alpha, Angle beta)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double sna = Math.Sin(alpha.Radians);
double cosAlpha = Math.Cos(alpha.Radians);
double sinBeta = Math.Sin(beta.Radians);
double cosBeta = Math.Cos(beta.Radians);
result.Matrix[0, 0] = cosBeta;
result.Matrix[0, 2] = sinBeta;
result.Matrix[1, 0] = sna * sinBeta;
result.Matrix[1, 1] = cosAlpha;
result.Matrix[1, 2] = -sna * cosBeta;
result.Matrix[2, 2] = 0;
return result;
}
// Axonometric projection matrix
public static Matrix3DHomogeneous Axonometric(Angle alpha, Angle beta)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double sna = Math.Sin(alpha.Radians);
double cosAlpha = Math.Cos(alpha.Radians);
double sinBeta = Math.Sin(beta.Radians);
double cosBeta = Math.Cos(beta.Radians);
result.Matrix[0, 0] = cosBeta;
result.Matrix[0, 2] = sinBeta;
result.Matrix[1, 0] = sna * sinBeta;
result.Matrix[1, 1] = cosAlpha;
result.Matrix[1, 2] = -sna * cosBeta;
result.Matrix[2, 2] = 0;
return(result);
}
// Multiply two matrices together
public static Matrix3DHomogeneous operator *(Matrix3DHomogeneous m1, Matrix3DHomogeneous m2)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
double element = 0;
for (int k = 0; k < 4; k++)
{
element += m1.Matrix[i, k] * m2.Matrix[k, j];
}
result.Matrix[i, j] = element;
}
}
return result;
}
// Multiply two matrices together
public static Matrix3DHomogeneous operator *(Matrix3DHomogeneous m1, Matrix3DHomogeneous m2)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
double element = 0;
for (int k = 0; k < 4; k++)
{
element += m1.Matrix[i, k] * m2.Matrix[k, j];
}
result.Matrix[i, j] = element;
}
}
return(result);
}
// Create matrix from Euler Angles
public static Matrix3DHomogeneous Euler(Angle alpha, Angle beta, Angle gamma)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double sinAlpha = Math.Sin(alpha.Radians);
double cosAlpha = Math.Cos(alpha.Radians);
double sinBeta = Math.Sin(beta.Radians);
double cosBeta = Math.Cos(beta.Radians);
double sinGamma = Math.Sin(gamma.Radians);
double cosGamma = Math.Cos(gamma.Radians);
result.Matrix[0, 0] = cosAlpha * cosGamma - sinAlpha * sinBeta * sinGamma;
result.Matrix[0, 1] = -sinBeta * sinGamma;
result.Matrix[0, 2] = sinAlpha * cosGamma - cosAlpha * cosBeta * sinGamma;
result.Matrix[1, 0] = -sinAlpha * sinBeta;
result.Matrix[1, 1] = cosBeta;
result.Matrix[1, 2] = cosAlpha * sinBeta;
result.Matrix[2, 0] = -cosAlpha * sinGamma - sinAlpha * cosBeta * cosGamma;
result.Matrix[2, 1] = -sinBeta * cosGamma;
result.Matrix[2, 2] = cosAlpha * cosBeta * cosGamma - sinAlpha * sinBeta;
return(result);
}
// Create matrix from azimuth and elevation
public static Matrix3DHomogeneous AzimuthElevation(double elevation, double azimuth, double oneOverd)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
Matrix3DHomogeneous rotate = new Matrix3DHomogeneous();
// 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 * Math.PI / 180.0f;
double sne = Math.Sin(elevation);
double cne = Math.Cos(elevation);
azimuth = azimuth * Math.PI / 180.0f;
double sna = Math.Sin(azimuth);
double cna = Math.Cos(azimuth);
rotate.Matrix[0, 0] = cna;
rotate.Matrix[0, 1] = sna;
rotate.Matrix[0, 2] = 0;
rotate.Matrix[1, 0] = -sne * sna;
rotate.Matrix[1, 1] = sne * cna;
rotate.Matrix[1, 2] = cne;
rotate.Matrix[2, 0] = cne * sna;
rotate.Matrix[2, 1] = -cne * cna;
rotate.Matrix[2, 2] = sne;
if (oneOverd <= 0)
result = rotate;
else if (oneOverd > 0)
{
//Point3DHomogeneous perspective = Point3DHomogeneous.Perspective(1 / oneOverd);
//result = perspective * rotate;
}
return result;
}
// Create matrix from Euler Angles
public static Matrix3DHomogeneous Euler(Angle alpha, Angle beta, Angle gamma)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double sinAlpha = Math.Sin(alpha.Radians);
double cosAlpha = Math.Cos(alpha.Radians);
double sinBeta = Math.Sin(beta.Radians);
double cosBeta = Math.Cos(beta.Radians);
double sinGamma = Math.Sin(gamma.Radians);
double cosGamma = Math.Cos(gamma.Radians);
result.Matrix[0, 0] = cosAlpha * cosGamma - sinAlpha * sinBeta * sinGamma;
result.Matrix[0, 1] = -sinBeta * sinGamma;
result.Matrix[0, 2] = sinAlpha * cosGamma - cosAlpha * cosBeta * sinGamma;
result.Matrix[1, 0] = -sinAlpha * sinBeta;
result.Matrix[1, 1] = cosBeta;
result.Matrix[1, 2] = cosAlpha * sinBeta;
result.Matrix[2, 0] = -cosAlpha * sinGamma - sinAlpha * cosBeta * cosGamma;
result.Matrix[2, 1] = -sinBeta * cosGamma;
result.Matrix[2, 2] = cosAlpha * cosBeta * cosGamma - sinAlpha * sinBeta;
return result;
}
////Multiply a matrix with a vector
//public double[] VectorMultiply(double[] vector)
//{
// double[] result = new double[4];
// for (int i = 0; i < 4; i++)
// {
// for (int j = 0; j < 4; j++)
// {
// result[i] += Matrix[i, j] * vector[j];
// }
// }
// return result;
//}
//public double[] VectorMultiply(Vector3DHomogeneous vector)
//{
// double[] _vector= new double[4];
// _vector[0] = vector.X;
// _vector[1] = vector.Y;
// _vector[2] = vector.Z;
// _vector[3] = vector.W;
// return VectorMultiply(_vector);
//}
////Multiply a matrix with a point
//public double[] VectorMultiply(Point3DHomogeneous point)
//{
// double[] _point = new double[4];
// _point[0] = point.X;
// _point[1] = point.Y;
// _point[2] = point.Z;
// _point[3] = point.W;
// return VectorMultiply(_point);
//}
//Create a translation matrix
public static Matrix3DHomogeneous CreateTraslation(double dx, double dy, double dz)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[0, 3] = dx;
result.Matrix[1, 3] = dy;
result.Matrix[2, 3] = dz;
return result;
}
// Oblique projection matrix
public static Matrix3DHomogeneous Oblique(Angle alpha, Angle theta)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double tanAlpha = Math.Tan(alpha.Radians);
double sinTheta = Math.Sin(theta.Radians);
double cosTheta = Math.Cos(theta.Radians);
result.Matrix[0, 2] = -cosTheta / tanAlpha;
result.Matrix[1, 2] = -sinTheta / tanAlpha;
result.Matrix[2, 2] = 0;
return result;
}
// Front view projection matrix
public static Matrix3DHomogeneous FrontView()
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[2, 2] = 0;
return result;
}
// Create a rotation matrix around the z axis:
public static Matrix3DHomogeneous RotationAroundZAxis(Angle angle)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
double sinAngle = Math.Sin(angle.Radians);
double cosAngle = Math.Cos(angle.Radians);
result.Matrix[0, 0] = cosAngle;
result.Matrix[0, 1] = -sinAngle;
result.Matrix[1, 0] = sinAngle;
result.Matrix[1, 1] = cosAngle;
return result;
}
// Create a reflection matrix across the Y-Z plane
public static Matrix3DHomogeneous ReflectionYZ()
{
Matrix3DHomogeneous result = CreateScale(-1, 1, 1);
return(result);
}
// Side view projection matrix
public static Matrix3DHomogeneous SideView()
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[0, 0] = 0;
result.Matrix[2, 2] = 0;
result.Matrix[0, 2] = -1;
return result;
}
// Top view projection matrix
public static Matrix3DHomogeneous TopView()
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[1, 1] = 0;
result.Matrix[2, 2] = 0;
result.Matrix[1, 2] = -1;
return result;
}
// Create a scaling matrix
public static Matrix3DHomogeneous CreateScale(double sx, double sy, double sz)
{
Matrix3DHomogeneous result = new Matrix3DHomogeneous();
result.Matrix[0, 0] = sx;
result.Matrix[1, 1] = sy;
result.Matrix[2, 2] = sz;
return result;
}