/*===========================================================================
*
* Local Function - boolean l_ComputeDFUVMatrixXY (Matrix, Params);
*
* Computes the UV conversion parameters from the given input based on
* the formula:
* U = AX + BY + D
*
* Returns FALSE on any error. For use on faces with 0 Z-coordinates.
*
*=========================================================================*/
private bool l_ComputeDFUVMatrixXY(ref df3duvmatrix_t matrix, ref df3duvparams_lt param)
{
float determinant;
float[] Xi = new float[3];
float[] Yi = new float[3];
float[] Zi = new float[3];
/* Compute the determinant of the coefficient matrix */
determinant = param.X[0] * param.Y[1] + param.Y[0] * param.X[2] +
param.X[1] * param.Y[2] - param.Y[1] * param.X[2] -
param.Y[0] * param.X[1] - param.X[0] * param.Y[2];
/* Check for a singular matrix indicating no valid solution */
if (determinant == 0)
{
return(false);
}
/* Compute parameters of the the inverted XYZ matrix */
Xi[0] = (param.Y[1] - param.Y[2]) / determinant;
Xi[1] = (-param.X[1] + param.X[2]) / determinant;
Xi[2] = (param.X[1] * param.Y[2] - param.X[2] * param.Y[1]) / determinant;
Yi[0] = (-param.Y[0] + param.Y[2]) / determinant;
Yi[1] = (param.X[0] - param.X[2]) / determinant;
Yi[2] = (-param.X[0] * param.Y[2] + param.X[2] * param.Y[0]) / determinant;
Zi[0] = (param.Y[0] - param.Y[1]) / determinant;
Zi[1] = (-param.X[0] + param.X[1]) / determinant;
Zi[2] = (param.X[0] * param.Y[1] - param.X[1] * param.Y[0]) / determinant;
/* Compute the UV conversion parameters */
matrix.UA = (param.U[0] * Xi[0] + param.U[1] * Yi[0] + param.U[2] * Zi[0]);
matrix.UB = (param.U[0] * Xi[1] + param.U[1] * Yi[1] + param.U[2] * Zi[1]);
matrix.UC = (float)0.0;
matrix.UD = (param.U[0] * Xi[2] + param.U[1] * Yi[2] + param.U[2] * Zi[2]);;
matrix.VA = (param.V[0] * Xi[0] + param.V[1] * Yi[0] + param.V[2] * Zi[0]);
matrix.VB = (param.V[0] * Xi[1] + param.V[1] * Yi[1] + param.V[2] * Zi[1]);
matrix.VC = (float)0.0;
matrix.VD = (param.V[0] * Xi[2] + param.V[1] * Yi[2] + param.V[2] * Zi[2]);
return(true);
}
/// <summary>
/// Calculates absolute UV values for all points of a face.
/// </summary>
/// <param name="faceVertsIn">Source array of native point values.</param>
/// <param name="faceVertsOut">Destination array for calculated UV values.</param>
/// <returns>True if successful, otherwise false.</returns>
public bool ComputeFaceUVCoordinates(ref DFPurePoint[] faceVertsIn, ref DFPurePoint[] faceVertsOut)
{
// Get first three vertices of ngon (these three vertices are always non-collinear)
Vector3 P0 = new Vector3(faceVertsIn[0].x, faceVertsIn[0].y, faceVertsIn[0].z);
Vector3 P1 = new Vector3(faceVertsIn[1].x, faceVertsIn[1].y, faceVertsIn[1].z);
Vector3 P2 = new Vector3(faceVertsIn[2].x, faceVertsIn[2].y, faceVertsIn[2].z);
// Create coplanar vectors from p1->p0 and p2->p0
Vector3 V0 = P1 - P0;
Vector3 V1 = P2 - P0;
// Orthogonalize V1
V1 = V1 - (V0 * (V1.DotProduct(V0) / (V0.DotProduct(V0))));
// Normalize both vectors
V0.Normalize();
V1.Normalize();
// Compute first three vertices in 2D space
DF2DPoint p0, p1, p2;
p0.x = (Int32)P0.DotProduct(V0);
p0.y = (Int32)P0.DotProduct(V1);
p1.x = (Int32)P1.DotProduct(V0);
p1.y = (Int32)P1.DotProduct(V1);
p2.x = (Int32)P2.DotProduct(V0);
p2.y = (Int32)P2.DotProduct(V1);
// Initialise the params struct
df3duvparams_lt Params = new df3duvparams_lt();
Params.X = new float[4];
Params.Y = new float[4];
Params.Z = new float[4];
Params.U = new float[4];
Params.V = new float[4];
// Initialise the conversion matrix
df3duvmatrix_t Matrix = new df3duvmatrix_t();
Matrix.UA = 1.0f;
Matrix.UB = 0.0f;
Matrix.UC = 0.0f;
Matrix.UD = 0.0f;
Matrix.VA = 0.0f;
Matrix.VB = 1.0f;
Matrix.VC = 0.0f;
Matrix.UD = 0.0f;
// Store the first 3 points of texture coordinates
Params.U[0] = faceVertsIn[0].u;
Params.U[1] = faceVertsIn[1].u + Params.U[0];
Params.U[2] = faceVertsIn[2].u + Params.U[1];
Params.V[0] = faceVertsIn[0].v;
Params.V[1] = faceVertsIn[1].v + Params.V[0];
Params.V[2] = faceVertsIn[2].v + Params.V[1];
// Get and store the 1st point coordinates in face
Params.X[0] = p0.x;
Params.Y[0] = p0.y;
Params.Z[0] = 0;
// Get and store the 2nd point coordinates in face
Params.X[1] = p1.x;
Params.Y[1] = p1.y;
Params.Z[1] = 0;
// Get and store the 3rd point coordinates in face
Params.X[2] = p2.x;
Params.Y[2] = p2.y;
Params.Z[2] = 0;
// Compute the solution using an XY linear equation
if (!l_ComputeDFUVMatrixXY(ref Matrix, ref Params))
{
return(false);
}
// Assign matrix to all points if successful
Int32 u = 0, v = 0;
for (int point = 0; point < faceVertsIn.Length; point++)
{
if (point > 2)
{
// Use generated matrix to calculate UV value from 2D point
DF2DPoint pn;
Vector3 PN = new Vector3(faceVertsIn[point].x, faceVertsIn[point].y, faceVertsIn[point].z);
pn.x = (Int32)PN.DotProduct(V0);
pn.y = (Int32)PN.DotProduct(V1);
u = (Int32)((pn.x * Matrix.UA) + (pn.y * Matrix.UB) + Matrix.UD);
v = (Int32)((pn.x * Matrix.VA) + (pn.y * Matrix.VB) + Matrix.VD);
}
else if (point == 0)
{
// UV[0] is absolute
u = faceVertsIn[0].u;
v = faceVertsIn[0].v;
}
else if (point == 1)
{
// UV[1] is a delta from UV[0]
u = faceVertsIn[0].u + faceVertsIn[1].u;
v = faceVertsIn[0].v + faceVertsIn[1].v;
}
else if (point == 2)
{
// UV[2] is a delta from UV[1] + UV[0]
u = faceVertsIn[0].u + faceVertsIn[1].u + faceVertsIn[2].u;
v = faceVertsIn[0].v + faceVertsIn[1].v + faceVertsIn[2].v;
}
// Write outgoing point
faceVertsOut[point].x = faceVertsIn[point].x;
faceVertsOut[point].y = faceVertsIn[point].y;
faceVertsOut[point].z = faceVertsIn[point].z;
faceVertsOut[point].nx = faceVertsIn[point].nx;
faceVertsOut[point].ny = faceVertsIn[point].ny;
faceVertsOut[point].nz = faceVertsIn[point].nz;
faceVertsOut[point].u = u;
faceVertsOut[point].v = v;
}
return(true);
}
/// <summary>
/// Calculates absolute UV values for all points of a face.
/// </summary>
/// <param name="faceVertsIn">Source array of native point values.</param>
/// <param name="faceVertsOut">Destination array for calculated UV values.</param>
/// <returns>True if successful, otherwise false.</returns>
public bool ComputeFaceUVCoordinates(ref DFPurePoint[] faceVertsIn, ref DFPurePoint[] faceVertsOut)
{
// Get first three vertices of ngon (these three vertices are always non-collinear)
Vector3 P0 = new Vector3(faceVertsIn[0].x, faceVertsIn[0].y, faceVertsIn[0].z);
Vector3 P1 = new Vector3(faceVertsIn[1].x, faceVertsIn[1].y, faceVertsIn[1].z);
Vector3 P2 = new Vector3(faceVertsIn[2].x, faceVertsIn[2].y, faceVertsIn[2].z);
// Create coplanar vectors from p1->p0 and p2->p0
Vector3 V0 = P1 - P0;
Vector3 V1 = P2 - P0;
// Orthogonalize V1
V1 = V1 - (V0 * (V1.DotProduct(V0) / (V0.DotProduct(V0))));
// Normalize both vectors
V0.Normalize();
V1.Normalize();
// Compute first three vertices in 2D space
DF2DPoint p0, p1, p2;
p0.x = (Int32)P0.DotProduct(V0);
p0.y = (Int32)P0.DotProduct(V1);
p1.x = (Int32)P1.DotProduct(V0);
p1.y = (Int32)P1.DotProduct(V1);
p2.x = (Int32)P2.DotProduct(V0);
p2.y = (Int32)P2.DotProduct(V1);
// Initialise the params struct
df3duvparams_lt Params = new df3duvparams_lt();
Params.X = new float[4];
Params.Y = new float[4];
Params.Z = new float[4];
Params.U = new float[4];
Params.V = new float[4];
// Initialise the conversion matrix
df3duvmatrix_t Matrix = new df3duvmatrix_t();
Matrix.UA = 1.0f;
Matrix.UB = 0.0f;
Matrix.UC = 0.0f;
Matrix.UD = 0.0f;
Matrix.VA = 0.0f;
Matrix.VB = 1.0f;
Matrix.VC = 0.0f;
Matrix.UD = 0.0f;
// Store the first 3 points of texture coordinates
Params.U[0] = faceVertsIn[0].u;
Params.U[1] = faceVertsIn[1].u + Params.U[0];
Params.U[2] = faceVertsIn[2].u + Params.U[1];
Params.V[0] = faceVertsIn[0].v;
Params.V[1] = faceVertsIn[1].v + Params.V[0];
Params.V[2] = faceVertsIn[2].v + Params.V[1];
// Get and store the 1st point coordinates in face
Params.X[0] = p0.x;
Params.Y[0] = p0.y;
Params.Z[0] = 0;
// Get and store the 2nd point coordinates in face
Params.X[1] = p1.x;
Params.Y[1] = p1.y;
Params.Z[1] = 0;
// Get and store the 3rd point coordinates in face
Params.X[2] = p2.x;
Params.Y[2] = p2.y;
Params.Z[2] = 0;
// Compute the solution using an XY linear equation
if (!l_ComputeDFUVMatrixXY(ref Matrix, ref Params))
return false;
// Assign matrix to all points if successful
Int32 u = 0, v = 0;
for (int point = 0; point < faceVertsIn.Length; point++)
{
if (point > 2)
{
// Use generated matrix to calculate UV value from 2D point
DF2DPoint pn;
Vector3 PN = new Vector3(faceVertsIn[point].x, faceVertsIn[point].y, faceVertsIn[point].z);
pn.x = (Int32)PN.DotProduct(V0);
pn.y = (Int32)PN.DotProduct(V1);
u = (Int32)((pn.x * Matrix.UA) + (pn.y * Matrix.UB) + Matrix.UD);
v = (Int32)((pn.x * Matrix.VA) + (pn.y * Matrix.VB) + Matrix.VD);
}
else if (point == 0)
{
// UV[0] is absolute
u = faceVertsIn[0].u;
v = faceVertsIn[0].v;
}
else if (point == 1)
{
// UV[1] is a delta from UV[0]
u = faceVertsIn[0].u + faceVertsIn[1].u;
v = faceVertsIn[0].v + faceVertsIn[1].v;
}
else if (point == 2)
{
// UV[2] is a delta from UV[1] + UV[0]
u = faceVertsIn[0].u + faceVertsIn[1].u + faceVertsIn[2].u;
v = faceVertsIn[0].v + faceVertsIn[1].v + faceVertsIn[2].v;
}
// Write outgoing point
faceVertsOut[point].x = faceVertsIn[point].x;
faceVertsOut[point].y = faceVertsIn[point].y;
faceVertsOut[point].z = faceVertsIn[point].z;
faceVertsOut[point].nx = faceVertsIn[point].nx;
faceVertsOut[point].ny = faceVertsIn[point].ny;
faceVertsOut[point].nz = faceVertsIn[point].nz;
faceVertsOut[point].u = u;
faceVertsOut[point].v = v;
}
return true;
}
/*===========================================================================
*
* Local Function - boolean l_ComputeDFUVMatrixXY (Matrix, Params);
*
* Computes the UV conversion parameters from the given input based on
* the formula:
* U = AX + BY + D
*
* Returns FALSE on any error. For use on faces with 0 Z-coordinates.
*
*=========================================================================*/
private bool l_ComputeDFUVMatrixXY(ref df3duvmatrix_t matrix, ref df3duvparams_lt param)
{
float determinant;
float[] Xi = new float[3];
float[] Yi = new float[3];
float[] Zi = new float[3];
/* Compute the determinant of the coefficient matrix */
determinant = param.X[0] * param.Y[1] + param.Y[0] * param.X[2] +
param.X[1] * param.Y[2] - param.Y[1] * param.X[2] -
param.Y[0] * param.X[1] - param.X[0] * param.Y[2];
/* Check for a singular matrix indicating no valid solution */
if (determinant == 0)
{
return false;
}
/* Compute parameters of the the inverted XYZ matrix */
Xi[0] = (param.Y[1] - param.Y[2]) / determinant;
Xi[1] = (-param.X[1] + param.X[2]) / determinant;
Xi[2] = (param.X[1] * param.Y[2] - param.X[2] * param.Y[1]) / determinant;
Yi[0] = (-param.Y[0] + param.Y[2]) / determinant;
Yi[1] = (param.X[0] - param.X[2]) / determinant;
Yi[2] = (-param.X[0] * param.Y[2] + param.X[2] * param.Y[0]) / determinant;
Zi[0] = (param.Y[0] - param.Y[1]) / determinant;
Zi[1] = (-param.X[0] + param.X[1]) / determinant;
Zi[2] = (param.X[0] * param.Y[1] - param.X[1] * param.Y[0]) / determinant;
/* Compute the UV conversion parameters */
matrix.UA = (param.U[0] * Xi[0] + param.U[1] * Yi[0] + param.U[2] * Zi[0]);
matrix.UB = (param.U[0] * Xi[1] + param.U[1] * Yi[1] + param.U[2] * Zi[1]);
matrix.UC = (float)0.0;
matrix.UD = (param.U[0] * Xi[2] + param.U[1] * Yi[2] + param.U[2] * Zi[2]); ;
matrix.VA = (param.V[0] * Xi[0] + param.V[1] * Yi[0] + param.V[2] * Zi[0]);
matrix.VB = (param.V[0] * Xi[1] + param.V[1] * Yi[1] + param.V[2] * Zi[1]);
matrix.VC = (float)0.0;
matrix.VD = (param.V[0] * Xi[2] + param.V[1] * Yi[2] + param.V[2] * Zi[2]);
return true;
}
