//
// TODO 3: ComputeHomography()
// Computes the homography H from the plane specified by "points" to the image plane,
// and its inverse Hinv.
// If the plane is the reference plane (isRefPlane == true), don't convert the
// coordinate system to the plane. Only do this for polygon patches where
// texture mapping is necessary.
// Coordinate system conversion is to be implemented in a separate routine
// ConvertToPlaneCoordinate.
// For more detailed explaination, see
// http://www.cs.cornell.edu/courses/cs4670/2012fa/projects/p4/homography.pdf.
//
void ComputeHomography(CTransform3x3 &H, CTransform3x3 &Hinv, const vector<SVMPoint> &points, vector<Vec3d> &basisPts, bool isRefPlane)
{
int i;
int numPoints = (int) points.size();
assert( numPoints >= 4 );
basisPts.clear();
if (isRefPlane) // reference plane
{
for (i=0; i < numPoints; i++) {
Vec3d tmp = Vec3d(points[i].X, points[i].Y, points[i].W); // was Z, not W
basisPts.push_back(tmp);
}
}
else // arbitrary polygon
{
double uScale, vScale; // unused in this function
ConvertToPlaneCoordinate(points, basisPts, uScale, vScale);
}
// A: 2n x 9 matrix where n is the number of points on the plane
// as discussed in lecture
int numRows = 2 * numPoints;
const int numCols = 9;
typedef Matrix<double, Dynamic, 9, RowMajor> MatrixType;
MatrixType A = MatrixType::Zero(numRows, numCols);
/******** BEGIN TODO ********/
/* Fill in the A matrix for the call to MinEig */
for (i = 0; i < numPoints; i++)
{
A(2*i,0) = basisPts[i][0];
A(2*i,1) = basisPts[i][1];
A(2*i,2) = 1;
A(2*i,6) = - points[i].u * basisPts[i][0];
A(2*i,7) = - points[i].u * basisPts[i][1];
A(2*i,8) = - points[i].u;
A(2*i+1,3) = basisPts[i][0];
A(2*i+1,4) = basisPts[i][1];
A(2*i+1,5) = 1;
A(2*i+1,6) = - points[i].v * basisPts[i][0];
A(2*i+1,7) = - points[i].v * basisPts[i][1];
A(2*i+1,8) = - points[i].v;
}
double eval, h[9];
MinEig(A, eval, h);
H[0][0] = h[0];
H[0][1] = h[1];
H[0][2] = h[2];
H[1][0] = h[3];
H[1][1] = h[4];
H[1][2] = h[5];
H[2][0] = h[6];
H[2][1] = h[7];
H[2][2] = h[8];
/******** END TODO ********/
// compute inverse of H
if (H.Determinant() == 0)
fl_alert("Computed homography matrix is uninvertible \n");
else
Hinv = H.Inverse();
int ii;
printf("\nH=[\n");
for (ii=0; ii<3; ii++)
printf("%e\t%e\t%e;\n", H[ii][0]/H[2][2], H[ii][1]/H[2][2], H[ii][2]/H[2][2]);
printf("]\nHinv=[\n");
for (ii=0; ii<3; ii++)
printf("%e\t%e\t%e;\n", Hinv[ii][0]/Hinv[2][2], Hinv[ii][1]/Hinv[2][2], Hinv[ii][2]/Hinv[2][2]);
printf("]\n\n");
}
//
// TODO 3: ComputeHomography()
// Computes the homography H from the plane specified by "points" to the image plane,
// and its inverse Hinv.
// If the plane is the reference plane (isRefPlane == true), don't convert the
// coordinate system to the plane. Only do this for polygon patches where
// texture mapping is necessary.
// Coordinate system conversion is to be implemented in a separate routine
// ConvertToPlaneCoordinate.
// For more detailed explaination, see
// http://www.cs.cornell.edu/courses/cs4670/2012fa/projects/p4/homography.pdf.
//
void ComputeHomography(CTransform3x3 &H, CTransform3x3 &Hinv, const vector<SVMPoint> &points, vector<Vec3d> &basisPts, bool isRefPlane)
{
int i,j;
int numPoints = (int) points.size();
printf("pts:%d",numPoints);
assert( numPoints >= 4 );
basisPts.clear();
if (isRefPlane) // reference plane
{
printf("ref plane\n");
for (i=0; i < numPoints; i++)
{
Vec3d tmp = Vec3d(points[i].X, points[i].Y, points[i].W); // was Z, not W
basisPts.push_back(tmp);
}
}
else // arbitrary polygon
{
printf("polygon\n");
double uScale, vScale; // unused in this function
ConvertToPlaneCoordinate(points, basisPts, uScale, vScale);
}
// A: 2n x 9 matrix where n is the number of points on the plane
// as discussed in lecture
int numRows = 2 * numPoints;
const int numCols = 9;
typedef Matrix<double, Dynamic, 9, RowMajor> MatrixType;
MatrixType A = MatrixType::Zero(numRows, numCols);
/******** BEGIN TODO ********/
// fill in the entries of A
//printf("TODO: svmmath.cpp:187\n");
//fl_message("TODO: svmmath.cpp:187\n");
int n=0;
for(j=0;j<numRows; j+=2){
A(j,0)=basisPts[n][0]; //x1
A(j,1)=basisPts[n][1]; //y1
A(j,2)=1;
A(j,3)=0;
A(j,4)=0;
A(j,5)=0;
A(j,6)=-points[n].u*basisPts[n][0]; //-x1'*x1
A(j,7)=-points[n].u*basisPts[n][1]; //-x1'*y1
A(j,8)=-points[n].u; //-x1'
//next row
A(j+1,0)=0;
A(j+1,1)=0;
A(j+1,2)=0;
A(j+1,3)=basisPts[n][0];
A(j+1,4)=basisPts[n][1];
A(j+1,5)=1;
A(j+1,6)=-points[n].v*basisPts[n][0];
A(j+1,7)=-points[n].v*basisPts[n][1];
A(j+1,8)=-points[n].v;
n++;
}
/******** END TODO ********/
double eval, h[9];
MinEig(A, eval, h);
H[0][0] = h[0];
H[0][1] = h[1];
H[0][2] = h[2];
H[1][0] = h[3];
H[1][1] = h[4];
H[1][2] = h[5];
H[2][0] = h[6];
H[2][1] = h[7];
H[2][2] = h[8];
// compute inverse of H
if (H.Determinant() == 0)
fl_alert("Computed homography matrix is uninvertible \n");
else
Hinv = H.Inverse();
int ii;
printf("\nH=[\n");
for (ii=0; ii<3; ii++)
printf("%e\t%e\t%e;\n", H[ii][0]/H[2][2], H[ii][1]/H[2][2], H[ii][2]/H[2][2]);
printf("]\nHinv=[\n");
for (ii=0; ii<3; ii++)
printf("%e\t%e\t%e;\n", Hinv[ii][0]/Hinv[2][2], Hinv[ii][1]/Hinv[2][2], Hinv[ii][2]/Hinv[2][2]);
printf("]\n\n");
}
