/**
* method to calculate a mapping K from two source positions C0, C1 to a plane C0 (C1) is the
* source position from the first (second) view
*/
public void createMappingToEpipolarPlane() {
// set up source matrices //
SimpleVector C0 = this.view1.C;
SimpleVector C1 = this.view2.C;
// compute Pluecker coordinates //
double L01 = C0.getElement(0) * C1.getElement(1) - C0.getElement(1) * C1.getElement(0);
double L02 = C0.getElement(0) * C1.getElement(2) - C0.getElement(2) * C1.getElement(0);
double L03 = C0.getElement(0) * C1.getElement(3) - C0.getElement(3) * C1.getElement(0);
double L12 = C0.getElement(1) * C1.getElement(2) - C0.getElement(2) * C1.getElement(1);
double L13 = C0.getElement(1) * C1.getElement(3) - C0.getElement(3) * C1.getElement(1);
double L23 = C0.getElement(2) * C1.getElement(3) - C0.getElement(3) * C1.getElement(2);
// construct B (6x1) //
SimpleVector B = new SimpleVector(L01, L02, L03, L12, L13, L23);
// compute infinity point in direction of B //
SimpleVector N = new SimpleVector(-L03, -L13, -L23, 0);
// compute plane E0 containing B and X0=(0,0,0,1) //
SimpleVector E0 = SimpleOperators.getPlueckerJoin(B, new SimpleVector(0, 0, 0, 1));
// find othonormal basis from plane normals //
// (vectors are of 3x1)
SimpleVector a2 = new SimpleVector(E0.getElement(0), E0.getElement(1), E0.getElement(2));
SimpleVector a3 = new SimpleVector(N.getElement(0), N.getElement(1), N.getElement(2));
// set vectors to unit length
a2.normalizeL2();
a3.normalizeL2();
// calculate cross product to get the last basis vector //
SimpleVector a1 = General.crossProduct(a2, a3).negated();
// (a1 is already of unit length -> no normalization needed)
// set up assembly matrix A (4x3) //
SimpleMatrix A = new SimpleMatrix(4, 3);
A.setSubColValue(0, 0, a1);
A.setSubColValue(0, 1, a2);
A.setSubColValue(0, 2, C0);
// store mapping matrix K (4x3 = 4x4 * 4x3) //
this.K = SimpleOperators.multiplyMatrixProd(SimpleOperators.getPlueckerMatrixDual(B), A);
}
/**
* Constructs the triangle corresponding to the i-th face in a mesh given the connectivity
* information fcs and the vertices vtc and adds it to the CompoundShape.
*
* @param vtc The vertices of the mesh.
* @param fcs The faces of the mesh, i.e connectivity information.
* @param i The index of the face to be constructed.
*/
private void addTriangleAtIndex(CompoundShape cs, SimpleMatrix vtc, SimpleMatrix fcs, int i) {
SimpleVector face = fcs.getRow(i);
SimpleVector dirU = vtc.getRow((int) face.getElement(1));
dirU.subtract(vtc.getRow((int) face.getElement(0)));
double l2 = dirU.normL2();
SimpleVector dirV = vtc.getRow((int) face.getElement(2));
dirV.subtract(vtc.getRow((int) face.getElement(0)));
if (dirV.normL2() < l2) {
l2 = dirV.normL2();
}
double nN = General.crossProduct(dirU.normalizedL2(), dirV.normalizedL2()).normL2();
if (l2 < Math.sqrt(CONRAD.DOUBLE_EPSILON) || nN < Math.sqrt(CONRAD.DOUBLE_EPSILON)) {
} else {
Triangle t =
new Triangle(
new PointND(vtc.getRow((int) face.getElement(0))),
new PointND(vtc.getRow((int) face.getElement(1))),
new PointND(vtc.getRow((int) face.getElement(2))));
cs.add(t);
}
}