/**
* Get the vector with the highest down slope in the plan associated to this triangle.
*
* @return return the steepest vector.
* @throws DelaunayError
*/
public final DPoint getSteepestVector() throws DelaunayError {
DPoint normal = getNormalVector();
if (Math.abs(normal.getX()) < Tools.EPSILON && Math.abs(normal.getY()) < Tools.EPSILON) {
return new DPoint(0, 0, 0);
}
DPoint pente;
if (Math.abs(normal.getX()) < Tools.EPSILON) {
pente = new DPoint(0, 1, -normal.getY() / normal.getZ());
} else if (Math.abs(normal.getY()) < Tools.EPSILON) {
pente = new DPoint(1, 0, -normal.getX() / normal.getZ());
} else {
pente =
new DPoint(
normal.getX() / normal.getY(),
1,
-1 / normal.getZ() * (normal.getX() * normal.getX() / normal.getY() + normal.getY()));
}
// We want the vector to be low-oriented.
if (pente.getZ() > Tools.EPSILON) {
pente.setX(-pente.getX());
pente.setY(-pente.getY());
pente.setZ(-pente.getZ());
}
// We normalize it
double length = Math.sqrt(pente.squareDistance(new DPoint(0, 0, 0)));
if (length > Tools.EPSILON) {
pente.setX(pente.getX() / length);
pente.setY(pente.getY() / length);
pente.setZ(pente.getZ() / length);
}
return pente;
}
/**
* Return the square of the minimal distance between pt and the apex of this triangle.
*
* @param pt
* @return the square of the minimal distance between pt and the apex of this triangle.
*/
public final double getMinSquareDistance(DPoint pt) {
double min = Double.POSITIVE_INFINITY;
for (int i = 0; i < PT_NB; i++) {
double dist = pt.squareDistance(getPoint(i));
min = dist < min ? dist : min;
}
return min;
}
/**
* Get the normal vector to this triangle, of length 1.
*
* @return Get the vector normal to the triangle.
* @throws DelaunayError
*/
public final DPoint getNormalVector() throws DelaunayError {
// We first perform a vectorial product between two of the edges
double dx1 = edges[0].getStartPoint().getX() - edges[0].getEndPoint().getX();
double dy1 = edges[0].getStartPoint().getY() - edges[0].getEndPoint().getY();
double dz1 = edges[0].getStartPoint().getZ() - edges[0].getEndPoint().getZ();
double dx2 = edges[1].getStartPoint().getX() - edges[1].getEndPoint().getX();
double dy2 = edges[1].getStartPoint().getY() - edges[1].getEndPoint().getY();
double dz2 = edges[1].getStartPoint().getZ() - edges[1].getEndPoint().getZ();
DPoint vec = new DPoint(dy1 * dz2 - dz1 * dy2, dz1 * dx2 - dx1 * dz2, dx1 * dy2 - dy1 * dx2);
double length = Math.sqrt(vec.squareDistance(new DPoint(0, 0, 0)));
vec.setX(vec.getX() / length);
vec.setY(vec.getY() / length);
vec.setZ(vec.getZ() / length);
return vec;
}
