/**
* Computes the 3D area of a triangle based on the same approach of JTS
*
* @return
*/
public final double getArea3D() {
DPoint p1, p2, pptNb;
p1 = edges[0].getStartPoint();
p2 = edges[0].getEndPoint();
pptNb = edges[1].getStartPoint();
if ((pptNb.equals(p1)) || (pptNb.equals(p2))) {
pptNb = edges[1].getEndPoint();
}
/**
* Uses the formula 1/2 * | u x v | where u,v are the side vectors of the triangle x is the
* vector cross-product
*/
// side vectors u and v
double ux = p2.getX() - p1.getX();
double uy = p2.getY() - p1.getY();
double uz = p2.getZ() - p1.getZ();
double vx = pptNb.getX() - p1.getX();
double vy = pptNb.getY() - p1.getY();
double vz = pptNb.getZ() - p1.getZ();
// cross-product = u x v
double crossx = uy * vz - uz * vy;
double crossy = uz * vx - ux * vz;
double crossz = ux * vy - uy * vx;
// tri area = 1/2 * | u x v |
double absSq = crossx * crossx + crossy * crossy + crossz * crossz;
return Math.sqrt(absSq) / 2;
}
/**
* Get Z value of a specific point in the triangle
*
* @param aPoint
* @return ZValue
*/
public final double interpolateZ(DPoint aPoint) {
double zValue = 0;
DPoint p1, p2, p3;
p1 = edges[0].getStartPoint();
p2 = edges[0].getEndPoint();
p3 = edges[1].getStartPoint();
if ((p3.equals(p1)) || (p3.equals(p2))) {
p3 = edges[1].getEndPoint();
}
double ux = p2.getX() - p1.getX();
double uy = p2.getY() - p1.getY();
double uz = p2.getZ() - p1.getZ();
double vx = p3.getX() - p1.getX();
double vy = p3.getY() - p1.getY();
double vz = p3.getZ() - p1.getZ();
double a = uy * vz - uz * vy;
double b = uz * vx - ux * vz;
double c = ux * vy - uy * vx;
double d = -a * p1.getX() - b * p1.getY() - c * p1.getZ();
if (Math.abs(c) > Tools.EPSILON) {
// Non vertical triangle
zValue = (-a * aPoint.getX() - b * aPoint.getY() - d) / c;
}
return zValue;
}
/**
* Compute the azimut of the triangle in degrees between north and steeepest vector. Aspect is
* measured clockwise in degrees from 0, due north, to 360, again due north, coming full circle.
*
* @return the aspect of the slope of this triangle.
* @throws DelaunayError
*/
public final double getSlopeAspect() throws DelaunayError {
double orientationPente;
DPoint c1 = new DPoint(0.0, 0.0, 0.0);
DPoint c2 = getSteepestVector();
if (c2.getZ() > 0.0) {
c2.setX(-c2.getX());
c2.setY(-c2.getY());
c2.setZ(-c2.getZ());
}
// l'ordre des coordonnees correspond a l'orientation de l'arc
// "sommet haut vers sommet bas"
double angleAxeXrad = Tools.angle(c1, c2);
// on considere que l'axe nord correspond a l'axe Y positif
double angleAxeNordrad = Tools.PI_OVER_2 - angleAxeXrad;
double angleAxeNorddeg = Math.toDegrees(angleAxeNordrad);
// on renvoie toujours une valeur d'angle >= 0
orientationPente = angleAxeNorddeg < 0.0 ? 360.0 + angleAxeNorddeg : angleAxeNorddeg;
return orientationPente;
}
/**
* 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;
}
/**
* 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;
}
/**
* Get the barycenter of the triangle as a DPoint
*
* @return isFlat
* @throws DelaunayError
*/
public final DPoint getBarycenter() throws DelaunayError {
double x = 0, y = 0, z = 0;
DPoint aPoint;
for (int i = 0; i < PT_NB; i++) {
aPoint = getPoint(i);
x += aPoint.getX();
y += aPoint.getY();
z += aPoint.getZ();
}
x /= (double) PT_NB;
y /= (double) PT_NB;
z /= (double) PT_NB;
return new DPoint(x, y, z);
}
/**
* Compute the intersection point according to the vector opposite to the steepest vector. If dp
* is outside the triangle, we return null.
*
* @param dp
* @return The point pt of the triangle's boundary for which (dp pt) is colinear to the steepest
* vector.
* @throws DelaunayError
*/
public final DPoint getCounterSteepestIntersection(DPoint dp) throws DelaunayError {
if (isInside(dp) || isOnAnEdge(dp)) {
for (DEdge ed : edges) {
if (!isTopoOrientedToEdge(ed)) {
DPoint counterSteep = getSteepestVector();
counterSteep.setX(-counterSteep.getX());
counterSteep.setY(-counterSteep.getY());
counterSteep.setZ(-counterSteep.getZ());
DPoint pt =
Tools.computeIntersection(
ed.getStartPoint(), ed.getDirectionVector(), dp, counterSteep);
if (ed.contains(pt)) {
return pt;
}
}
}
}
return null;
}
