/**
* Perpendicular bisector of two Pnts. Works in any dimension. The coefficients are returned as
* a Pnt of one higher dimension (e.g., (A,B,C,D) for an equation of the form Ax + By + Cz + D =
* 0).
*
* @param point the other point
* @return the coefficients of the perpendicular bisector
*/
public Pnt bisector(Pnt point) {
dimCheck(point);
Pnt diff = this.subtract(point);
Pnt sum = this.add(point);
float dot = diff.dot(sum);
return diff.extend(-dot / 2);
}
/**
* Locate the triangle with point inside it or on its boundary.
*
* @param point the point to locate
* @return the triangle that holds point; null if no such triangle
*/
public Triangle locate(Pnt point) {
Triangle triangle = mostRecent;
if (!this.contains(triangle)) triangle = null;
// Try a directed walk (this works fine in 2D, but can
// fail in 3D)
Set<Triangle> visited = new HashSet<Triangle>();
while (triangle != null) {
if (visited.contains(triangle)) { // This should
// never
// happen
; // System.out.println("Warning: Caught in a locate loop");
break;
}
visited.add(triangle);
// Corner opposite point
Pnt corner = point.isOutside(triangle.toArray(new Pnt[0]));
if (corner == null) return triangle;
triangle = this.neighborOpposite(corner, triangle);
}
// No luck; try brute force
; // System.out.println("Warning: Checking all triangles for " + point);
for (Triangle tri : this) {
if (point.isOutside(tri.toArray(new Pnt[0])) == null) return tri;
}
// No such triangle
; // System.out.println("Warning: No triangle holds " + point);
return null;
}
/**
* Determine the cavity caused by site.
*
* @param site the site causing the cavity
* @param triangle the triangle containing site
* @return set of all triangles that have site in their circumcircle
*/
private Set<Triangle> getCavity(Pnt site, Triangle triangle) {
Set<Triangle> encroached = new HashSet<Triangle>();
Queue<Triangle> toBeChecked = new LinkedList<Triangle>();
Set<Triangle> marked = new HashSet<Triangle>();
toBeChecked.add(triangle);
marked.add(triangle);
while (!toBeChecked.isEmpty()) {
triangle = toBeChecked.remove();
if (site.vsCircumcircle(triangle.toArray(new Pnt[0])) == 1)
continue; // Site outside triangle =>
// triangle not in
// cavity
encroached.add(triangle);
// Check the neighbors
for (Triangle neighbor : triGraph.neighbors(triangle)) {
if (marked.contains(neighbor)) continue;
marked.add(neighbor);
toBeChecked.add(neighbor);
}
}
return encroached;
}
/**
* Angle (in radians) between two Pnts (treated as vectors).
*
* @param p the other Pnt
* @return the angle (in radians) between the two Pnts
*/
public float angle(Pnt p) {
return (float) Math.acos(this.dot(p) / (this.magnitude() * p.magnitude()));
}