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import java.awt.Point;
import java.awt.geom.Point2D;
public class QuadEdge {
// pointer to the next (direct order) QuadEdge
private QuadEdge onext;
// pointer to the dual QuadEdge (faces graph <-> edges graph)
private QuadEdge rot;
// origin point of the edge/face
private Point2D.Double orig;
// marker for triangle generation
public boolean mark=false;
/**
* (private) constructor. Use makeEdge() to create a new QuadEdge
*
* @param onext pointer to the next QuadEdge on the ring
* @param rot pointer to the next (direct order) crossing edge
* @param orig Origin point
*/
private QuadEdge(QuadEdge Onext, QuadEdge rot, Point2D.Double orig) {
this.onext = Onext;
this.rot = rot;
this.orig = orig;
}
// ----------------------------------------------------------------
// Getter/Setter
// ----------------------------------------------------------------
public QuadEdge onext() {
return onext;
}
public QuadEdge rot() {
return rot;
}
public Point2D.Double orig() {
return orig;
}
public void setOnext(QuadEdge next) {
onext = next;
}
public void setRot(QuadEdge rot) {
this.rot = rot;
}
public void setOrig(Point2D.Double p) {
this.orig = p;
}
// ----------------------------------------------------------------
// QuadEdge Navigation
// ----------------------------------------------------------------
/**
* @return the symetric (reverse) QuadEdge
*/
public QuadEdge sym() {
return rot.rot();
}
/**
* @return the other extremity point
*/
public Point2D.Double dest() {
return sym().orig();
}
/**
* @return the symetric dual QuadEdge
*/
public QuadEdge rotSym() {
return rot.sym();
}
/**
* @return the previous QuadEdge (pointing to this.orig)
*/
public QuadEdge oprev() {
return rot.onext().rot();
}
/**
* @return the previous QuadEdge starting from dest()
*/
public QuadEdge dprev() {
return rotSym().onext().rotSym();
}
/**
* @return the next QuadEdge on left Face
*/
public QuadEdge lnext() {
return rotSym().onext().rot();
}
/**
* @return the previous QuadEdge on left Face
*/
public QuadEdge lprev() {
return onext().sym();
}
// ************************** STATIC ******************************
/**
* Create a new edge (i.e. a segment)
*
* @param orig origin of the segment
* @param dest end of the segment
* @return the QuadEdge of the origin point
*/
public static QuadEdge makeEdge(Point2D.Double orig, Point2D.Double dest) {
QuadEdge q0 = new QuadEdge(null, null, orig);
QuadEdge q1 = new QuadEdge(null, null, null);
QuadEdge q2 = new QuadEdge(null, null, dest);
QuadEdge q3 = new QuadEdge(null, null, null);
// create the segment
q0.onext = q0; q2.onext = q2; // lonely segment: no "next" quadedge
q1.onext = q3; q3.onext = q1; // in the dual: 2 communicating facets
// dual switch
q0.rot = q1; q1.rot = q2;
q2.rot = q3; q3.rot = q0;
return q0;
}
/**
* attach/detach the two edges = combine/split the two rings in the dual space
*
* @param q1,q2 the 2 QuadEdge to attach/detach
*/
public static void splice(QuadEdge a, QuadEdge b) {
QuadEdge alpha = a.onext().rot();
QuadEdge beta = b.onext().rot();
QuadEdge t1 = b.onext();
QuadEdge t2 = a.onext();
QuadEdge t3 = beta.onext();
QuadEdge t4 = alpha.onext();
a.setOnext(t1);
b.setOnext(t2);
alpha.setOnext(t3);
beta.setOnext(t4);
}
/**
* Create a new QuadEdge by connecting 2 QuadEdges
*
* @param e1,e2 the 2 QuadEdges to connect
* @return the new QuadEdge
*/
public static QuadEdge connect(QuadEdge e1, QuadEdge e2) {
QuadEdge q = makeEdge(e1.dest(), e2.orig());
splice(q, e1.lnext());
splice(q.sym(), e2);
return q;
}
public static void swapEdge(QuadEdge e) {
QuadEdge a = e.oprev();
QuadEdge b = e.sym().oprev();
splice(e, a);
splice(e.sym(), b);
splice(e, a.lnext());
splice(e.sym(), b.lnext());
e.orig = a.dest();
e.sym().orig = b.dest();
}
/**
* Delete a QuadEdge
*
* @param q the QuadEdge to delete
*/
public static void deleteEdge(QuadEdge q) {
splice(q, q.oprev());
splice(q.sym(), q.sym().oprev());
}
// ----------------------------------------------------------------
// Geometric computation
// ----------------------------------------------------------------
/**
* Test if the Point p is on the line porting the edge
*
* @param e QuadEdge
* @param p Point to test
* @return true/false
*/
public static boolean isOnLine(QuadEdge e, Point2D.Double p) {
// test if the vector product is zero
if ((p.x-e.orig().x)*(p.y-e.dest().y)==(p.y-e.orig().y)*(p.x-e.dest().x))
return true;
return false;
}
/**
* Test if the Point p is at the right of the QuadEdge q.
*
* @param QuadEdge reference
* @param p Point to test
* @return true/false
*/
public static boolean isAtRightOf(QuadEdge q, Point2D.Double p) {
return isCounterClockwise(p, q.dest(), q.orig());
}
/** return true if a, b and c turn in Counter Clockwise direction
*
* @param a,b,c the 3 points to test
* @return true if a, b and c turn in Counter Clockwise direction
*/
public static boolean isCounterClockwise(Point2D.Double a, Point2D.Double b, Point2D.Double c) {
// test the sign of the determinant of ab x cb
if ( (a.x - b.x)*(b.y - c.y) > (a.y - b.y)*(b.x - c.x) ) return true;
return false;
}
/**
* The Delaunay criteria:
*
* test if the point d is inside the circumscribed circle of triangle a,b,c
*
* @param a,b,c triangle
* @param d point to test
* @return true/false
*/
public static boolean inCircle(Point2D.Double a, Point2D.Double b, Point2D.Double c, Point2D.Double d) {
/*
if "d" is strictly INSIDE the circle, then
|d² dx dy 1|
|a² ax ay 1|
det |b² bx by 1| < 0
|c² cx cy 1|
*/
double a2 = a.x*a.x + a.y*a.y;
double b2 = b.x*b.x + b.y*b.y;
double c2 = c.x*c.x + c.y*c.y;
double d2 = d.x*d.x + d.y*d.y;
double det44 = 0;
det44 += d2 * det33( a.x,a.y, 1, b.x,b.y, 1, c.x,c.y, 1 );
det44 -= d.x * det33( a2 ,a.y, 1, b2 ,b.y, 1, c2 ,c.y, 1 );
det44 += d.y * det33( a2 ,a.x, 1, b2 ,b.x, 1, c2 ,c.x, 1 );
det44 -= 1 * det33( a2,a.x,a.y, b2,b.x,b.y, c2,c.x,c.y );
if (det44<0) return true;
return false;
}
private static double det33( double... m ) {
double det33=0;
det33 += m[0] * (m[4]*m[8] - m[5]*m[7]);
det33 -= m[1] * (m[3]*m[8] - m[5]*m[6]);
det33 += m[2] * (m[3]*m[7] - m[4]*m[6]);
return det33;
}
} |
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