import java.util.collections.*;
import org.ibex.util.*;
+// TODO:
+// - allow edge-constraint removal
+//
+// ~30% of our time spent finding vertices => use a balanced quadtree
+//
+// - store "which curve is inside me" pointer in Triangle
+// - split if two curves enter
+// - go to treating Vertex as a value class (epsilon==0)
+// - union()
+// - subtract()
+// - [??] preserve in/out-ness every time we delete() a triangle
+
/**
- * An incremental, adaptive, constrained Delaunay Triangulation.
- * @see Kallmann, Bieri, and Thalmann: Fully Dynamic Constrained Delaunay Triangulations
+ * An incremental, adaptive, addWeighted Delaunay Triangulation.
+ * @see Kallmann, Bieri, and Thalmann: Fully Dynamic AddWeighted Delaunay Triangulations
*/
public final class Mesh {
- //#define Vertex int
-
- private static final float epsilon = (float)0.001;
+ private static final float epsilon = (float)0.0001;
+ private static final float epsilon2 = (float)0.001;
private static final boolean debug = false;
- private Vector triangles = new Vector();
-
- public static float B = (float)5.0;
- public static float Q = (float)0.4;
+ private Vector triangles = new Vector(); /* we no longer need this */
+ private Hash edges = new Hash(); /* we no longer need this either */
+ private int numvertices = 0;
+ private Triangle triangle0 = null;
+ private Vertex vertex0 = null;
+ private Vertex vertex1 = null;
+ private Vertex start = null;
+ private Vertex last = null;
+
+ public Mesh copy() {
+ Mesh m = new Mesh();
+ m.vertex(triangle0.v(1));
+ m.vertex(triangle0.v(2));
+ m.vertex(triangle0.v(3));
+ Object[] edges = this.edges.vals();
+ for(int i=0; i<edges.length; i++) {
+ Edge e = (Edge)edges[i];
+ Vertex mv1 = m.vertex(e.v(1));
+ Vertex mv2 = m.vertex(e.v(2));
+ Edge me = m.getEdge(mv1, mv2);
+ if (e.locked()) {
+ me.lock(mv1, 0);
+ me.weight = e.weight;
+ }
+ }
+ m.setIn(true);
+ return m;
+ }
- public static Hashtable nexter = new Hashtable();
- public static LinkedList next(Vertex v) {
- LinkedList hs = (LinkedList)nexter.get(new Integer(v));
- if (hs == null) nexter.put(new Integer(v), hs = new LinkedList());
- return hs;
+ public void reset() {
+ triangles.setSize(0);
+ start = null;
+ last = null;
}
- // Vertices //////////////////////////////////////////////////////////////////////////////
-
- public Vertex v(float x, float y) {
- if (numvertices >= this.x.length-1) {
- if (debug) Log.debug(Mesh.class, "expanding vertex arrays from " + this.x.length + " to " + this.x.length*2);
- float[] newx = new float[this.x.length * 2];
- float[] newy = new float[this.y.length * 2];
- System.arraycopy(this.x, 0, newx, 0, this.x.length);
- System.arraycopy(this.y, 0, newy, 0, this.y.length);
- this.x = newx;
- this.y = newy;
- }
- this.x[numvertices] = x;
- this.y[numvertices] = y;
- return numvertices++;
+ // Chain //////////////////////////////////////////////////////////////////////////////
+
+ public static interface Chain {
+ public Mesh.Chain getMeshChainParent();
+ public Affine getAffine();
+ public Mesh getMesh();
}
- public int numvertices = 0;
- public float x[] = new float[255];
- public float y[] = new float[255];
- public String s(Vertex v) { return "("+x(v)+","+y(v)+")"; }
- public float x(Vertex v) { return x[v]; }
- public float y(Vertex v) { return y[v]; }
-
- public static final Vertex NULLVERTEX = -1;
-
- public Vertex newVertex(float x, float y) {
- Vertex ret = NULLVERTEX;
- for(int k=0; k<numvertices; k++) {
- Vertex v = k;
- if (distance(v,x,y)<epsilon) if (ret==NULLVERTEX || distance(v,x,y) < distance(ret,x,y)) ret = v;
- }
- if (ret != NULLVERTEX) return ret;
- Vector vec = new Vector();
- boolean interior = false;
- int edges = 0;
- Vertex v = v(x,y);
- if (numvertices<=2) return v;
- if (numvertices==3) { newTriangle(0, 1, 2, "first three points"); return v; }
- for(int i=0; i<triangles.size(); i++) {
- Triangle t = (Triangle)triangles.elementAt(i);
- if (t.contains(v)) {
- Triangle t12 = t.t12;
- Triangle t23 = t.t23;
- Triangle t31 = t.t31;
- t.delete();
- vec.addElement(newTriangle(v, t.v1, t.v2, "vertexinsertion " + v));
- vec.addElement(newTriangle(v, t.v3, t.v2, "vertexinsertion " + v));
- vec.addElement(newTriangle(v, t.v1, t.v3, "vertexinsertion " + v));
- //#repeat t23/t31/t12 v1/v2/v3 v2/v3/v1 v3/v1/v2
- } else if (t.t23 != null && isect(t.v2, t.v3, v)) {
- Triangle tt = t.t23;
- Vertex va = tt.opposingVertex(t);
- tt.delete();
- t.delete();
- vec.addElement(newTriangle(v, t.v1, t.v3, "vertexinsertion " + v));
- vec.addElement(newTriangle(v, t.v1, t.v2, "vertexinsertion " + v));
- vec.addElement(newTriangle(v, t.v3, va , "vertexinsertion " + v));
- vec.addElement(newTriangle(v, t.v2, va , "vertexinsertion " + v));
- //#end
- } else {
- continue;
- }
- fixup(vec, v);
- return v;
- }
- boolean good = false;
- while(true) {
- for(int j=0; j<triangles.size(); j++) {
- Triangle t = (Triangle)triangles.elementAt(j);
- if (t.v1==v || t.v2==v || t.v3==v) continue;
- //#repeat t12/t23/t31 v3/v1/v2 v2/v3/v1 v1/v2/v3
- if (t.t12==null) {
- boolean bad = false;
- for(int k=0; k<triangles.size(); k++) {
- Triangle tt = (Triangle)triangles.elementAt(k);
- if (tt.intersectsSegment(v, t.v1)) { bad = true; break; }
- if (tt.intersectsSegment(v, t.v2)) { bad = true; break; }
+
+ // Constructor //////////////////////////////////////////////////////////////////////////////
+
+ public Mesh() { }
+ public Mesh(Path p, boolean evenOdd) { p.addTo(this, evenOdd); }
+
+ public void subtract(Mesh m, Affine a) { clipOp(m,a,true); }
+ public void intersect(Mesh m, Affine a) { clipOp(m,a,false); }
+ public void add(Mesh m, Affine a) { iterateTriangles(ITERATE_ADD, m, a); }
+ public static long seekTime = 0;
+
+ public static final int ITERATE_SUBTRACT = 1;
+ public static final int ITERATE_INTERSECT = 2;
+ public static final int ITERATE_ADD = 3;
+ public static final int ITERATE_CLEAR_WASSET = 4;
+ public static final int ITERATE_CLEAR = 5;
+ public static final int ITERATE_STROKE = 6;
+ int tick = 0;
+ Triangle[] iter = new Triangle[100];
+
+ private void iterateTriangles(int mode, Mesh m, Affine a) { iterateTriangles(mode, m, a, null, 0); }
+ private void iterateTriangles(int mode, Mesh m, Affine a, PixelBuffer buf, int color) {
+ tick++;
+ int numiter = 0;
+ if (iter.length < triangles.size()) iter = new Triangle[triangles.size()];
+ iter[numiter++] = triangle0;
+ while(numiter > 0) {
+ Triangle t = iter[--numiter];
+ if (t.tick >= this.tick) continue;
+ switch(mode) {
+ case ITERATE_STROKE: t.stroke(buf, a, color); break;
+ case ITERATE_CLEAR: t.clear(); break;
+ case ITERATE_CLEAR_WASSET: t.inWasSet = false; break;
+ case ITERATE_INTERSECT:
+ case ITERATE_SUBTRACT: {
+ if (!t.in) break;
+ boolean oin = m.queryPoint(t.c().multiply(a));
+ t.in = (mode==ITERATE_SUBTRACT) ? (t.in && !oin) : (t.in && oin);
+ break;
}
- if (!bad) {
- vec.addElement(newTriangle(v,t.v1,t.v2, "hull expansion"));
- good = true;
+ case ITERATE_ADD: {
+ for(int i=1; i<=3; i++) {
+ Edge e = t.e(i);
+ if (e.t1 != null && e.t1.tick >= this.tick) continue;
+ if (e.t2 != null && e.t2.tick >= this.tick) continue;
+ if (!e.locked()) continue;
+ if ((e.t1==null || !e.t1.in) && (e.t2==null || !e.t2.in)) continue;
+ Point p1 = e.v(1).multiply(a);
+ Point p2 = e.v(2).multiply(a);
+ Vertex v1=null, v2=null;
+ v1 = m.vertex(p1);
+ v2 = m.vertex(p2);
+ if (v1==v2) continue;
+ m.getEdge(v1, v2).lock(v1, 0);
}
+ break;
}
- //#end
}
- break;
+ t.tick = this.tick;
+ for(int i=1; i<=3; i++) {
+ Triangle ti = t.t(i);
+ if (ti == null) continue;
+ if (ti.tick >= this.tick) continue;
+ iter[numiter++] = ti;
+ }
}
- if (!good) throw new Error("couldn't figure out where to put " + s(v));
- fixup(vec, v);
- return v;
}
- public void fixup(Vector vec, Vertex v) {
- while(vec.size() > 0) {
- Triangle t = (Triangle)vec.lastElement();
- vec.setSize(vec.size() - 1);
- if (t.deleted) continue;
- //if (t.wind(t.nextVertex(v), t.prevVertex(v)) != 0) continue; // FIXME
- Triangle to = t.opposingTriangle(v);
- if (to==null) continue; //throw new Error("fixup invoked with a triangle which does not have me as a vertex");
- if (to.deleted) throw new Error("v should not happen");
- if (to.r < distance(v,to.ccx, to.ccy)) continue;
- Vertex v2 = to.opposingVertex(t);
- t.delete();
- to.delete();
- vec.addElement(newTriangle(v, t.nextVertex(v), v2, "fixup"));
- vec.addElement(newTriangle(v, t.prevVertex(v), v2, "fixup"));
- }
+ public void clipOp(Mesh m, Affine a, boolean subtract) {
+ seekTime = 0;
+ long start = System.currentTimeMillis();
+ m.add(this, a);
+ iterateTriangles(subtract ? ITERATE_SUBTRACT : ITERATE_INTERSECT, m, a.inverse());
+ float total = (float)((System.currentTimeMillis() - start));
+ float seek = (float)seekTime;
+ if (total > 80) System.out.println("clip in " + (100 * (seek/total)) + "%");
}
- // Static //////////////////////////////////////////////////////////////////////////////
-
- public Triangle newTriangle(Vertex v1, Vertex v2, Vertex v3, String source) {
- if (v1==v2 || v2==v3 || v3==v1) throw new Error("identical vertices");
- for(int i=0; i<triangles.size(); i++) {
- Triangle t = (Triangle)triangles.elementAt(i);
- if (t.v1==v1&&t.v2==v2&&t.v3==v3) return t;
- if (t.v1==v1&&t.v2==v3&&t.v3==v2) return t;
- if (t.v1==v2&&t.v2==v3&&t.v3==v1) return t;
- if (t.v1==v2&&t.v2==v1&&t.v3==v3) return t;
- if (t.v1==v3&&t.v2==v1&&t.v3==v2) return t;
- if (t.v1==v3&&t.v2==v2&&t.v3==v1) return t;
- }
- Triangle t = new Triangle(source, v1, v2, v3, false, false);
- if (debug) checktri();
- return t;
+ // Geometry //////////////////////////////////////////////////////////////////////////////
+
+ public static double ddistance(double x1, double y1, double x2, double y2) {
+ return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));}
+ public static float area(Point p1, Point p2, Point p3) {
+ float x1 = p1.x;
+ float x2 = p2.x;
+ float x3 = p3.x;
+ float y1 = p1.y;
+ float y2 = p2.y;
+ float y3 = p3.y;
+ double a = ddistance(x1,y1,x2,y2);
+ double b = ddistance(x2,y2,x3,y3);
+ double c = ddistance(x3,y3,x1,y1);
+ double s = (a+b+c)/2;
+ double t = s*(s-a)*(s-b)*(s-c);
+ if (t < 0) return 0;
+ return (float)Math.sqrt(t);
}
- public void checktri() {
- for(int i=0; i<triangles.size(); i++) {
- Triangle t = (Triangle)triangles.elementAt(i);
- if (t.t12 != null && (t.t12.t12 != t && t.t12.t23 != t && t.t12.t31 != t)) throw new Error("t12");
- if (t.t23 != null && (t.t23.t12 != t && t.t23.t23 != t && t.t23.t31 != t)) throw new Error("t23");
- if (t.t31 != null && (t.t31.t12 != t && t.t31.t23 != t && t.t31.t31 != t)) throw new Error("t31");
- for(int j=0; j<triangles.size(); j++) {
- Triangle t2 = (Triangle)triangles.elementAt(j);
- if (t2==t) continue;
- if (t.v1==t2.v1&&t.v2==t2.v2&&t.v3==t2.v3) throw new Error("poo");
- if (t.v1==t2.v1&&t.v2==t2.v3&&t.v3==t2.v2) throw new Error("poo");
- if (t.v1==t2.v2&&t.v2==t2.v3&&t.v3==t2.v1) throw new Error("poo");
- if (t.v1==t2.v2&&t.v2==t2.v1&&t.v3==t2.v3) throw new Error("poo");
- if (t.v1==t2.v3&&t.v2==t2.v1&&t.v3==t2.v2) throw new Error("poo");
- if (t.v1==t2.v3&&t.v2==t2.v2&&t.v3==t2.v1) throw new Error("poo");
- }
- }
+ public Point intersect(Point v1, Point v2, Point v3, Point v4) {
+ double a1 = v2.y-v1.y;
+ double a2 = v4.y-v3.y;
+ double b1 = v1.x-v2.x;
+ double b2 = v3.x-v4.x;
+ double c1 = -1 * (a1*v1.x+b1*v1.y);
+ double c2 = -1 * (a2*v3.x+b2*v3.y);
+ double x = (b2*c1-c2*b1)/(b1*a2-b2*a1);
+ double y = (a2*c1-c2*a1)/(a1*b2-a2*b1);
+ if (Double.isNaN(x) || Double.isNaN(y)) throw new Error("cannot intersect:\n ");
+ return point((float)x,(float)y);
+ }
+
+ public static int side(Point p1, Point p2, Point p3) {
+ float x0 = p1.x;
+ float x = p2.x;
+ float x2 = p3.x;
+ float y0 = p1.y;
+ float y = p2.y;
+ float y2 = p3.y;
+ // this MUST be done to double precision
+ double a = y-y0, b = x0-x, c = a*(x0 - x2) + b*(y0 - y2);
+ if (c > 0) return b>=0 ? -1 : 1;
+ if (c < 0) return b>=0 ? 1 : -1;
+ return 0;
}
// Vertex //////////////////////////////////////////////////////////////////////////////
- public boolean triangulate(Vertex vv, HashSet orphans, Vertex v, boolean first) {
- if (first) {
- HashSet left = new HashSet();
- HashSet right = new HashSet();
- for(Iterator it=orphans.iterator(); it.hasNext();) {
- Vertex o = ((Integer)it.next()).intValue();
- if (o==v||o==vv) continue;
- if (side(vv, v, o) == -1) left.add(new Integer(o));
- else if (side(vv, v, o) == 1) right.add(new Integer(o));
- else throw new Error("impossible "+vv+" "+v + " " + o);
- }
- triangulate(vv, left, v, false);
- triangulate(v, right, vv, false);
- return false;
- }
- Vertex farthest = NULLVERTEX;
- float dist = 0;
- if (orphans.size()==0) return true;
- Vertex o = ((Integer)orphans.iterator().next()).intValue();
- if (orphans.size()==1) {
- Triangle t = newTriangle(vv, v, o, "triangulate2 " + v + " " + vv);
- if (((t.v1==vv && t.v2==v)||(t.v1==v && t.v2==vv)) && t.t12==null) return true;
- if (((t.v3==vv && t.v2==v)||(t.v3==v && t.v2==vv)) && t.t23==null) return true;
- if (((t.v1==vv && t.v3==v)||(t.v1==v && t.v3==vv)) && t.t31==null) return true;
- return false;
+ public Vertex vertex(Point p, Affine a) { return vertex(p.multiply(a)); }
+ public Vertex vertex(Point p) {
+ Vertex ret = null;
+ switch(numvertices) {
+ case 0: return (vertex0 = new Vertex(p));
+ case 1: return vertex0.distance(p)<=epsilon ? vertex0 : (vertex1 = new Vertex(p));
+ case 2: {
+ if (vertex0.distance(p)<=epsilon) return vertex0;
+ if (vertex1.distance(p)<=epsilon) return vertex1;
+ Vertex v2 = new Vertex(p);
+ triangle(newEdge(vertex0,vertex1), newEdge(vertex1,v2), newEdge(v2,vertex0));
+ return v2;
}
-
- Vertex best = NULLVERTEX;
- OUTER: for(Iterator it=orphans.iterator(); it.hasNext();) {
- o = ((Integer)it.next()).intValue();
- if (o==v) continue;
- Triangle t = new Triangle("temp", vv, v, o, true);
- for(Iterator it2=orphans.iterator(); it2.hasNext();) {
- Vertex z = ((Integer)it2.next()).intValue();
- if (z==o) continue;
- if (z==v) continue;
- if (z==vv) continue;
- if (distance(z,t.ccx,t.ccy) < t.r || t.contains(z)) continue OUTER;
- }
- if (best==NULLVERTEX || new Triangle("temp",vv,v,best,true).area() > new Triangle("temp",vv,v,o,true).area())
- best = o;
+ default: {
+ Triangle t = null;
+ t = triangle0.seek(p);
+ for(int i=1; i<=3; i++)
+ for(int j=1; j<=2; j++)
+ if (t != null && t.e(i).v(j).distance(p)<=epsilon) return t.e(i).v(j);
+ Vertex v = new Vertex(p);
+ if (t.e(3).intersects(p)) t.e(3).bisect(v);
+ else if (t.e(1).intersects(p)) t.e(1).bisect(v);
+ else if (t.e(2).intersects(p)) t.e(2).bisect(v);
+ else if (t.contains(v)) t.trisect(v);
+ else t.addHull(v);
+ return v;
}
- if (best==NULLVERTEX) throw new Error("notgood, #orphans = " + orphans.size());
- o = best;
- HashSet left = new HashSet();
- HashSet right = new HashSet();
- for(Iterator it2=orphans.iterator(); it2.hasNext();) {
- Vertex x = ((Integer)it2.next()).intValue();
- if (o==x||vv==x||v==x) continue;
- int side_of_x = side(o,(x(vv)+x(v))/2,(y(vv)+y(v))/2,x);
- int side_of_v = side(o,(x(vv)+x(v))/2,(y(vv)+y(v))/2,v);
- int side_of_vv = side(o,(x(vv)+x(v))/2,(y(vv)+y(v))/2,vv);
- if (side_of_x==side_of_vv && side_of_vv!=0) right.add(new Integer(x));
- else if (side_of_x==side_of_v && side_of_v!=0) left.add(new Integer(x));
- else throw new Error("impossible "+vv+" "+v + " " + o + " ==> " + x);
- }
- boolean doit = true;
- doit &= triangulate(o, left, v, false);
- doit &= triangulate(o, right, vv, false);
- if (doit) {
- Triangle t = newTriangle(v, vv, o,"triangulate 0/0");
- if (((t.v1==vv && t.v2==v)||(t.v1==v && t.v2==vv)) && t.t12==null) return true;
- if (((t.v3==vv && t.v2==v)||(t.v3==v && t.v2==vv)) && t.t23==null) return true;
- if (((t.v1==vv && t.v3==v)||(t.v1==v && t.v3==vv)) && t.t31==null) return true;
- return false;
- }
- return true;
}
+ }
- public void force() {
- while(true) {
- boolean redo = false;
- for(int k=0; k<numvertices; k++) {
- Vertex v = k;
- redo |= force(v);
- }
- if (!redo) break;
+ private Point point(float x, float y) { return new Point(x,y); }
+ private Point point(Point a, Point b) { return new Point((a.x+b.x)/2,(a.y+b.y)/2); }
+ private Point point(Point p, Affine a) { return point(p.x(a), p.y(a)); }
+ private class Point {
+ public float x;
+ public float y;
+ public String toString() { return "("+x+","+y+")"; }
+ public Point multiply(Affine a) { return point(x(a),y(a)); }
+ public Point(float x, float y) { this.x = x; this.y = y; }
+ public Point(Point p) { this(p.x,p.y); }
+ public boolean equals(float x, float y) { return distance(x,y) <= epsilon; }
+ public boolean equals(Object o) { return (!(o instanceof Point)) ? false : ((Point)o).distance(this) <= epsilon; }
+ public float distance(Point v) { return distance(v.x,v.y); }
+ private float distance(float x, float y) { return (float)Math.sqrt(distance2(x, y)); }
+ public float distance2(Point v) { return distance2(v.x, v.y); }
+ private float distance2(float x, float y) { return (this.x-x)*(this.x-x)+(this.y-y)*(this.y-y); }
+ public float x(Affine a) { return a.multiply_px(x,y); }
+ public float y(Affine a) { return a.multiply_py(x,y); }
+ public int xi(Affine a) { return (int)x(a); }
+ public int yi(Affine a) { return (int)y(a); }
+ public boolean intersects(Point p1, Point p2) {
+ return
+ Mesh.side(p1,p2,this)==0 &&
+ x <= Math.max(p1.x,p2.x) &&
+ x >= Math.min(p1.x,p2.x) &&
+ y <= Math.max(p1.y,p2.y) &&
+ y >= Math.min(p1.y,p2.y);
}
}
- public boolean force(Vertex vv) {
- boolean ret = false;
- OUTER: for(Iterator it=next(vv).iterator(); it.hasNext();) {
- Vertex v = ((Integer)it.next()).intValue();
- for(int k=0; k<numvertices; k++) {
- Vertex v2 = k;
- if (v2==vv||v2==v) continue;
- //if (next(vv).contains(v2) || next(v2).contains(vv)) continue;
- if (isect(v,vv,v2)) {
- if (debug) Log.debug(Mesh.class,"breaking line " + vv+"-"+v + " at vertex " + v2);
- next(vv).remove(new Integer(v));
- next(vv).add(new Integer(v2));
- next(v2).add(new Integer(v));
- ret = true;
- break OUTER;
- }
- }
- boolean good = false;
- for (int i=0; i<triangles.size(); i++)
- if (((Triangle)triangles.elementAt(i)).hasEdge(vv,v)) { good = true; break; }
- if (good) continue;
- HashSet orphans = new HashSet();
- for (int i=0; i<triangles.size(); i++) {
- Triangle t = ((Triangle)triangles.elementAt(i));
- if (t.deleted) continue;
- if (t.intersectsSegment(vv, v)) {
- if (debug) Log.debug(Mesh.class,"removing triangle " + t + " because it intersects segment " + vv+"-"+v);
- Vector vec = new Vector();
- orphans.add(new Integer(t.v1));
- orphans.add(new Integer(t.v2));
- orphans.add(new Integer(t.v3));
- orphans.remove(new Integer(v));
- orphans.remove(new Integer(vv));
- t.delete();
- i--;
- ret = true;
- }
- }
- orphans.remove(new Integer(vv));
- orphans.remove(new Integer(v));
- triangulate(vv, orphans, v, true);
- break;
+
+ private final class Vertex extends Point implements org.ibex.arenaj.Gladiator {
+ public Vertex(Point p) { super(p); numvertices++; }
+ }
+
+ // Edge //////////////////////////////////////////////////////////////////////////////
+
+ public Edge newEdge(Vertex v1, Vertex v2) {
+ return getEdge(v1,v2);
+ /*
+ if (v1==v2) throw new Error();
+ Edge ret = (Edge)edges.get(v1,v2);
+ //if (ret != null) throw new Error("tried to get an edge that already exists!");
+ if (ret == null) ret = new Edge(v1,v2);
+ return ret;
+ */
+ }
+
+ public Edge getEdge(Vertex v1, Vertex v2) {
+ if (v1==v2) throw new Error();
+ //Edge ret = (Edge)edges.get(v1,v2);
+ Edge ret = null;
+ Triangle t = null;
+ if (triangle0 != null) {
+ t = triangle0.seek(point(v1,v2));
+ if (t != null)
+ for(int i=1; i<=3; i++)
+ if (t.e(i).hasVertex(v1) && t.e(i).hasVertex(v2)) ret = t.e(i);
}
+ if (ret == null) {
+ ret = (Edge)edges.get(v1,v2);
+ if (ret != null && (ret.t1 != null || ret.t2 != null)) throw new Error("bah! " + ret);
+ }
+ if (ret == null) ret = new Edge(v1,v2);
return ret;
}
- public void makeNonDegenerate() {
- while(true) {
- boolean redo = false;
- for(int k=0; k<numvertices; k++) {
- Vector vec = new Vector();
- Vertex vx = k;
- redo |= makeNonDegenerate(vec, vx);
+ private final class Edge implements org.ibex.arenaj.Gladiator {
+ private final Vertex v1;
+ private final Vertex v2;
+ Triangle t1 = null;
+ Triangle t2 = null;
+
+ private int locks = 0;
+ private int weight = 0;
+
+ public void delete() {
+ if (t1!=null || t2!=null) throw new Error("tried to remove an edge before its triangles");
+ edges.put(v1,v2,null);
+ edges.put(v2,v1,null);
+ }
+
+ public Vertex v(int i) { return i==1?v1:i==2?v2:null; }
+
+ public Edge rotate(Vertex v, boolean clockwise) {
+ Triangle t = v==v1 ? (clockwise?t1:t2) : v==v2 ? (clockwise?t2:t1) : null;
+ if (t==null) return null;
+ for(int i=1; i<=3; i++) if (t.e(i)!=this && t.e(i).hasVertex(v)) return t.e(i);
+ return null;
+ }
+ public Edge rotateHull(boolean clockwise) {
+ if (t1!=null && t2!=null) throw new Error("nextHull() called on non-hull edge");
+ Vertex v = rotate(v1, !clockwise) == null ? v2 : v1;
+ Edge e = rotate(v, !clockwise);
+ while(!e.hasTriangle(null) && e!=this) e = e.rotate(v, !clockwise);
+ if (e==this) throw new Error("confused");
+ return e;
+ }
+
+ public boolean isNear(Point p) { return area(v1,v2,p) < epsilon2; }
+ public Vertex commonVertex(Edge e) { return v1==e.v(1) || v1==e.v(2) ? v1 : v2==e.v(1) || v2==e.v(2) ? v2 : null; }
+ public Vertex unCommonVertex(Edge e) { return v1!=e.v(1) && v1!=e.v(2) ? v1 : v2!=e.v(1) && v2!=e.v(2) ? v2 : null; }
+ public Vertex opposingVertex(Vertex v) { return v1==v ? v2 : v1; }
+ public int weight() { return weight; }
+ public int weight(Vertex v) { return v==v1?weight:(-1*weight); }
+ public boolean locked() { return locks > 0; }
+ public boolean partitions(Point va, Point vb) { return side(va,vb)==-1; }
+ public int side(Point a, Point b) { return side(a) * side(b); }
+ public int side(Point a) { return Mesh.side(v(1), v(2), a); }
+ public boolean hasVertex(Vertex v) { return v1==v || v2==v; }
+ public boolean hasTriangle(Triangle t) { return t==t1 || t==t2; }
+ public String toString() { return v(1) + "--" + v(2); }
+ public void rmTriangle(Triangle t) {
+ if (t1==t) t1 = null;
+ else if (t2==t) t2 = null;
+ else throw new Error();
+ if (t1==null && t2==null) delete();
+ }
+ public boolean convex() { return this.intersects(t1.opposingVertex(t2), t2.opposingVertex(t1)); }
+
+ public boolean colinear(Point v) { return area(v,v1,v2)<=epsilon; }
+
+ public boolean intersects(Point p) {
+ return
+ side(p)==0 &&
+ p.x <= Math.max(v1.x,v2.x) &&
+ p.x >= Math.min(v1.x,v2.x) &&
+ p.y <= Math.max(v1.y,v2.y) &&
+ p.y >= Math.min(v1.y,v2.y);
+ }
+ public boolean intersects(Edge e) { return intersects(e.v(1), e.v(2)); }
+ public boolean intersects(Point va, Point vb) {
+ return
+ !v1.equals(va) &&
+ !v1.equals(vb) &&
+ !v2.equals(va) &&
+ !v2.equals(vb) &&
+ partitions(va, vb) &&
+ Mesh.side(va, vb, v1) * Mesh.side(va, vb, v2) == -1;
+ }
+ public Triangle opposingTriangle(Triangle t) {
+ if (t1 == t) return t2;
+ if (t2 == t) return t1;
+ throw new Error();
+ }
+ public void addTriangle(Triangle tnew) {
+ if (t1==null) t1 = tnew;
+ else if (t2==null) t2 = tnew;
+ else throw new Error("attempted to addTriangle("+tnew+")\n t1="+t1+"\n t2="+t2);
+ if (t1==t2) throw new Error("same triangle can't be both sides of an edge");
+ if (v1.x==v2.x) {
+ boolean b = side(t1.opposingVertex(this)) == side(point(Float.MAX_VALUE, v1.y));
+ Triangle right = b ? t1 : t2; // right side
+ Triangle left = b ? t2 : t1; // left side
+ t1 = right;
+ t2 = left;
+ } else {
+ boolean b = side(t1.opposingVertex(this)) == side(point(0, Float.MAX_VALUE));
+ Triangle top = b ? t1 : t2;
+ Triangle bottom = b ? t2 : t1;
+ if (v1.y==v2.y) { // horizontal
+ t1 = bottom;
+ t2 = top;
+ } else if (v1.x > v2.x) { // positive slope
+ t1 = top;
+ t2 = bottom;
+ } else { // negative slope
+ t1 = bottom;
+ t2 = top;
+ }
}
- if (!redo) break;
}
- }
- public boolean makeNonDegenerate(Vector vec, Vertex v1) {
- for(int i2 = 0; i2<next(v1).size(); i2++) {
- Vertex v2 = ((Integer)next(v1).get(i2)).intValue();
- for(int i3 = 0; i3<numvertices; i3++) {
- Vertex v3 = i3;
- for(int i4=0; i4<next(v3).size(); i4++) {
- Vertex v4 = ((Integer)next(v3).get(i4)).intValue();
- if (v1==v3||v1==v4||v2==v3||v2==v4) continue;
- if (isect(v1,v2,v3,v4)) {
- float a1 = y(v2)-y(v1);
- float a2 = y(v4)-y(v3);
- float b1 = x(v1)-x(v2);
- float b2 = x(v3)-x(v4);
- float c1 = -1 * (a1*x(v1)+b1*y(v1));
- float c2 = -1 * (a2*x(v3)+b2*y(v3));
- // a1x+b1y+c1=0
- // y=-(a1x+c1)/b1
- // a2x-(a1x+c1)(b2/b1)+c2=0
- // a2b1x-b2(a1x+c1)+b1c2=0
- // a2b1x-a1b2x-b2c1+b1c2=0
- // x(a2b1-a1b2)-b2c1+b1c2=0
- // x(a2b1-a1b2)=b2c1-b1c2
- // x=(b2c1-b1c2)/(a2b1-a1b2)
- float xq = (b2*c1-c2*b1)/(b1*a2-b2*a1);
- Vertex v0 = newVertex(xq, -1 * (a1*xq+c1) / b1);
- //if (v0==v1||v0==v2||v0==v3||v0==v4) continue;
- if (debug) Log.debug(this,"inserting new vertex " + v0+" between " + v1+"-"+v2 +" and "+ v3+"-"+v4);
- next(v1).remove(new Integer(v2));
- next(v1).add(new Integer(v0));
- next(v0).add(new Integer(v2));
- next(v3).remove(new Integer(v4));
- next(v3).add(new Integer(v0));
- next(v0).add(new Integer(v4));
- return true;
+ public void bisect(Vertex v) {
+ Edge e = this;
+ Triangle t1 = this.t1==null?this.t2:this.t1;
+ Triangle t = t1==this.t1?this.t2:this.t1;
+ Vertex opposing = t1.opposingVertex(e);
+ Triangle top = null, ton = null;
+ Vertex left = e.v(1);
+ Vertex right = e.v(2);
+ Vertex tov = null;
+ boolean in1 = t1.in;
+ boolean in2 = false;
+ Triangle opposingTriangleLeft = t1.opposingTriangle(left);
+ Triangle opposingTriangleRight = t1.opposingTriangle(right);
+ Edge right_v = newEdge(right, v);
+ Edge left_v = newEdge(left, v);
+ Edge opposing_v = newEdge(opposing, v);
+ Edge tov_v = null;
+ Edge right_tov = null;
+ Edge left_tov = null;
+ Edge right_opposing = t1.opposingEdge(left);
+ Edge left_opposing = t1.opposingEdge(right);
+ if (t != null) {
+ t.check();
+ right_tov = t.opposingEdge(left);
+ left_tov = t.opposingEdge(right);
+ top = t.opposingTriangle(left);
+ ton = t.opposingTriangle(right);
+ tov = t.opposingVertex(t1);
+ in2 = t.in;
+ tov_v = newEdge(tov, v);
+ if (top == t1) top = null;
+ if (ton == t1) ton = null;
+ if (opposingTriangleLeft == t) opposingTriangleLeft = null;
+ if (opposingTriangleRight == t) opposingTriangleRight = null;
+ t.delete();
+ }
+ t1.delete();
+ Triangle ta, tb, tc, td;
+ ta = triangle(right_opposing, opposing_v, right_v);
+ tb = triangle(left_opposing, opposing_v, left_v);
+ ta.in = in1;
+ tb.in = in1;
+ if (t != null) {
+ tc = triangle(left_tov, tov_v, left_v);
+ td = triangle(right_tov, tov_v, right_v);
+ tc.in = in2;
+ td.in = in2;
+ }
+ if (locked()) fracture(v);
+ else ta.fixup();
+ }
+ public Edge flip() {
+ if (locked()) throw new Error("attempted to remove a locked edge: " + this);
+ boolean in = t1.in && t2.in;
+
+ Edge e3 = rotate(v1, true);
+ Vertex vb = e3.unCommonVertex(this);
+ Edge e6 = e3.rotate(vb, true);
+
+ Edge e4 = rotate(v2, true);
+ Vertex va = e4.unCommonVertex(this);
+ Edge e1 = e4.rotate(va, true);
+
+ Edge e = newEdge(va, vb);
+
+ t1.delete();
+ t2.delete();
+ Triangle ta, tb;
+ ta = triangle(e1, e, e3);
+ tb = triangle(e4, e, e6);
+ ta.in = in;
+ tb.in = in;
+ return ta.getSharedEdge(tb);
+ }
+ public void fracture(Vertex vx) {
+ if (!locked()) throw new Error("attempt to fracture an edge which does not exist: " + v1 + " " + v2);
+ // delete-me
+ Edge v1vx = newEdge(v1, vx);
+ Edge vxv2 = newEdge(vx, v2);
+ v1vx.locks += locks;
+ vxv2.locks += locks;
+ locks = 0;
+ v1vx.weight += v(1)==v1vx.v(1) ? weight : (-1 * weight);
+ vxv2.weight += v(2)==vxv2.v(2) ? weight : (-1 * weight);
+ weight = 0;
+ v1vx.lock();
+ vxv2.lock();
+ }
+ public void fracture(Edge e) {
+ triangle0=e.t1==null?e.t2:e.t1;
+ Vertex v0 = vertex(Mesh.this.intersect(v1,v2,e.v(1),e.v(2)));
+ if (v0 != e.v(1) && v0 != e.v(2) && e.locked()) e.fracture(v0);
+ if (v0 != v1 && v0 != v2) fracture(v0);
+ }
+ public void lock(Vertex v1, int delta) {
+ weight += this.v(1)==v1 ? delta : (-1 * delta);
+ locks += 1;
+ lock();
+ }
+ public void lock() {
+ Triangle t = t1==null ? t2 : t1;
+ if (t==null) t = triangle0.seek(v1);
+ if (!t.hasVertex(v1)) throw new Error("this sucks balls");
+ boolean skipfo = false;
+ for(Triangle told = null; t != told; t = told==null ? t : t.followVector(v1,v2)) {
+ told = t;
+ if (!t.encounters(v1,v2)) break;
+ if (!t.encounters(v2,v1)) break;
+ Triangle tlast = t.followVector(v2,v1);
+ if (tlast == null) throw new Error("seek from: " + tlast + "\n " + v1 + " -> " + v2);
+ if (tlast == t) { if (t.hasVertex(v1)) continue; throw new Error("no predecessor"); }
+ Edge e = t.getSharedEdge(tlast);
+ if (!e.convex()) continue;
+ if (e.v(1)==v1 || e.v(1)==v2 || e.v(2)==v1 || e.v(2)==v2) { continue; }
+ if (this.intersects(e.v(1))) { fracture(e.v(1)); return; }
+ if (this.intersects(e.v(2))) { fracture(e.v(2)); return; }
+ if (!this.intersects(e)) continue;
+ if (e.locked()) {
+ fracture(e);
+ return;
+ } else {
+ Edge eold = e = e.flip();
+ t = e.t1;
+ if (t==null || !t.intersects(this)) t = e.t2;
+ told = t;
+ if (eold.intersects(this)) {
+ t = t.followVector(v1,v2);
+ if (t != e.t1 && t != e.t2) t = told;
+ continue;
+ } else {
+ told = null;
+ while(t.intersects(this)) {
+ if (t==told) break;
+ told = t;
+ t = t.followVector(v2,v1);
+ }
+ t = told;
+ told = null;
+ continue;
}
}
}
+ if (t1!=null) t1.fixup();
+ if (t2!=null) t2.fixup();
+ }
+
+ public void stroke(PixelBuffer buf, Affine a, int color) {
+ int c = debug
+ ? (weight() == 0 ? color : 0xffff0000)
+ : (weight() != 0 ? color : 0);
+ if (c != 0) buf.drawLine(v1.xi(a), v1.yi(a), v2.xi(a), v2.yi(a), c);
+ }
+ public Edge(Vertex v1, Vertex v2) {
+ boolean b = v1.y < v2.y || (v1.y==v2.y && v1.x < v2.x);
+ this.v1 = b ? v1 : v2;
+ this.v2 = b ? v2 : v1;
+ edges.put(v1, v2, this);
+ edges.put(v2, v1, this);
}
- return false;
}
// Triangle //////////////////////////////////////////////////////////////////////////////
- private final class Triangle {
- Triangle t12=null, t23=null, t31=null;
- final Vertex v1, v2, v3;
+ public Triangle triangle(Edge e1, Edge e2, Edge e3) {
+ float x = (e1.v(1).x+e1.v(2).x+e2.v(1).x+e2.v(2).x+e3.v(1).x+e3.v(2).x)/6;
+ float y = (e1.v(1).y+e1.v(2).y+e2.v(1).y+e2.v(2).y+e3.v(1).y+e3.v(2).y)/6;
+ Point p = point(x,y);
+ Triangle t = triangle0==null ? null : triangle0.seek(p);
+ if (t != null &&
+ (t.contains(p) || t.intersects(p)) &&
+ t.hasEdge(e1) &&
+ t.hasEdge(e2) &&
+ t.hasEdge(e3))
+ return triangle0 = t;
+ t = new Triangle(e1, e2, e3);
+ if (debug) t.check();
+ if (triangle0 == null) triangle0 = t;
+ return t;
+ }
+
+ public static boolean fixing = false;
+ private final class Triangle implements org.ibex.arenaj.Gladiator {
+
+ final float r2;
+ final Point cc;
+
+ private Edge e1, e2, e3; // should be final =(
+ public int tick;
+
boolean in = false;
- boolean deleted = false;
+ boolean inWasSet = false;
boolean painted = false;
- boolean special = false;
- final String source;
- final float ccx, ccy, r;
-
- public boolean hasEdge(Vertex a, Vertex b) { return a!=b && (a==v1||a==v2||a==v3) && (b==v1||b==v2||b==v3); }
- public Vertex opposingVertex(Triangle t) { return t12==t ? v3 : t23==t ? v1 : t31==t ? v2 : NULLVERTEX; }
- public Triangle opposingTriangle(Vertex v) { return v1==v ? t23 : v2==v ? t31 : v3==v ? t12 : null; }
- public Vertex nextVertex(Vertex v) { return v1==v ? v2 : v2==v ? v3 : v3==v ? v1 : NULLVERTEX; }
- public Vertex prevVertex(Vertex v) { return v1==v ? v3 : v2==v ? v1 : v3==v ? v2 : NULLVERTEX; }
- public String toString() { return "<<"+v1+""+v2+""+v3+">>"; }
- public boolean intersectsSegment(Vertex a, Vertex b) { return isect(v1,v2,a,b) || isect(v3,v2,a,b) || isect(v1,v3,a,b); }
- public float area() {
- float a = distance(v1,v2);
- float b = distance(v2,v3);
- float c = distance(v3,v1);
- float s = (a+b+c)/2;
- return (float)Math.sqrt(s*(s-a)*(s-b)*(s-c));
- }
-
- public boolean checkSkinny() {
- if (!(r / Math.min(Math.min(distance(v1,v2), distance(v2,v3)), distance(v3,v1)) > B)) return false;
- if (debug) Log.debug(this,"skinny triangle " + this);
- for (Vertex v=0; v<numvertices; v++) {
- for (Iterator nit = next(v).iterator(); nit.hasNext();) {
- Vertex v2 = ((Integer)nit.next()).intValue();
- float midx = (x(v)+x(v2))/2;
- float midy = (y(v)+y(v2))/2;
- if (distance(midx,midy,ccx,ccy) <= distance(v,midx,midy)) {
- if (debug) Log.debug(this," but splitting it would encroach on a segment");
- return false;
- }
+ boolean dirty = true;
+
+ public Edge e(int i) { return i==1?e1:i==2?e2:i==3?e3:null; }
+ public Vertex v(int i) { return e(i==1?2:i==2?3:i==3?1:0).unCommonVertex(e(i)); }
+ public Triangle t(int i) { return e(i).t1==this ? e(i).t2 : e(i).t1; }
+
+ public boolean encounters(Point p1, Point p2) {
+ for(int i=1; i<=3; i++) {
+ if (v(i).equals(p1)) return true;
+ if (v(i).equals(p2)) return true;
+ if (v(i).intersects(p1,p2)) return true;
+ if (e(i).intersects(p1,p2)) return true;
+ }
+ return contains(p1) || contains(p2);
+ }
+ public Edge getSharedEdge(Triangle t) { return e(1).t1==t||e(1).t2==t?e(1):e(2).t1==t||e(2).t2==t?e(2):e(3).t1==t||e(3).t2==t?e(3):null; }
+ public boolean contains(Point p) { return e(1).side(v(1),p)==1 && e(2).side(v(2),p)==1 && e(3).side(v(3),p)==1; }
+ public Point c() { return point(cx(),cy()); }
+ public float cx() { return (float)(((double)v(1).x+(double)v(2).x+(double)v(3).x)/3); }
+ public float cy() { return (float)(((double)v(1).y+(double)v(2).y+(double)v(3).y)/3); }
+ public boolean intersects(Vertex va, Vertex vb){return e(1).intersects(va,vb)||e(2).intersects(va,vb)||e(3).intersects(va,vb);}
+ public boolean intersects(Edge e){ return intersects(e.v(1),e.v(2)); }
+ public boolean intersects(Point p){ return e(1).intersects(p) || e(2).intersects(p) || e(3).intersects(p); }
+ public boolean hasEdge(Edge e) { return e.t1==this || e.t2==this; }
+ public boolean hasEdge(Vertex a, Vertex b) { return a!=b && (a==v(1)||a==v(2)||a==v(3)) && (b==v(1)||b==v(2)||b==v(3)); }
+ public boolean hasVertex(Vertex a) { return a==v(1) || a==v(2) || a==v(3); }
+ public Vertex opposingVertex(Triangle t) { return t(3)==t ? v(3) : t(1)==t ? v(1) : t(2)==t ? v(2) : null; }
+ public Vertex opposingVertex(Edge e) { return e==e(1) ? v(1) : e==e(2) ? v(2) : e==e(3) ? v(3) : null; }
+ public Edge opposingEdge(Vertex v) { return v==v(1) ? e(1) : v==v(2) ? e(2) : v==v(3) ? e(3) : null; }
+ public Triangle opposingTriangle(Vertex v) { return v(1)==v ? t(1) : v(2)==v ? t(2) : v(3)==v ? t(3) : null; }
+ public String toString() { return "<<"+v(1)+""+v(2)+""+v(3)+">>"; }
+
+ public void stroke(PixelBuffer buf, Affine a, int color) {
+ for(int i=1; i<=3; i++) if (in || debug) e(i).stroke(buf, a, color);
+ }
+ public Triangle fixup() {
+ if (!dirty) return this;
+ dirty = false;
+ for(int i=1; i<=3; i++) {
+ Triangle t = t(i);
+ if (t==null) continue;
+ if (t.r2 <= v(i).distance2(t.cc)) continue;
+ Edge e = e(i);
+ if (e.locked()) { t.fixup(); continue; }
+ return e.flip().t1.fixup();
+ }
+ return this;
+ }
+ public void addHull(Vertex vnew) {
+ Edge e = e(1).hasTriangle(null) ? e(1) : e(2).hasTriangle(null) ? e(2) : e(3).hasTriangle(null) ? e(3) : null;
+ Triangle t = e.opposingTriangle(null), newt = null;
+ while (!e.partitions(vnew, t.opposingVertex(e))) {
+ e = e.rotateHull(true);
+ t = e.opposingTriangle(null);
+ }
+ Edge ea = newEdge(e.v(1), vnew);
+ Edge eb = newEdge(e.v(2), vnew);
+ newt = triangle(e, ea, eb);
+ if (ea.rotateHull(true) != eb) { Edge temp = ea; ea = eb; eb = temp; }
+ for(int i=1; i<=2; i++)
+ for(Edge ex = i==1?eb:ea; ;) {
+ e = ex.rotateHull(i==1);
+ t = e.opposingTriangle(null);
+ if (!e.partitions(vnew, t.opposingVertex(e))) break;
+ Edge ep = newEdge(vnew, e.unCommonVertex(ex));
+ newt = triangle(e, ex, ep);
+ ex = ep;
+ }
+ if (newt==null) throw new Error("couldn't find a place to add a triangle for " + vnew);
+ newt.fixup();
+ }
+ public Triangle seek(Point p) {
+ Triangle t = this;
+ try {
+ while (true) {
+ if (t.contains(p) || t.intersects(p)) return t;
+ else if (t.e(3).intersects(p)) return (t.t(3)!=null && t.t(3).contains(p)) ? t.t(3) : t;
+ else if (t.e(1).intersects(p)) return (t.t(1)!=null && t.t(1).contains(p)) ? t.t(1) : t;
+ else if (t.e(2).intersects(p)) return (t.t(2)!=null && t.t(2).contains(p)) ? t.t(2) : t;
+ else {
+ Triangle t2 = t.followVector(t.c(), p);
+ if (t2==null || t2==t) return t;
+ t = t2;
}
}
- newVertex(ccx, ccy);
- return true;
+ } finally { if (t!=null) triangle0 = t; }
}
- public void fill(PixelBuffer buf, Affine a, int color, boolean evenOdd, int count, boolean strokeOnly) {
- if (painted) return;
- if (deleted) throw new Error("gargh!");
- if (!strokeOnly) {
- if (special) {
- buf.fillTriangle((int)a.multiply_px((float)x(v1), (float)y(v1)),
- (int)a.multiply_py((float)x(v1), (float)y(v1)),
- (int)a.multiply_px((float)x(v2), (float)y(v2)),
- (int)a.multiply_py((float)x(v2), (float)y(v2)),
- (int)a.multiply_px((float)x(v3), (float)y(v3)),
- (int)a.multiply_py((float)x(v3), (float)y(v3)),
- 0xff0000ff);
- } else if ((evenOdd && count%2!=0) || (!evenOdd && count!=0)) {
- buf.fillTriangle((int)a.multiply_px((float)x(v1), (float)y(v1)),
- (int)a.multiply_py((float)x(v1), (float)y(v1)),
- (int)a.multiply_px((float)x(v2), (float)y(v2)),
- (int)a.multiply_py((float)x(v2), (float)y(v2)),
- (int)a.multiply_px((float)x(v3), (float)y(v3)),
- (int)a.multiply_py((float)x(v3), (float)y(v3)),
- color);
- } else {
- if (debug)
- buf.fillTriangle((int)a.multiply_px((float)x(v1), (float)y(v1)),
- (int)a.multiply_py((float)x(v1), (float)y(v1)),
- (int)a.multiply_px((float)x(v2), (float)y(v2)),
- (int)a.multiply_py((float)x(v2), (float)y(v2)),
- (int)a.multiply_px((float)x(v3), (float)y(v3)),
- (int)a.multiply_py((float)x(v3), (float)y(v3)),
- 0xff000000 | ((color & 0x00ffffff) >> 8));
+ // gives the triangle across the edge through which the ray v(1)-->v(2) exits this triangle
+ public Triangle followVector(Point p1, Point p2) {
+ Triangle ret = followVector2(p1, p2);
+ if (ret==null) return ret;
+ triangle0 = ret;
+ if (!ret.encounters(p1,p2)) return this;
+ return ret;
+ }
+ public Triangle followVector2(Point p1, Point p2) {
+ if (contains(p2) || intersects(p2) || v(1).equals(p2) || v(2).equals(p2) || v(3).equals(p2)) return this;
+ for(int i=1; i<=3; i++) if (!v(i).equals(p1) && v(i).intersects(p1,p2)) return followVector(v(i),p2);
+ Triangle t1 = t(1);
+ Triangle t2 = t(2);
+ Triangle t3 = t(3);
+ for(int i=1; i<=3; i++) {
+ int k1 = i==1?3:i==2?1:i==3?2:0;
+ int k2 = i==1?2:i==2?3:i==3?1:0;
+ int k3 = i==1?1:i==2?2:i==3?3:0;
+ if (v(i).equals(p1)) {
+ if (e(k1).partitions(v(k1),p2)) return t(k1);
+ if (e(k2).partitions(v(k2),p2)) return t(k2);
+ if (e(k3).partitions(v(k3),p2)) return t(k3);
+ throw new Error("bad!");
}
}
- painted = true;
- //#repeat t12/t23/t31 v1/v2/v3 v2/v3/v1
- if (t12 != null && !t12.painted) {
- t12.fill(buf, a, color, evenOdd, count + wind(v1, v2), strokeOnly);
- if (debug)
- drawLine(buf, (x(v1)*2+x(v2))/3, (y(v1)*2+y(v2))/3, (x(v1)+2*x(v2))/3, (y(v1)+2*y(v2))/3, a,
- wind(v2,v1)==0?0xff000000:0xff0000ff);
+ if (!e(1).intersects(p1,p2) && !e(2).intersects(p1,p2) && !e(3).intersects(p1,p2))
+ throw new Error("invoked followVector() on a Triangle which it does not encounter:\n" +
+ " p1=" + p1 + "\n" +
+ " p2=" + p2 + "\n" +
+ " t =" + this + " (area "+area(v(1),v(2),v(3))+")\n");
+ for(int i=1; i<=3; i++) if (e(i).intersects(p1,p2) && e(i).side(v(i)) * e(i).side(p2) == -1) return t(i);
+ throw new Error("giving up: \n "+p1+" -> "+p2+"\n " + this);
+ }
+
+ public void check() {
+ if (debug) {
+ for(int i=1; i<=3; i++) {
+ if (e(i).v(1) != v(1) && e(i).v(1) != v(2) && e(i).v(1) != v(3)) throw new Error("inconsistent");
+ if (e(i).t1 != this && e(i).t2 != this) throw new Error("inconsistent");
+ if (e(i).t1 == e(i).t2) throw new Error("same triangle on both sides of edge");
+ }
+ if (e(1)==e(2) || e(2)==e(3) || e(3)==e(1)) throw new Error("identical edges");
+ for(int i=1; i<=3; i++) {
+ if (t(i) != null) if (!t(i).hasEdge(e(i))) throw new Error("t1 doesn't have e(1)");
+ if (t(i) != null) {
+ if (t(i).getSharedEdge(this) != e(i)) throw new Error("blark");
+ if (!e(i).hasTriangle(t(i))) throw new Error("blark2");
+ if (!e(i).hasTriangle(this)) throw new Error("blark3");
+ }
+ }
+ // check that edges all join up
}
- //#end
}
- public int wind(Vertex a, Vertex b) {
- if (next(a).contains(new Integer(b)) && next(b).contains(new Integer(a))) return 0;
- if (y(a) < y(b) || (y(a)==y(b) && x(a)<x(b))) return wind(b, a);
- if (next(a).contains(new Integer(b))) return 1;
- if (next(b).contains(new Integer(a))) return -1;
- return 0;
+
+ public void trisect(Vertex v) {
+ if (!contains(v)) throw new Error("trisect(v) but I don't contain v = " + v);
+ if (hasVertex(v)) throw new Error("attempt to trisect a triangle at one of its own vertices");
+ for(int i=3; i>0; i--) if (e(i).isNear(v)) { e(i).bisect(v); return; }
+ Triangle a=null,b=null,c=null;
+
+ boolean oldIn = in;
+ Edge v1v = newEdge(v(1), v);
+ Edge v2v = newEdge(v(2), v);
+ Edge v3v = newEdge(v(3), v);
+ Edge e1 = this.e(1);
+ Edge e2 = this.e(2);
+ Edge e3 = this.e(3);
+ delete();
+
+ a = triangle(e3, v1v, v2v);
+ b = triangle(e2, v1v, v3v);
+ c = triangle(e1, v3v, v2v);
+ a.in = oldIn;
+ b.in = oldIn;
+ c.in = oldIn;
+ a.fixup();
}
- public void clear() {
- if (!painted) return;
- painted = false;
- if (t12 != null) t12.clear();
- if (t23 != null) t23.clear();
- if (t31 != null) t31.clear();
- }
- public Triangle(String source, Vertex v1, Vertex v2, Vertex v3) { this(source, v1, v2, v3, false, false); }
- public Triangle(String source, Vertex v1, Vertex v2, Vertex v3, boolean fake) { this(source, v1,v2,v3,fake,false); }
- public Triangle(String source, Vertex v1, Vertex v2, Vertex v3, boolean fake, boolean ignoreProblems) {
- this.source = source;
+
+ public void setIn(boolean evenOdd, int weight) {
+ if (inWasSet) return;
+ inWasSet = true;
+ in = (evenOdd && weight%2!=0) || (!evenOdd && weight!=0);
+ for(int i=1; i<=3; i++) if (t(i) != null) t(i).setIn(evenOdd, weight + e(i).weight());
+ }
+
+ public void fill(PixelBuffer buf, Affine a, Mesh.Chain clip, int color, boolean strokeOnly) {
+ if (painted) return;
+ painted = true;
+ if (in) buf.fillTriangle(v(1).xi(a), v(1).yi(a), v(2).xi(a), v(2).yi(a), v(3).xi(a), v(3).yi(a), color);
+ for(int i=1; i<=3; i++)
+ if (t(i) != null) {
+ boolean prepaint = t(i).painted;
+ if (debug) e(i).stroke(buf, a, color);
+ t(i).fill(buf, a, clip, color, strokeOnly);
+ }
+ }
+
+ public Triangle(Edge e1, Edge e2, Edge e3) {
+ this.e1 = e1;
+ this.e2 = e2;
+ this.e3 = e3;
+ Vertex v1 = e(2).unCommonVertex(e(1));
+ Vertex v2 = e(3).unCommonVertex(e(2));
+ Vertex v3 = e(1).unCommonVertex(e(3));
+ if (e(1).intersects(v1)) throw new Error("triangle points are colinear");
+ if (e(2).intersects(v2)) throw new Error("triangle points are colinear");
+ if (e(3).intersects(v3)) throw new Error("triangle points are colinear");
+ e(1).addTriangle(this);
+ e(2).addTriangle(this);
+ e(3).addTriangle(this);
+
float a = 0;
- for(int i=0; i<3; i++) {
- a=(y(v2)-y(v3))*(x(v2)-x(v1))-(y(v2)-y(v1))*(x(v2)-x(v3));
- if (a!=0) break;
- Vertex t = v2; v2=v3; v3=v1; v1 = t;
+ Q: for(int q=0; q<2; q++) {
+ for(int i=0; i<3; i++) {
+ if ((a=(v2.y-v3.y)*(v2.x-v1.x)-(v2.y-v1.y)*(v2.x-v3.x))!=0) break Q;
+ Vertex t = v2; v2=v3; v3=v1; v1 = t;
+ }
+ Vertex t = v2; v2=v3; v3=t;
}
if (a==0) throw new Error("a==0 for " + v1 + " " + v2 + " " + v3);
- this.v1 = v1; this.v2 = v2; this.v3 = v3;
- float a1=(x(v1)+x(v2))*(x(v2)-x(v1))+(y(v2)-y(v1))*(y(v1)+y(v2));
- float a2=(x(v2)+x(v3))*(x(v2)-x(v3))+(y(v2)-y(v3))*(y(v2)+y(v3));
- ccx=(a1*(y(v2)-y(v3))-a2*(y(v2)-y(v1)))/a/2;
- ccy=(a2*(x(v2)-x(v1))-a1*(x(v2)-x(v3)))/a/2;
- r = distance(v1,ccx, ccy);
- if (fake) return;
- for(int i=0; i<triangles.size(); i++) {
- Triangle t = (Triangle)triangles.elementAt(i);
- if ((t.v1==v1&&t.v2==v2)||(t.v1==v2&&t.v2==v1)) { if (t.t12!=null) throw new Error(); t.t12=this; t12=t; }
- if ((t.v1==v2&&t.v2==v3)||(t.v1==v3&&t.v2==v2)) { if (t.t12!=null) throw new Error(); t.t12=this; t23=t; }
- if ((t.v1==v3&&t.v2==v1)||(t.v1==v1&&t.v2==v3)) { if (t.t12!=null) throw new Error(); t.t12=this; t31=t; }
- if ((t.v2==v1&&t.v3==v2)||(t.v2==v2&&t.v3==v1)) { if (t.t23!=null) throw new Error(); t.t23=this; t12=t; }
- if ((t.v2==v2&&t.v3==v3)||(t.v2==v3&&t.v3==v2)) { if (t.t23!=null) throw new Error(); t.t23=this; t23=t; }
- if ((t.v2==v3&&t.v3==v1)||(t.v2==v1&&t.v3==v3)) { if (t.t23!=null) throw new Error(); t.t23=this; t31=t; }
- if ((t.v3==v1&&t.v1==v2)||(t.v3==v2&&t.v1==v1)) { if (t.t31!=null) throw new Error(); t.t31=this; t12=t; }
- if ((t.v3==v2&&t.v1==v3)||(t.v3==v3&&t.v1==v2)) { if (t.t31!=null) throw new Error(); t.t31=this; t23=t; }
- if ((t.v3==v3&&t.v1==v1)||(t.v3==v1&&t.v1==v3)) { if (t.t31!=null) throw new Error(); t.t31=this; t31=t; }
- }
+ float a1=(v1.x+v2.x)*(v2.x-v1.x)+(v2.y-v1.y)*(v1.y+v2.y);
+ float a2=(v2.x+v3.x)*(v2.x-v3.x)+(v2.y-v3.y)*(v2.y+v3.y);
+ cc=point((a1*(v2.y-v3.y)-a2*(v2.y-v1.y))/a/2, (a2*(v2.x-v1.x)-a1*(v2.x-v3.x))/a/2);
+ r2 = v1.distance2(cc);
triangles.add(this);
}
+ public void clear() {
+ if (!painted) return;
+ painted = false;
+ if (t(3) != null) t(3).clear();
+ if (t(1) != null) t(1).clear();
+ if (t(2) != null) t(2).clear();
+ }
public void delete() {
- if (deleted) return;
- deleted = true;
+ if (triangle0 == this) {
+ if (t(1) != null) triangle0 = t(1);
+ else if (t(2) != null) triangle0 = t(2);
+ else if (t(3) != null) triangle0 = t(3);
+ else triangle0 = null;
+ }
triangles.remove(this);
- if (t12 != null) { if (t12.t12==this) t12.t12=null; if (t12.t23==this) t12.t23=null; if (t12.t31==this) t12.t31=null; }
- if (t23 != null) { if (t23.t12==this) t23.t12=null; if (t23.t23==this) t23.t23=null; if (t23.t31==this) t23.t31=null; }
- if (t31 != null) { if (t31.t12==this) t31.t12=null; if (t31.t23==this) t31.t23=null; if (t31.t31==this) t31.t31=null; }
- }
- public boolean contains(Vertex v) {
- float x = x(v);
- float y = y(v);
- if (v==v1) return false;
- if (v==v2) return false;
- if (v==v3) return false;
- if (isect(v1,v2,v)) return false;
- if (isect(v2,v3,v)) return false;
- if (isect(v3,v1,v)) return false;
- return (side(v1,v2,x,y)==side(v1,v2,v3)) && (side(v3,v2,x,y)==side(v3,v2,v1)) && (side(v1,v3,x,y)==side(v1,v3,v2));
+ e(1).rmTriangle(this);
+ e(2).rmTriangle(this);
+ e(3).rmTriangle(this);
+ e1 = null;
+ e2 = null;
+ e3 = null;
}
}
- // Constructor //////////////////////////////////////////////////////////////////////////////
-
- public Mesh(Polygon p) {
- p.sort();
- triangles.setSize(0);
- for(int i=0; i<p.numcontours-1; i++) {
- Vertex last = NULLVERTEX, first = NULLVERTEX;
- boolean good = false;
- for(int j=p.contours[i]; j<p.contours[i+1]; j++) {
- Vertex v = newVertex(p.x[j], p.y[j]);
- if (v==last) continue;
- if (v==first) continue;
- if (last == NULLVERTEX) { last = v; continue; }
- if (first == NULLVERTEX) { first = v; continue; }
- good = true;
- break;
- }
- if (debug) Log.debug(this,"contour " + i + " is " + (good?"good":"bad"));
- if (!good) continue;
- last = NULLVERTEX; first = NULLVERTEX;
- for(int j=p.contours[i]; j<p.contours[i+1]; j++) {
- Vertex v = newVertex(p.x[j], p.y[j]);
- if (v==last) continue;
- if (first==NULLVERTEX) first=v;
- if (last != NULLVERTEX) next(last).add(new Integer(v));
- last = v;
- makeNonDegenerate();
- force();
- }
- if (last!=first) next(last).add(new Integer(first));
- }
- makeNonDegenerate();
- force();
- /*
- redo = true;
- for(; redo;) {
- redo = false;
- for(int k=0; k<triangles.size(); k++) {
- Triangle t = (Triangle)triangles.elementAt(k);
- redo |= t.checkSkinny();
- }
- break;
- }
- System.out.println("I now have " + numvertices + " vertices");
- */
-
+ // Queries /////////////////////////////////////////////////////////////////////////////////
+
+ public boolean queryPoint(Point p) {
+ if (triangle0==null) return false;
+ Triangle ret = triangle0.seek(p);
+ return (ret.contains(p) || ret.intersects(p)) && ret.in;
}
+
// Drawing //////////////////////////////////////////////////////////////////////////////
- private void drawLine(PixelBuffer buf, float x1, float y1, float x2, float y2, Affine a, int color) {
- buf.drawLine((int)a.multiply_px(x1, y1), (int)a.multiply_py(x1, y1),
- (int)a.multiply_px(x2, y2), (int)a.multiply_py(x2, y2),
- color);
+ public void setIn(boolean evenOdd) {
+ iterateTriangles(ITERATE_CLEAR_WASSET, null, null);
+ triangle0.setIn(evenOdd, 1);
}
- public void fill(PixelBuffer buf, Affine a, int color, boolean evenOdd, boolean strokeOnly) {
- for (int i=0; i<triangles.size(); i++) ((Triangle)triangles.elementAt(i)).clear();
- ((Triangle)triangles.elementAt(0)).fill(buf, a, color, evenOdd, 1, strokeOnly);
+
+ public void fill(PixelBuffer buf, Affine a, Mesh.Chain clip, int color, boolean strokeOnly) {
+ if (triangle0==null) return;
+ iterateTriangles(ITERATE_CLEAR, null, null);
+ triangle0.fill(buf, a, clip, color, strokeOnly);
}
public void stroke(PixelBuffer buf, Affine a, int color) {
- if (debug)
- for (int i=0; i<numvertices; i++) {
- Vertex v = i;
- for(Iterator it = next(v).iterator(); it.hasNext();) {
- Vertex v2 = ((Integer)it.next()).intValue();
- drawLine(buf, x(v), y(v), x(v2), y(v2), a, 0xffff0000);
- }
- }
- for (int i=0; i<triangles.size(); i++) {
- Triangle t = ((Triangle)triangles.elementAt(i));
- Vertex v1 = t.v1;
- Vertex v2 = t.v2;
- Vertex v3 = t.v3;
- if (debug||t.wind(v1,v2)!=0) drawLine(buf,x(v1),y(v1),x(v2),y(v2),a,(debug && t.wind(v1,v2)!=0) ?0xffffffff:color);
- if (debug||t.wind(v3,v2)!=0) drawLine(buf,x(v3),y(v3),x(v2),y(v2),a,(debug && t.wind(v3,v2)!=0) ?0xffffffff:color);
- if (debug||t.wind(v1,v3)!=0) drawLine(buf,x(v1),y(v1),x(v3),y(v3),a,(debug && t.wind(v1,v3)!=0) ?0xffffffff:color);
- }
+ if (triangle0==null) return;
+ iterateTriangles(ITERATE_STROKE, null, a, buf, color);
}
- // Geometric Utility Functions //////////////////////////////////////////////////////////////////////////////
-
- public float distance(Vertex v1, Vertex v2) { return distance(x(v1), y(v1), x(v2), y(v2)); }
- public float distance(Vertex v1, float x, float y) { return distance(x(v1),y(v1),x,y); }
- public float distance(float x1,float y1,float x2,float y2) {return (float)Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));}
- public int side(Vertex v1, Vertex v2, Vertex v3) { return side(v1, v2, x(v3), y(v3)); }
- public int side(Vertex v1, Vertex v2, float x, float y) { return side(v1, x(v2), y(v2), x, y); }
- public int side(Vertex v1, float x, float y, Vertex v3) { return side(v1, x, y, x(v3), y(v3)); }
- public int side(Vertex v1, float x, float y, float x2, float y2) {
- float a = y-y(v1), b = x(v1)-x, c = -1 * (a*x(v1)+b*y(v1));
- return (- (a*x2+c)/b > y2) ? -1 : (- (a*x2+c)/b < y2) ? 1 : 0;
+ public void newcontour() {
+ if (start != null) add(start.x, start.y);
+ start = null;
+ last = null;
}
- public boolean isect(Vertex v1, Vertex v2, Vertex v3, Vertex v4) {
- if (v1==v3 || v1==v4 || v2==v3 || v2==v4) return false;
- float a = side(v1,v2,v3);
- float b = side(v1,v2,v4);
- float c = side(v3,v4,v1);
- float d = side(v3,v4,v2);
- return a!=b && c!=d && a!=0 && b!=0 && c!=0 && d!=0;
+ public Mesh addRect(float x, float y, float w, float h) {
+ if (w==0 || h==0) return this;
+ Vertex v1 = vertex(point(x,y));
+ Vertex v2 = vertex(point(x+w,y));
+ Vertex v3 = vertex(point(x+w,y+h));
+ Vertex v4 = vertex(point(x,y+h));
+ newEdge(v1,v2).lock(v1,1);
+ newEdge(v2,v3).lock(v2,1);
+ newEdge(v3,v4).lock(v3,1);
+ newEdge(v4,v1).lock(v4,1);
+ setIn(true);
+ return this;
}
- public boolean isect(Vertex v1, Vertex v2, Vertex v) {
- return
- side(v1,v2,v)==0 &&
- x(v) - Math.max(x(v1),x(v2)) < 0 &&
- x(v) - Math.min(x(v1),x(v2)) > 0 &&
- y(v) - Math.max(y(v1),y(v2)) < 0 &&
- y(v) - Math.min(y(v1),y(v2)) > 0;
+ public void add(float x, float y) {
+ Vertex vx = vertex(point(x,y));
+ if (vx==last) return;
+ if (start==null) start = vx;
+ try {
+ if (last==null) return;
+ if (numvertices<3) return;
+ if (numvertices==3) getEdge(start, last).lock(start,1);
+ getEdge(last,vx).lock(last,1);
+ } finally {
+ last = vx;
+ }
}
-
}