import javax.media.opengl.*;
import javax.media.opengl.glu.*;
+// FEATURE: octree for nearest-point queries? Could make moving points around problematic.
+
public class Geom implements Iterable<Geom.T> {
+ public static float EPSILON = (float)0.000001;
+
private HashMap<P,P> ps = new HashMap<P,P>();
private HashMap<E,E> es = new HashMap<E,E>();
private HashSet<T> ts = new HashSet<T>();
public Iterator<T> iterator() { return ts.iterator(); }
+ public P newP(double x, double y, double z) { return newP((float)x, (float)y, (float)z); }
public P newP(float x, float y, float z) {
P p = new P(x, y, z);
P p2 = ps.get(p);
return e;
}
- public T newT(E e1, E e2, E e3) {
+ public T newT(P p1, P p2, P p3) {
+ return newT(newE(p1, p2), newE(p2, p3), newE(p3, p1), p3.minus(p1).cross(p2.minus(p1)));
+ }
+
+ /** ensures that e1.cross(e2).norm()==e2.cross(e3).norm()==e3.cross(e1).norm()==t.norm() */
+ public T newT(E e1, E e2, E e3, V norm) {
+ P p12 = e1.shared(e2);
+ P p23 = e2.shared(e3);
+ P p31 = e3.shared(e1);
+ V norm2 = p31.minus(p12).cross(p23.minus(p12));
+ float dot = norm.dot(norm2);
+ if (Math.abs(dot) < EPSILON) throw new Error("dot products within epsilon of each other: "+norm+" "+norm2);
+ if (dot < 0) { E t = e1; e1 = e3; e2 = e2; e3 = t; }
if (e1.t1 != null && e1.t1.hasE(e1) && e1.t1.hasE(e2) && e1.t1.hasE(e3)) return e1.t1;
if (e1.t2 != null && e1.t2.hasE(e1) && e1.t2.hasE(e2) && e1.t2.hasE(e3)) return e1.t2;
if (e2.t1 != null && e2.t1.hasE(e1) && e2.t1.hasE(e2) && e2.t1.hasE(e3)) return e2.t1;
if (e2.t2 != null && e2.t2.hasE(e1) && e2.t2.hasE(e2) && e2.t2.hasE(e3)) return e2.t2;
if (e3.t1 != null && e3.t1.hasE(e1) && e3.t1.hasE(e2) && e3.t1.hasE(e3)) return e3.t1;
if (e3.t2 != null && e3.t2.hasE(e1) && e3.t2.hasE(e2) && e3.t2.hasE(e3)) return e3.t2;
- return new T(e1, e2, e3);
+ T ret = new T(e1, e2, e3);
+ ts.add(ret);
+ return ret;
}
/** [UNIQUE] point in 3-space */
public final class P {
- public final float x, y, z;
+
+ float x, y, z;
+
+ private T t = null; // any of the triangles incident at this point
+
+ private M binding = new M();
+ private P bound_to = this;
+
+ public void unbind() { bound_to = null; binding = null; }
+ public void bind(P p) { bind(p, new M()); }
+ public void bind(P p, M binding) {
+
+ P px = p;
+ do {
+ if (px==this) return; // already bound
+ px = px.bound_to;
+ } while(px != p);
+
+ P temp_bound_to = p.bound_to;
+ M temp_binding = p.binding;
+ p.bound_to = this.bound_to;
+ p.binding = binding.times(this.binding); // FIXME: may have order wrong here
+ this.bound_to = temp_bound_to;
+ this.binding = temp_binding.times(temp_binding); // FIXME: may have order wrong here
+ }
+
+ public void move(V v) {
+ P p = this;
+ do {
+ p.x = p.x+v.x;
+ p.y = p.y+v.y;
+ p.z = p.z+v.z;
+ v = v.times(binding);
+ p = p.bound_to;
+ } while (p != this);
+ }
+
public P(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
public V minus(P p) { return new V(x-p.x, y-p.y, z-p.z); }
+ public P plus(V v) { return newP(x+v.x, y+v.y, z+v.z); }
+ public P times(M m) { return m.apply(this); }
public boolean equals(Object o) {
if (o==null || !(o instanceof P)) return false;
P p = (P)o;
Float.floatToIntBits(z);
}
public void glVertex(GL gl) { gl.glVertex3f(x, y, z); }
+ public String toString() { return "("+x+","+y+","+z+")"; }
+ public V norm() {
+ if (t==null) throw new Error("attempt to get vertex normal for point which does not belong to any triangles");
+ T ti = t;
+ V norm = new V(0, 0, 0);
+ do {
+ norm = norm.plus(ti.norm().times((float)ti.angle(this)));
+ ti = ti.nextT(this);
+ } while(ti != t);
+ return norm.norm();
+ }
}
/** vector in 3-space */
public final class V {
- private final float x, y, z;
+ public final float x, y, z;
+ public V(double x, double y, double z) { this((float)x, (float)y, (float)z); }
public V(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
- public boolean sameDirection(V v) { throw new Error(); }
public V cross(V v) { return new V(y*v.z-z*v.y, z*v.x-x*v.z, x*v.y-y*v.x); }
+ public V plus(V v) { return new V(x+v.x, y+v.y, z+v.z); }
+ public V norm() { return div(mag()); }
+ public V times(M m) { return m.apply(this); }
public float mag() { return (float)Math.sqrt(x*x+y*y+z*z); }
- public V norm() { float m = mag(); return new V(x/m, y/m, z/m); }
+ public float dot(V v) { return x*v.x + y*v.y + z*v.z; }
+ public V times(float mag) { return new V(x*mag, y*mag, z*mag); }
+ public V div(float mag) { return new V(x/mag, y/mag, z/mag); }
+ public String toString() { return "<"+x+","+y+","+z+">"; }
}
/** [UNIQUE] an edge */
public final class E {
public final P p1, p2;
T t1, t2;
- public E(P p1, P p2) { this.p1 = p1; this.p2 = p2; }
+ public E(P p1, P p2) {
+ if (p1==p2) throw new Error("attempt to create edge with single vertex: " + p1);
+ this.p1 = p1;
+ this.p2 = p2;
+ }
public int hashCode() { return p1.hashCode() ^ p2.hashCode(); }
+ public float length() { return p1.minus(p2).mag(); }
public boolean equals(Object o) {
if (o==null || !(o instanceof E)) return false;
E e = (E)o;
if (p2==e.p2) return p1;
throw new Error("no shared vertex in unshared()");
}
+ public T other(T t) {
+ if (t1==t) return t2;
+ if (t2==t) return t1;
+ throw new Error("edge " + this + " does not own triangle " + t);
+ }
+ public P other(P p) {
+ if (p==p1) return p2;
+ if (p==p2) return p1;
+ throw new Error("edge " + this + " does not own point " + p);
+ }
}
/** [UNIQUE] a triangle (face) */
public final class T {
public final E e1, e2, e3;
- public T(E e1, E e2, E e3, V normal) {
- P p1 = e1.shared(e2);
- P p2 = e2.shared(e3);
- P p3 = e3.shared(e1);
- V norm = p2.minus(p1).cross(p3.minus(p1));
- if (norm.sameDirection(normal)) {
- this.e1 = e1;
- this.e2 = e2;
- this.e3 = e3;
- } else {
- this.e1 = e3;
- this.e2 = e2;
- this.e3 = e1;
- }
+ T(E e1, E e2, E e3) {
+ if (e1.p1.t==null) e1.p1.t = this;
+ if (e1.p2.t==null) e1.p2.t = this;
+ if (e2.p1.t==null) e2.p1.t = this;
+ if (e2.p2.t==null) e2.p2.t = this;
+ if (e3.p1.t==null) e3.p1.t = this;
+ if (e3.p2.t==null) e3.p2.t = this;
+ if (e1==e2) throw new Error("attempt to create triangle with duplicate edge: " + e1);
+ if (e2==e3) throw new Error("attempt to create triangle with duplicate edge: " + e2);
+ if (e3==e1) throw new Error("attempt to create triangle with duplicate edge: " + e3);
+ // check that each pair of edges shares a vertex
+ e1.shared(e2);
+ e2.shared(e3);
+ e3.shared(e1);
+ this.e1 = e1;
+ this.e2 = e2;
+ this.e3 = e3;
+ // FEATURE: colinearity/sliverness check?
if (e1.t1 == null) e1.t1 = this; else if (e1.t2 == null) e1.t2 = this; else throw new Error("non-manifold surface");
if (e2.t1 == null) e2.t1 = this; else if (e2.t2 == null) e2.t2 = this; else throw new Error("non-manifold surface");
if (e3.t1 == null) e3.t1 = this; else if (e3.t2 == null) e3.t2 = this; else throw new Error("non-manifold surface");
- ts.add(this);
+ // FIXME: check that triangles we share an edge with agree on the direction of the normal vector
+ // FIXME: check for sealed/watertight surface once construction is complete (and infer normal(s)?)
}
public V norm() {
P p1 = e1.shared(e2);
P p3 = e3.shared(e1);
return p2.minus(p1).cross(p3.minus(p1)).norm();
}
- public T(E e1, E e2, E e3) {
- this.e1 = e1;
- this.e2 = e2;
- this.e3 = e3;
- if (e1.t1 == null) e1.t1 = this; else if (e1.t2 == null) e1.t2 = this; else throw new Error("non-manifold surface");
- if (e2.t1 == null) e2.t1 = this; else if (e2.t2 == null) e2.t2 = this; else throw new Error("non-manifold surface");
- if (e3.t1 == null) e3.t1 = this; else if (e3.t2 == null) e3.t2 = this; else throw new Error("non-manifold surface");
- ts.add(this);
- }
public boolean hasE(E e) { return e1==e || e2==e || e3==e; }
public void glVertices(GL gl) {
- e1.unshared(e2).glVertex(gl);
- e1.shared(e2).glVertex(gl);
- e2.shared(e3).glVertex(gl);
+ p1().glVertex(gl);
+ p2().glVertex(gl);
+ p3().glVertex(gl);
}
+ public P p1() { return e1.shared(e2); }
+ public P p2() { return e1.shared(e3); }
+ public P p3() { return e3.shared(e2); }
+ public P centroid() { return newP((p1().x+p2().x+p3().x)/3,
+ (p1().y+p2().y+p3().y)/3,
+ (p1().z+p2().z+p3().z)/3); }
+ public float diameter() {
+ // FIXME: what is this supposed to be?
+ return Math.max(Math.max(e1.length(), e2.length()), e3.length()) / 2;
+ }
+
+ /** returns the next triangle walking clockwise around the vertex normal */
+ public T nextT(P p) { return prevE(p).other(this); }
+ public T prevT(P p) { return nextE(p).other(this); }
+
+ /** edge "after" this point, moving clockwise around the normal */
+ public E nextE(P p) {
+ if (p == e1.shared(e2)) return e1;
+ else if (p == e2.shared(e3)) return e2;
+ else if (p == e3.shared(e1)) return e3;
+ else throw new Error("triangle " + this + " does not own point " + p);
+ }
+
+ /** edge "before" this point, moving clockwise around the normal */
+ public E prevE(P p) {
+ if (p == e1.shared(e2)) return e2;
+ else if (p == e2.shared(e3)) return e3;
+ else if (p == e3.shared(e1)) return e1;
+ else throw new Error("triangle " + this + " does not own point " + p);
+ }
+
+ /** returns the angle at point p */
+ public double angle(P p) {
+ V v1 = nextE(p).other(p).minus(p);
+ V v2 = prevE(p).other(p).minus(p);
+ return Math.acos(v1.norm().dot(v2.norm()));
+ }
+
}
+
/** matrix */
public class M {
+ public M() { }
+ public P apply(P p) { return p; }
+ public V apply(V v) { return v; }
+ public M invert() { return this; }
+ public M times(M m) { return this; }
}
}
projects / anneal.git / blobdiff