1 package edu.berkeley.qfat.geom;
2 import javax.media.opengl.*;
5 * An oriented triangle, defined by three points in clockwise order;
6 * note that the Point objects returned by p1/p2/p3 may vary over time.
8 public abstract class Triangle implements HasBoundingBox {
9 public abstract Point p1();
10 public abstract Point p2();
11 public abstract Point p3();
13 /** the face normal vector */
15 return p2().minus(p1()).cross(p3().minus(p1())).norm();
18 /** the area of the triangle */
21 (float)Math.abs(0.5*p1().distance(p2())
22 * new Vec(p1(), p2()).norm().dot(new Vec(p2(), p3())));
25 /** issue gl.glVertex() for each of the triangle's points */
26 public void glVertices(GL gl) {
32 public void glVertices(GL gl, Matrix m) {
33 m.times(norm()).glNormal(gl);
34 m.times(p1()).glVertex(gl);
35 m.times(p2()).glVertex(gl);
36 m.times(p3()).glVertex(gl);
39 /** the triangle's centroid */
40 public Point centroid() {
41 return new Point((p1().x+p2().x+p3().x)/3,
42 (p1().y+p2().y+p3().y)/3,
43 (p1().z+p2().z+p3().z)/3);
46 /** ratio of the area of the triangle to that of the square formed from its longest edge */
48 public float aspect() {
49 float max = Math.max(Math.max(p1().distance(p2()),
51 p3().distance(p1())) / 2;
52 return 1/(1+area()/(max*max));
56 public float circumcircleRadius() {
57 double a = p1().distance(p2());
58 double b = p2().distance(p3());
59 double c = p3().distance(p1());
60 return (float)((a*b*c)/Math.sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c)));
63 public float shortestEdgeLength() {
64 float a = p1().distance(p2());
65 float b = p2().distance(p3());
66 float c = p3().distance(p1());
67 return Math.min(a, Math.min(b,c));
70 /** a number ranging from 0..1 with 0 being lower quality */
71 public float quality() {
72 float d = shortestEdgeLength();
73 float r = circumcircleRadius();
74 if (r==0) throw new Error();
75 float ret = (float)((d*Math.cos(Math.PI/6))/(r*2));
76 if (ret < 0 || ret > 1) throw new Error("ret="+ret);
80 // FIXME: I stole this off the net, and I need to credit whoever wrote it
81 /** decide if the segment from p1-p2 intersects this triangle */
82 public boolean intersects(Point p1, Point p2) {
83 double A0=p1().x, A1=p1().y, A2=p1().z;
84 double B0=p2().x, B1=p2().y, B2=p2().z;
85 double C0=p3().x, C1=p3().y, C2=p3().z;
86 double j0=p1.x, j1=p1.y, j2=p1.z;
87 double k0=p2.x, k1=p2.y, k2=p2.z;
95 double R00, R01, R02, R03,
109 /* c = a × b */
110 c0 = a1 * b2 - a2 * b1;
111 c1 = a2 * b0 - a0 * b2;
112 c2 = a0 * b1 - a1 * b0;
114 /* M^(-1) = (1/det(M)) * adj(M) */
115 in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
116 R00 = (b1 * c2 - b2 * c1) * in_det;
117 R01 = (b2 * c0 - b0 * c2) * in_det;
118 R02 = (b0 * c1 - b1 * c0) * in_det;
119 R10 = (c1 * a2 - c2 * a1) * in_det;
120 R11 = (c2 * a0 - c0 * a2) * in_det;
121 R12 = (c0 * a1 - c1 * a0) * in_det;
127 R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
128 R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
129 R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
131 /* fill in last row of 4x4 matrix */
135 J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
136 K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
137 if (J2 * K2 >= 0) return false;
139 J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
140 K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
141 i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
142 if (i0 < 0 || i0 > 1) return false;
144 J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
145 K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
146 i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
147 if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
152 public float getMaxX() { return Math.max(p1().x, Math.max(p2().x, p3().x)); }
153 public float getMinX() { return Math.min(p1().x, Math.min(p2().x, p3().x)); }
154 public float getMaxY() { return Math.max(p1().y, Math.max(p2().y, p3().y)); }
155 public float getMinY() { return Math.min(p1().y, Math.min(p2().y, p3().y)); }
156 public float getMaxZ() { return Math.max(p1().z, Math.max(p2().z, p3().z)); }
157 public float getMinZ() { return Math.min(p1().z, Math.min(p2().z, p3().z)); }