package edu.berkeley.qfat.geom;
import javax.media.opengl.*;
+/**
+ * An oriented triangle, defined by three points in order;
+ * note that the Point objects returned by p1/p2/p3 may vary over time.
+ */
public abstract class Triangle implements HasBoundingBox {
public abstract Point p1();
public abstract Point p2();
public abstract Point p3();
+ /** the face normal vector */
public Vec norm() {
return p2().minus(p1()).cross(p3().minus(p1())).norm();
}
+
+ /** the area of the triangle */
public float area() {
return
(float)Math.abs(0.5*p1().distance(p2())
* new Vec(p1(), p2()).norm().dot(new Vec(p2(), p3())));
}
- public void glVertices(GL gl) {
- p1().glVertex(gl);
- p2().glVertex(gl);
- p3().glVertex(gl);
+
+ /** issue gl.glVertex() for each of the triangle's points */
+ public void glVertices(GL gl, Matrix m) {
+ if (m==null) {
+ norm().glNormal(gl);
+ p1().glVertex(gl);
+ p2().glVertex(gl);
+ p3().glVertex(gl);
+ } else {
+ m.times(norm()).glNormal(gl);
+ m.times(p1()).glVertex(gl);
+ m.times(p2()).glVertex(gl);
+ m.times(p3()).glVertex(gl);
+ }
}
+
+ /** the triangle's centroid */
public Point centroid() {
return new Point((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(p1().distance(p2()),
- p2().distance(p3())),
- p3().distance(p1())) / 2;
- }
+ /** ratio of the area of the triangle to that of the square formed from its longest edge */
+ /*
public float aspect() {
float max = Math.max(Math.max(p1().distance(p2()),
p2().distance(p3())),
p3().distance(p1())) / 2;
return 1/(1+area()/(max*max));
}
- public float aspect0() {
- float max = Math.max(Math.max(p1().distance(p2()),
- p2().distance(p3())),
- p3().distance(p1())) / 2;
- return (area()/(max*max));
+ */
+
+ public float circumcircleRadius() {
+ double a = p1().distance(p2());
+ double b = p2().distance(p3());
+ double c = p3().distance(p1());
+ return (float)((a*b*c)/Math.sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c)));
+ }
+
+ public float shortestEdgeLength() {
+ float a = p1().distance(p2());
+ float b = p2().distance(p3());
+ float c = p3().distance(p1());
+ return Math.min(a, Math.min(b,c));
+ }
+
+ /** a number ranging from 0..1 with 0 being lower quality */
+ public float quality() {
+ float d = shortestEdgeLength();
+ float r = circumcircleRadius();
+ if (r==0) throw new Error();
+ float ret = (float)((d*Math.cos(Math.PI/6))/(r*2));
+ if (ret < 0 || ret > 1) throw new Error("ret="+ret);
+ return ret;
+ }
+
+ // FIXME: I stole this off the net, and I need to credit whoever wrote it
+ /** decide if the segment from p1-p2 intersects this triangle */
+ public boolean intersects(Point p1, Point p2) {
+ double A0=p1().x, A1=p1().y, A2=p1().z;
+ double B0=p2().x, B1=p2().y, B2=p2().z;
+ double C0=p3().x, C1=p3().y, C2=p3().z;
+ double j0=p1.x, j1=p1.y, j2=p1.z;
+ double k0=p2.x, k1=p2.y, k2=p2.z;
+ double J0, J1, J2;
+ double K0, K1, K2;
+ double i0, i1, i2;
+ double a0, a1, a2;
+ double b0, b1, b2;
+ double c0, c1, c2;
+ double in_det;
+ double R00, R01, R02, R03,
+ R10, R11, R12, R13,
+ R20, R21, R22, R23,
+ R30, R31, R32, R33;
+
+
+ /* a = B - A */
+ a0 = B0 - A0;
+ a1 = B1 - A1;
+ a2 = B2 - A2;
+ /* b = C - B */
+ b0 = C0 - A0;
+ b1 = C1 - A1;
+ b2 = C2 - A2;
+ /* c = a × b */
+ c0 = a1 * b2 - a2 * b1;
+ c1 = a2 * b0 - a0 * b2;
+ c2 = a0 * b1 - a1 * b0;
+
+ /* M^(-1) = (1/det(M)) * adj(M) */
+ in_det = 1 / (c0 * c0 + c1 * c1 + c2 * c2);
+ R00 = (b1 * c2 - b2 * c1) * in_det;
+ R01 = (b2 * c0 - b0 * c2) * in_det;
+ R02 = (b0 * c1 - b1 * c0) * in_det;
+ R10 = (c1 * a2 - c2 * a1) * in_det;
+ R11 = (c2 * a0 - c0 * a2) * in_det;
+ R12 = (c0 * a1 - c1 * a0) * in_det;
+ R20 = (c0) * in_det;
+ R21 = (c1) * in_det;
+ R22 = (c2) * in_det;
+
+ /* O = M^(-1) * A */
+ R03 = -(R00 * A0 + R01 * A1 + R02 * A2);
+ R13 = -(R10 * A0 + R11 * A1 + R12 * A2);
+ R23 = -(R20 * A0 + R21 * A1 + R22 * A2);
+
+ /* fill in last row of 4x4 matrix */
+ R30 = R31 = R32 = 0;
+ R33 = 1;
+
+ J2 = R20 * j0 + R21 * j1 + R22 * j2 + R23;
+ K2 = R20 * k0 + R21 * k1 + R22 * k2 + R23;
+ if (J2 * K2 >= 0) return false;
+
+ J0 = R00 * j0 + R01 * j1 + R02 * j2 + R03;
+ K0 = R00 * k0 + R01 * k1 + R02 * k2 + R03;
+ i0 = J0 + J2 * ((K0 - J0) / (J2 - K2));
+ if (i0 < 0 || i0 > 1) return false;
+
+ J1 = R10 * j0 + R11 * j1 + R12 * j2 + R13;
+ K1 = R10 * k0 + R11 * k1 + R12 * k2 + R13;
+ i1 = J1 + J2 * ((K1 - J1) / (J2 - K2));
+ if (i1 < 0 || i1 > 1 || i0 + i1 > 1) return false;
+
+ return true;
}
public float getMaxX() { return Math.max(p1().x, Math.max(p2().x, p3().x)); }
projects / anneal.git / blobdiff