// intersectRayAndTriangle(): intersect a ray with a 3D triangle
// Input: a ray R, and a triangle T
// Output: *I = intersection point (when it exists)
// Return: -1 = triangle is degenerate (a segment or point)
// 0 = disjoint (no intersect)
// 1 = intersect in unique point I1
// 2 = are in the same plane
public static int intersectRayAndTriangle(Ray R, Triangle T, float[] I) {
float[] u, v, n; // triangle vectors
float[] dir, w0, w; // ray vectors
float r, a, b; // params to calc ray-plane intersect
// get triangle edge vectors and plane normal
u = Vector.minus(T.V1, T.V0);
v = Vector.minus(T.V2, T.V0);
n = Vector.crossProduct(u, v); // cross product
if (Arrays.equals(n, new float[] {0.0f, 0.0f, 0.0f})) { // triangle is degenerate
return -1; // do not deal with this case
}
dir = Vector.minus(R.P1, R.P0); // ray direction vector
w0 = Vector.minus(R.P0, T.V0);
a = -Vector.dot(n, w0);
b = Vector.dot(n, dir);
if (Math.abs(b) < SMALL_NUM) { // ray is parallel to triangle plane
if (a == 0) { // ray lies in triangle plane
return 2;
} else {
return 0; // ray disjoint from plane
}
}
// get intersect point of ray with triangle plane
r = a / b;
if (r < 0.0f) { // ray goes away from triangle
return 0; // => no intersect
}
// for a segment, also test if (r > 1.0) => no intersect
float[] tempI =
Vector.addition(R.P0, Vector.scalarProduct(r, dir)); // intersect point of ray and a plane
I[0] = tempI[0];
I[1] = tempI[1];
I[2] = tempI[2];
// is I inside T?
float uu, uv, vv, wu, wv, D;
uu = Vector.dot(u, u);
uv = Vector.dot(u, v);
vv = Vector.dot(v, v);
w = Vector.minus(I, T.V0);
wu = Vector.dot(w, u);
wv = Vector.dot(w, v);
D = (uv * uv) - (uu * vv);
// get and test parametric coords
float s, t;
s = ((uv * wv) - (vv * wu)) / D;
if (s < 0.0f || s > 1.0f) // I is outside T
return 0;
t = (uv * wu - uu * wv) / D;
if (t < 0.0f || (s + t) > 1.0f) // I is outside T
return 0;
return 1; // I is in T
}
public Vector getSurfaceNormal(Coordinates c) {
Vector s = immerseVector(c, ddu);
Vector t = immerseVector(c, ddv);
s.normalize();
t.normalize();
return s.crossProduct(t);
}
public static float distanceBetween(Point point, Ray ray) {
Vector p1ToPoint = vectorBetween(ray.point, point);
Vector p2ToPoint = vectorBetween(ray.point.translate(ray.vector), point);
float areaOfTriangleTimesTwo = p1ToPoint.crossProduct(p2ToPoint).length();
float lengthOfBase = ray.vector.length();
float distanceFromPointToRay = areaOfTriangleTimesTwo / lengthOfBase;
return distanceFromPointToRay;
}
