public boolean intersects(Circle circle) {
// using Vector Projection
// https://en.wikipedia.org/wiki/Vector_projection
Vector c = Vector.create(circle.x(), circle.y());
Vector a = Vector.create(x1, y1);
Vector cMinusA = c.minus(a);
float radiusSquared = circle.radius() * circle.radius();
if (x1 == x2 && y1 == y2) {
return cMinusA.modulusSquared() <= radiusSquared;
} else {
Vector b = Vector.create(x2, y2);
Vector bMinusA = b.minus(a);
float bMinusAModulus = bMinusA.modulus();
float lambda = cMinusA.dot(bMinusA) / bMinusAModulus;
// if projection is on the segment
if (lambda >= 0 && lambda <= bMinusAModulus) {
Vector dMinusA = bMinusA.times(lambda / bMinusAModulus);
// calculate distance to line from c using pythagoras' theorem
return cMinusA.modulusSquared() - dMinusA.modulusSquared() <= radiusSquared;
} else {
// return true if and only if an endpoint is within radius of
// centre
return cMinusA.modulusSquared() <= radiusSquared
|| c.minus(b).modulusSquared() <= radiusSquared;
}
}
}
public void testMinus() throws Exception {
Vector val = test.minus(test);
assertEquals("size", test.size(), val.size());
for (int i = 0; i < test.size(); i++) {
assertEquals("get [" + i + ']', 0.0, val.get(i));
}
val = test.minus(test).minus(test);
assertEquals("cardinality", test.size(), val.size());
for (int i = 0; i < test.size(); i++) {
assertEquals("get [" + i + ']', 0.0, val.get(i) + test.get(i));
}
Vector val1 = test.plus(1);
val = val1.minus(test);
for (int i = 0; i < test.size(); i++) {
assertEquals("get [" + i + ']', 1.0, val.get(i));
}
val1 = test.plus(-1);
val = val1.minus(test);
for (int i = 0; i < test.size(); i++) {
assertEquals("get [" + i + ']', -1.0, val.get(i));
}
}
// 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 void testGetDistanceSquared() {
Vector other = new RandomAccessSparseVector(test.size());
other.set(1, -2);
other.set(2, -5);
other.set(3, -9);
other.set(4, 1);
double expected = test.minus(other).getLengthSquared();
assertTrue(
"a.getDistanceSquared(b) != a.minus(b).getLengthSquared",
Math.abs(expected - test.getDistanceSquared(other)) < 10.0E-7);
}
