void Cylinder::getRandomSurfacePoint(Vector3& p, Vector3& N) const {
float h = height();
float r = radius();
// Create a random point on a standard cylinder and then rotate to the global frame.
// Relative areas (factor of 2PI already taken out)
float capRelArea = square(r) / 2.0f;
float sideRelArea = r * h;
float r1 = uniformRandom(0, capRelArea * 2 + sideRelArea);
if (r1 < capRelArea * 2) {
// Select a point uniformly at random on a disk
// @cite http://mathworld.wolfram.com/DiskPointPicking.html
float a = uniformRandom(0, (float)twoPi());
float r2 = sqrt(uniformRandom(0, 1)) * r;
p.x = cos(a) * r2;
p.z = sin(a) * r2;
N.x = 0;
N.z = 0;
if (r1 < capRelArea) {
// Top
p.y = h / 2.0f;
N.y = 1;
} else {
// Bottom
p.y = -h / 2.0f;
N.y = -1;
}
} else {
// Side
float a = uniformRandom(0, (float)twoPi());
N.x = cos(a);
N.y = 0;
N.z = sin(a);
p.x = N.x * r;
p.z = N.y * r;
p.y = uniformRandom(-h / 2.0f, h / 2.0f);
}
// Transform to world space
CoordinateFrame cframe;
getReferenceFrame(cframe);
p = cframe.pointToWorldSpace(p);
N = cframe.normalToWorldSpace(N);
}
void Capsule::getRandomSurfacePoint(Vector3& p, Vector3& N) const {
float h = height();
float r = radius();
// Create a random point on a standard capsule and then rotate to the global frame.
// Relative areas
float capRelArea = sqrt(r) / 2.0f;
float sideRelArea = r * h;
float r1 = uniformRandom(0, capRelArea * 2 + sideRelArea);
if (r1 < capRelArea * 2) {
// Select a point uniformly at random on a sphere
N = Sphere(Vector3::zero(), 1).randomSurfacePoint();
p = N * r;
p.y += sign(p.y) * h / 2.0f;
} else {
// Side
float a = uniformRandom(0, (float)twoPi());
N.x = cos(a);
N.y = 0;
N.z = sin(a);
p.x = N.x * r;
p.z = N.y * r;
p.y = uniformRandom(-h / 2.0f, h / 2.0f);
}
// Transform to world space
CoordinateFrame cframe;
getReferenceFrame(cframe);
p = cframe.pointToWorldSpace(p);
N = cframe.normalToWorldSpace(N);
}
