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/**
@file Capsule.cpp
@maintainer Morgan McGuire, http://graphics.cs.williams.edu
@created 2003-02-07
@edited 2005-08-18
Copyright 2000-2009, Morgan McGuire.
All rights reserved.
*/
#include "G3D/Capsule.h"
#include "G3D/BinaryInput.h"
#include "G3D/BinaryOutput.h"
#include "G3D/LineSegment.h"
#include "G3D/Sphere.h"
#include "G3D/CoordinateFrame.h"
#include "G3D/Line.h"
#include "G3D/AABox.h"
namespace G3D {
Capsule::Capsule(class BinaryInput& b) {
deserialize(b);
}
Capsule::Capsule() {
}
Capsule::Capsule(const Vector3& _p1, const Vector3& _p2, float _r)
: p1(_p1), p2(_p2), _radius(_r) {
}
void Capsule::serialize(class BinaryOutput& b) const {
p1.serialize(b);
p2.serialize(b);
b.writeFloat64(_radius);
}
void Capsule::deserialize(class BinaryInput& b) {
p1.deserialize(b);
p2.deserialize(b);
_radius = (float)b.readFloat64();
}
Line Capsule::axis() const {
return Line::fromTwoPoints(p1, p2);
}
float Capsule::volume() const {
return
// Sphere volume
pow(_radius, 3) * (float)pi() * 4 / 3 +
// Cylinder volume
pow(_radius, 2) * (p1 - p2).magnitude();
}
float Capsule::area() const {
return
// Sphere area
pow(_radius, 2) * 4 * (float)pi() +
// Cylinder area
(float)twoPi() * _radius * (p1 - p2).magnitude();
}
void Capsule::getBounds(AABox& out) const {
Vector3 min = p1.min(p2) - (Vector3(1, 1, 1) * _radius);
Vector3 max = p1.max(p2) + (Vector3(1, 1, 1) * _radius);
out = AABox(min, max);
}
bool Capsule::contains(const Vector3& p) const {
return LineSegment::fromTwoPoints(p1, p2).distanceSquared(p) <= square(radius());
}
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);
}
void Capsule::getReferenceFrame(CoordinateFrame& cframe) const {
cframe.translation = center();
Vector3 Y = (p1 - p2).direction();
Vector3 X = (abs(Y.dot(Vector3::unitX())) > 0.9) ? Vector3::unitY() : Vector3::unitX();
Vector3 Z = X.cross(Y).direction();
X = Y.cross(Z);
cframe.rotation.setColumn(0, X);
cframe.rotation.setColumn(1, Y);
cframe.rotation.setColumn(2, Z);
}
Vector3 Capsule::randomInteriorPoint() const {
float h = height();
float r = radius();
// Create a random point in a standard capsule and then rotate to the global frame.
Vector3 p;
float hemiVolume = (float)pi() * (r*r*r) * 4 / 6.0f;
float cylVolume = (float)pi() * square(r) * h;
float r1 = uniformRandom(0, 2.0f * hemiVolume + cylVolume);
if (r1 < 2.0 * hemiVolume) {
p = Sphere(Vector3::zero(), r).randomInteriorPoint();
p.y += sign(p.y) * h / 2.0f;
} else {
// Select a point uniformly at random on a disk
float a = uniformRandom(0, (float)twoPi());
float r2 = sqrt(uniformRandom(0, 1)) * r;
p = Vector3(cos(a) * r2,
uniformRandom(-h / 2.0f, h / 2.0f),
sin(a) * r2);
}
// Transform to world space
CoordinateFrame cframe;
getReferenceFrame(cframe);
return cframe.pointToWorldSpace(p);
}
} // namespace
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