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/**
@file Cone.cpp
Cone class
@maintainer Morgan McGuire, http://graphics.cs.williams.edu
@created 2001-07-09
@edited 2006-01-29
*/
#include "G3D/platform.h"
#include "G3D/Cone.h"
#include "G3D/Line.h"
#include "G3D/Sphere.h"
#include "G3D/Box.h"
namespace G3D {
float Cone::solidAngleFromHalfAngle(float halfAngle){
return 2.0f * pif() * (1 - cosf(halfAngle));
}
double Cone::solidAngleFromHalfAngle(double halfAngle){
return 2.0 * pi() * (1.0 - cos(halfAngle));
}
float Cone::halfAngleFromSolidAngle(float solidAngle){
return acos((1.0f - (solidAngle / (2.0f * pif()))));
}
double Cone::halfAngleFromSolidAngle(double solidAngle){
return aCos((1.0 - (solidAngle / (2.0 * pi()))));
}
Cone::Cone(const Vector3 &tip, const Vector3 &direction, float angle) {
this->tip = tip;
this->direction = direction.direction();
this->angle = angle;
debugAssert(angle >= 0);
debugAssert(angle <= pi());
}
Vector3 Cone::randomDirectionInCone(Random& rng) const {
const float cosThresh = cos(angle);
float cosAngle;
float normalizer;
Vector3 v;
do {
float vlenSquared;
// Sample uniformly on a sphere by rejection sampling and then normalizing
do {
v.x = rng.uniform(-1, 1);
v.y = rng.uniform(-1, 1);
v.z = rng.uniform(-1, 1);
// Sample uniformly on a cube
vlenSquared = v.squaredLength();
} while (vlenSquared > 1);
const float temp = v.dot(direction);
// Compute 1 / ||v||, but
// if the vector is in the wrong hemisphere, flip the sign
normalizer = rsqrt(vlenSquared) * sign(temp);
// Cosine of the angle between v and the light's negative-z axis
cosAngle = temp * normalizer;
} while (cosAngle < cosThresh);
// v was within the cone. Normalize it and maybe flip the hemisphere.
return v * normalizer;
}
/**
Forms the smallest cone that contains the box. Undefined if
the tip is inside or on the box.
*/
Cone::Cone(const Vector3& tip, const Box& box) {
this->tip = tip;
this->direction = (box.center() - tip).direction();
// Find the biggest angle
float smallestDotProduct = direction.dot((box.corner(0) - tip).direction());
for (int i = 1; i < 8; ++i) {
float dp = direction.dot((box.corner(i) - tip).direction());
debugAssert(dp > 0);
if (dp < smallestDotProduct) {
smallestDotProduct = dp;
}
}
angle = acosf(smallestDotProduct);
}
bool Cone::intersects(const Sphere& b) const {
// If the bounding sphere contains the tip, then
// they definitely touch.
if (b.contains(this->tip)) {
return true;
}
// Move the tip backwards, effectively making the cone bigger
// to account for the radius of the sphere.
Vector3 tip = this->tip - direction * b.radius / sinf(angle);
return Cone(tip, direction, angle).contains(b.center);
}
bool Cone::contains(const Vector3& v) const {
Vector3 d = (v - tip).direction();
float x = d.dot(direction);
return (x > 0) && (x >= cosf(angle));
}
}; // namespace
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