bool rayIntersects(RayN<N, T> const & ray, T max_time = -1) const
{
if (max_time >= 0)
return rayIntersectionTime(ray, max_time) >= 0;
VectorT co = ray.getOrigin() - center;
T c = co.squaredNorm() - radius * radius;
if (c <= 0) // origin is inside ball
return true;
T a = ray.getDirection().squaredNorm();
T b = 2 * co.dot(ray.getDirection());
// Solve quadratic a * t^2 + b * t + c = 0
T b2 = b * b;
T det = b2 - 4 * a * c;
if (det < 0) return false;
if (a > 0)
return b <= 0 || det >= b2;
else if (a < 0)
return b >= 0 || det >= b2;
else
return false;
}
/**
* Add a new set of update vectors to the history.
*
* @param yk Difference between the current and previous gradient vector.
* @param sk Difference between the current and previous state vector.
* @param reset Whether to reset the approximation, forgetting about
* previous values.
* @return In the case of a reset, returns the optimal scaling of the
* initial Hessian
* approximation which is useful for predicting step-sizes.
**/
inline Scalar update(const VectorT &yk, const VectorT &sk,
bool reset = false) {
Scalar skyk = yk.dot(sk);
Scalar B0fact;
if (reset) {
B0fact = yk.squaredNorm()/skyk;
_buf.clear();
} else {
B0fact = 1.0;
}
// New updates are pushed to the "back" of the circular buffer
Scalar invskyk = 1.0/skyk;
_gammak = skyk/yk.squaredNorm();
_buf.push_back();
_buf.back() = boost::tie(invskyk, yk, sk);
return B0fact;
}
T rayIntersectionTime(RayN<N, T> const & ray, T max_time = -1) const
{
VectorT co = ray.getOrigin() - center;
T c = co.squaredNorm() - radius * radius;
if (c <= 0) // origin is inside ball
return 0;
// We could do an early test to see if the distance from the ray origin to the ball is less than
// max_time * ray.getDirection().norm(), but it would involve a square root so might as well solve the quadratic.
T a = ray.getDirection().squaredNorm();
T b = 2 * co.dot(ray.getDirection());
// Solve quadratic a * t^2 + b * t + c = 0
T det = b * b - 4 * a * c;
if (det < 0) return -1;
T d = std::sqrt(det);
T t = -1;
if (a > 0)
{
T s0 = -b - d;
if (s0 >= 0)
t = s0 / (2 * a);
else
{
T s1 = -b + d;
if (s1 >= 0)
t = s1 / (2 * a);
}
}
else if (a < 0)
{
T s0 = -b + d;
if (s0 <= 0)
t = s0 / (2 * a);
else
{
T s1 = -b - d;
if (s1 <= 0)
t = s1 / (2 * a);
}
}
if (max_time >= 0 && t > max_time)
return -1;
else
return t;
}