void planeFromPoints(const vec3* a, const vec3* b, const vec3* c, plane3* p) {
vec3 d1, d2;
sub(a,b,&d1);
sub (b,c,&d2);
crossProduct(&d1,&d2,&(p->n));
normalize(&(p->n));
p->d = 0.0;
p->d = -signedDistance(a,p);
}
Scalar Plane<Scalar>::distance(const Vector<Scalar,3> &point) const
{
Scalar signed_dist = signedDistance(point);
Scalar dist = signed_dist>=0?signed_dist:-signed_dist;
return dist;
}
/** Reflect a point in the hyperplane. */
VectorT reflect(VectorT const & p) const
{
return p - 2 * signedDistance(p) * normal;
}
/**
* Check if the negative half space (the side of the hyperplane <b>not</b> containing the normal) contains a given point.
* Returns true if the point lies on the hyperplane.
*/
bool negativeHalfSpaceContains(VectorT const & p) const
{
return signedDistance(p) <= 0;
}
/**
* Check if the positive half space (the side of the hyperplane containing the normal) contains a given point. Returns true
* if the point lies on the hyperplane.
*/
bool positiveHalfSpaceContains(VectorT const & p) const
{
return signedDistance(p) >= 0;
}
/** Get the point on the hyperplane closest to a given point. */
VectorT closestPoint(VectorT const & p) const
{
return p - signedDistance(p) * normal;
}
/** Get the square of the distance of the hyperplane from a given point. */
T squaredDistance(VectorT const & p) const
{
return Math::square(signedDistance(p));
}
/** Get the (unsigned) distance of a given point from the hyperplane. */
T distance(VectorT const & p) const
{
return std::abs(signedDistance(p));
}
