source/geometry/hypersphere.h

   1 #ifndef MSP_GEOMETRY_HYPERSPHERE_H_
   2 #define MSP_GEOMETRY_HYPERSPHERE_H_
   3
   4 #include <cmath>
   5 #include <stdexcept>
   6 #include <msp/linal/vector.h>
   7 #include "shape.h"
   8
   9 namespace Msp {
  10 namespace Geometry {
  11
  12 /**
  13 A shape consisting of the points within a specific distance from the origin.
  14 Two- and three-dimensional cases are Circle and Sphere, respectively.
  15 */
  16 template<typename T, unsigned D>
  17 class HyperSphere: public Shape<T, D>
  18 {
  19 private:
  20         T radius;
  21
  22 public:
  23         HyperSphere(): radius(1) { }
  24         explicit HyperSphere(T);
  25
  26         virtual HyperSphere *clone() const;
  27
  28         T get_radius() const { return radius; }
  29
  30         virtual BoundingBox<T, D> get_axis_aligned_bounding_box() const;
  31         virtual bool contains(const LinAl::Vector<T, D> &) const;
  32         virtual unsigned get_max_ray_intersections() const { return 2; }
  33         virtual unsigned get_intersections(const Ray<T, D> &, SurfacePoint<T, D> *, unsigned) const;
  34 };
  35
  36 template<typename T, unsigned D>
  37 inline HyperSphere<T, D>::HyperSphere(T r):
  38         radius(r)
  39 {
  40         if(r<=T(0))
  41                 throw std::invalid_argument("HyperSphere::HyperShpere");
  42 }
  43
  44 template<typename T, unsigned D>
  45 inline HyperSphere<T, D> *HyperSphere<T, D>::clone() const
  46 {
  47         return new HyperSphere<T, D>(radius);
  48 }
  49
  50 template<typename T, unsigned D>
  51 inline BoundingBox<T, D> HyperSphere<T, D>::get_axis_aligned_bounding_box() const
  52 {
  53         LinAl::Vector<T, D> extent;
  54         for(unsigned i=0; i<D; ++i)
  55                 extent[i] = radius;
  56         return BoundingBox<T, D>(-extent, extent);
  57 }
  58
  59 template<typename T, unsigned D>
  60 inline bool HyperSphere<T, D>::contains(const LinAl::Vector<T, D> &point) const
  61 {
  62         return inner_product(point, point)<=radius*radius;
  63 }
  64
  65 template<typename T, unsigned D>
  66 inline unsigned HyperSphere<T, D>::get_intersections(const Ray<T, D> &ray, SurfacePoint<T, D> *points, unsigned size) const
  67 {
  68         using std::sqrt;
  69
  70         T mid = -inner_product(ray.get_direction(), ray.get_start());
  71         LinAl::Vector<T, D> nearest = ray.get_start()+ray.get_direction()*mid;
  72         T offset_sq = radius*radius-inner_product(nearest, nearest);
  73         if(offset_sq<0)
  74                 return 0;
  75         T offset = sqrt(offset_sq);
  76
  77         unsigned n = 0;
  78         for(int i=-1; (n<size && i<=1); i+=2)
  79         {
  80                 T x = mid+offset*i;
  81                 if(ray.check_limits(x))
  82                 {
  83                         if(points)
  84                         {
  85                                 points[n].position = ray.get_start()+ray.get_direction()*x;
  86                                 points[n].normal = normalize(points[n].position);
  87                                 points[n].distance = x;
  88                         }
  89
  90                         ++n;
  91                 }
  92         }
  93
  94         return n;
  95 }
  96
  97 } // namespace Geometry
  98 } // namespace Msp
  99
 100 #endif