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 "hyperbox.h"
   8 #include "ray.h"
   9 #include "shape.h"
  10 #include "surfacepoint.h"
  11
  12 namespace Msp {
  13 namespace Geometry {
  14
  15 /**
  16 A shape consisting of the points within a specific distance from the origin.
  17 Two- and three-dimensional cases are Circle and Sphere, respectively.
  18 */
  19 template<typename T, unsigned D>
  20 class HyperSphere: public Shape<T, D>
  21 {
  22 private:
  23         T radius;
  24
  25 public:
  26         HyperSphere(): radius(1) { }
  27         explicit HyperSphere(T);
  28
  29         virtual HyperSphere *clone() const;
  30
  31         T get_radius() const { return radius; }
  32
  33         virtual HyperBox<T, D> get_axis_aligned_bounding_box() const;
  34         virtual bool contains(const LinAl::Vector<T, D> &) const;
  35         virtual bool check_intersection(const Ray<T, D> &) const;
  36         virtual unsigned get_max_ray_intersections() const { return 2; }
  37         virtual unsigned get_intersections(const Ray<T, D> &, SurfacePoint<T, D> *, unsigned) const;
  38 };
  39
  40 template<typename T, unsigned D>
  41 inline HyperSphere<T, D>::HyperSphere(T r):
  42         radius(r)
  43 {
  44         if(r<=T(0))
  45                 throw std::invalid_argument("HyperSphere::HyperShpere");
  46 }
  47
  48 template<typename T, unsigned D>
  49 inline HyperSphere<T, D> *HyperSphere<T, D>::clone() const
  50 {
  51         return new HyperSphere<T, D>(radius);
  52 }
  53
  54 template<typename T, unsigned D>
  55 inline HyperBox<T, D> HyperSphere<T, D>::get_axis_aligned_bounding_box() const
  56 {
  57         LinAl::Vector<T, D> dimensions;
  58         for(unsigned i=0; i<D; ++i)
  59                 dimensions[i] = radius;
  60         return HyperBox<T, D>(dimensions);
  61 }
  62
  63 template<typename T, unsigned D>
  64 inline bool HyperSphere<T, D>::contains(const LinAl::Vector<T, D> &point) const
  65 {
  66         return inner_product(point, point)<=radius*radius;
  67 }
  68
  69 template<typename T, unsigned D>
  70 inline bool HyperSphere<T, D>::check_intersection(const Ray<T, D> &ray) const
  71 {
  72         T x = inner_product(ray.get_direction(), ray.get_start());
  73         if(x>0)
  74                 return contains(ray.get_start());
  75         else
  76                 return contains(ray.get_start()-ray.get_direction()*x);
  77 }
  78
  79 template<typename T, unsigned D>
  80 inline unsigned HyperSphere<T, D>::get_intersections(const Ray<T, D> &ray, SurfacePoint<T, D> *points, unsigned size) const
  81 {
  82         using std::sqrt;
  83
  84         T mid = -inner_product(ray.get_direction(), ray.get_start());
  85         LinAl::Vector<T, D> nearest = ray.get_start()+ray.get_direction()*mid;
  86         T offset_sq = radius*radius-inner_product(nearest, nearest);
  87         if(offset_sq<0)
  88                 return 0;
  89         T offset = sqrt(offset_sq);
  90
  91         unsigned n = 0;
  92         for(int i=-1; (n<size && i<=1); i+=2)
  93         {
  94                 T x = mid+offset*i;
  95                 if(ray.check_limits(x))
  96                 {
  97                         if(points)
  98                         {
  99                                 points[n].position = ray.get_start()+ray.get_direction()*x;
 100                                 points[n].normal = normalize(points[n].position);
 101                                 points[n].distance = x;
 102                         }
 103
 104                         ++n;
 105                 }
 106         }
 107
 108         return n;
 109 }
 110
 111 } // namespace Geometry
 112 } // namespace Msp
 113
 114 #endif