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         virtual Coverage get_coverage(const BoundingBox<T, D> &) const;
  35 };
  36
  37 template<typename T, unsigned D>
  38 inline HyperSphere<T, D>::HyperSphere(T r):
  39         radius(r)
  40 {
  41         if(r<=T(0))
  42                 throw std::invalid_argument("HyperSphere::HyperShpere");
  43 }
  44
  45 template<typename T, unsigned D>
  46 inline HyperSphere<T, D> *HyperSphere<T, D>::clone() const
  47 {
  48         return new HyperSphere<T, D>(radius);
  49 }
  50
  51 template<typename T, unsigned D>
  52 inline BoundingBox<T, D> HyperSphere<T, D>::get_axis_aligned_bounding_box() const
  53 {
  54         LinAl::Vector<T, D> extent;
  55         for(unsigned i=0; i<D; ++i)
  56                 extent[i] = radius;
  57         return BoundingBox<T, D>(-extent, extent);
  58 }
  59
  60 template<typename T, unsigned D>
  61 inline bool HyperSphere<T, D>::contains(const LinAl::Vector<T, D> &point) const
  62 {
  63         return inner_product(point, point)<=radius*radius;
  64 }
  65
  66 template<typename T, unsigned D>
  67 inline unsigned HyperSphere<T, D>::get_intersections(const Ray<T, D> &ray, SurfacePoint<T, D> *points, unsigned size) const
  68 {
  69         using std::sqrt;
  70
  71         T mid = -inner_product(ray.get_direction(), ray.get_start());
  72         LinAl::Vector<T, D> nearest = ray.get_start()+ray.get_direction()*mid;
  73         T offset_sq = radius*radius-inner_product(nearest, nearest);
  74         if(offset_sq<T(0))
  75                 return 0;
  76         T offset = sqrt(offset_sq);
  77
  78         unsigned n = 0;
  79         for(int i=-1; (n<size && i<=1); i+=2)
  80         {
  81                 T x = mid+offset*i;
  82                 if(ray.check_limits(x))
  83                 {
  84                         if(points)
  85                         {
  86                                 points[n].position = ray.get_start()+ray.get_direction()*x;
  87                                 points[n].normal = normalize(points[n].position);
  88                                 points[n].distance = x;
  89                                 points[n].entry = (i<0);
  90                         }
  91
  92                         ++n;
  93                 }
  94         }
  95
  96         return n;
  97 }
  98
  99 template<typename T, unsigned D>
 100 inline Coverage HyperSphere<T, D>::get_coverage(const BoundingBox<T, D> &bbox) const
 101 {
 102         const LinAl::Vector<T, D> &min_pt = bbox.get_minimum_point();
 103         const LinAl::Vector<T, D> &max_pt = bbox.get_maximum_point();
 104
 105         LinAl::Vector<T, D> far_point;
 106         for(unsigned i=0; i<D; ++i)
 107                 far_point[i] = std::max(std::abs(min_pt[i]), std::abs(max_pt[i]));
 108
 109         if(contains(far_point))
 110                 return FULL_COVERAGE;
 111
 112         unsigned spanned_dimensions = 0;
 113         for(unsigned i=0; i<D; ++i)
 114                 if(min_pt[i]<T(0) && max_pt[i]>T(0))
 115                         spanned_dimensions |= 1<<i;
 116
 117         for(unsigned i=0; i<(1<<D); ++i)
 118         {
 119                 if(i&spanned_dimensions)
 120                         continue;
 121
 122                 LinAl::Vector<T, D> point;
 123                 for(unsigned j=0; j<D; ++j)
 124                         if(!((spanned_dimensions>>j)&1))
 125                                 point[j] = ((i>>j)&1 ? max_pt[j] : min_pt[j]);
 126
 127                 if(contains(point))
 128                         return PARTIAL_COVERAGE;
 129         }
 130
 131         return NO_COVERAGE;
 132 }
 133
 134 } // namespace Geometry
 135 } // namespace Msp
 136
 137 #endif