• The Idea:
  • Model light rays/photons/waves from the source(s), onto and off of objects in the scene/world, to the eye/camera
• Requirements:
  • Understanding of elecromagnetic waves
  • Understanding of materials

• The Idea:
  • Model light as multiple rays with different energy levels/intensities for different colors/wavelengths
  • Start from the source and end at the view plane
• A Shortcoming:
  • Many rays are not seen
  • It's too computationally expensive to trace rays that don't contribute to the image

• The Major Difference:
  • Consider the rays that certainly contribute to the image by starting at the view plane and trace backwards to the light source(s)
• Odd Terminology:
  • The "first object" that could have emitted a given ray is first in the backwards sense

• Feeler Ray:
  • A ray sent from the eye
• Illumination Ray:
  • A feeler ray that reaches a light
• Shadow Ray:
  • A feeler ray that does not reach a light

• Ray Tracing:
  • A ray can give rise to multiple rays (e.g., reflected, transmitted) as it moves through the scene/world, each of which is traced
• Path Tracing:
  • Each trace involves a single path through the scene that is stochastic in nature (e.g., as a result of reflection/transmission probabilities); multiple rays are traced for each pixel

• Tracing (Event-Based):
  • Calculates the intersection between the ray and the objects in the scene
• Marching (Space-Based):
  • The array is moved a small amount each step until it contacts an object in the scene

• An Observation:
  • Pixels are large relative to light rays
• An Implication:
  • Pixels may have sharp distinctions between them (i.e., "jaggies" of aliasing) if one ray is used for each pixel
• Antialiasing Methods:
  • Supersampling - Use multiple rays per pixel (e.g., 9) and average the result
  • Adaptive Supersampling - Start with a smaller number ofrays per pixel (e.g., 5) and subdivide further if the colors are different
  • Stochastic Sampling - Randomly generate multiple rays for each pixel and average the result

• Bounding Volume Hierarchies:
  • Selects volumes based on given objects
• Spatial Subdivision:
  • Selects objects based on given volumes

• Trivial:
  • Divide the view plane into subsets and use a different processor for each subset
• Other Techniques:
  • Vector processors (SIMD)
  • "Custom" algorithms

• A Ray class
• An empty (for semantics only) Material interface
• A Shape3D interface
• An Intersection class
• A CompositeShape (in the sense of the composite pattern) class
• Some classes that implement the Shape3D interface
• A Light class

The Specification

cppexamples/graphics3d/Ray.h

        #ifndef edu_jmu_cs_Ray_h
#define edu_jmu_cs_Ray_h
#include <glm/glm.hpp>

/**
 * An encapsulation of a Ray.
 *
 * @author Prof. David Bernstein, James Madison University
 */
class Ray {
 public:
  glm::vec3 o;
  glm::vec3 d;

  /**
   * Default Constructor.
   */
  Ray();

  /**
   * Explicit Value Constructor.
   *
   * @param origin     The origin
   * @param direction  The direction
   */
  Ray(const glm::vec3& origin, const glm::vec3& direction);

  /**
   * Get the pointAt t along the direction from the origin.
   *
   * @return  The point
   */
  glm::vec3 pointAt(float t) const;
};

#endif


        

The Implementation

cppexamples/graphics3d/Ray.cpp

        #include "Ray.h"

Ray::Ray() {
}

Ray::Ray(const glm::vec3& origin, const glm::vec3& destination) {
  o = origin;
  d = destination;
}

glm::vec3 Ray::pointAt(float t) const {
  return o + t*d;
}


        

cppexamples/graphics3d/Shape3D.h

        #ifndef edu_jmu_cs_Shape3D_h
#define edu_jmu_cs_Shape3D_h

#include "Ray.h"
#include "Intersection.h"

/**
 * The requirements of Shape3D objects.
 *
 * @author Prof. David Bernstein, James Madison University
 */
class Shape3D  {
 public:
  /**
   * Find the intersection (if any) of the given Ray with this Shape3D
   * (within given bounds).
   *
   * @param r            The Ray
   * @param tMin         The lower bound of the parameter
   * @param tMax         The upper bound of the parameter
   * @param intersection The (outbound) point of intersection
   * @return             true if there is an intersection; false otherwise
   */
  virtual bool intersectsWith(const Ray& r,
                              float tMin, float tMax,
                              Intersection* intersection) const = 0;
};

#endif




        

The Specification

cppexamples/graphics3d/Intersection.h

        #ifndef edu_jmu_cs_Intersection_h
#define edu_jmu_cs_Intersection_h

#include "Material.h"
#include "Shape3D.h"
#include <glm/glm.hpp>

class Shape3D;

/**
 * An encapsulation of the intersection between a Ray and
 * a Shape3D.
 *
 * @author Prof. David Bernstein, James Madison Univesity
 */
class Intersection {
 public:
  const Shape3D*   shape;
  float      t;
  glm::vec3  p;
  glm::vec3  n;
  const Material*  material;

  /**
   * Default Constructor.
   */
  Intersection();

  /**
   * Explicit Value Constructor.
   *
   * @param s      The Shape3D
   * @param t      The portion of the Intersection on the Ray
   * @param point  The point on the Shape3D
   * @param normal The normal at the point
   * @param m      The Material of the Shape3D
   */
  Intersection(const Shape3D* s, float tOnRay, const glm::vec3& point,
               const glm::vec3& normal, const Material* m);
};

#endif
        

The Implementation

cppexamples/graphics3d/Intersection.cpp

        #include "Intersection.h"

Intersection::Intersection() {
}

Intersection::Intersection(const Shape3D* s, float tOnRay,
                           const glm::vec3& point, const glm::vec3& normal,
                           const Material* m):
    shape(s), t(tOnRay), p(point), n(normal), material(m) {
}
        

The Specification

cppexamples/graphics3d/CompositeShape3D.h

        #ifndef edu_jmu_cs_CompositeShape3D_h
#define edu_jmu_cs_CompositeShape3D_h

#include "Intersection.h"
#include "Ray.h"
#include "Shape3D.h"

/**
 * A Shape3D that contains other Shape3D objects (in the
 * sense of the composite pattern.
 *
 * @author Prof. David Bernstein, James Madison University
 */
class CompositeShape3D: public Shape3D  {
 private:
  Shape3D **shapes;
  int     length;

 public:
  /**
   * Default Constuctor.
   */
  CompositeShape3D();

  /**
   * Explicit Value Constructor.
   *
   * @param s   The array of Shape3D objects
   * @param n   The number of Shape3D objects
   */
  CompositeShape3D(Shape3D** s, int n);

  virtual bool intersectsWith(const Ray& r,
                              float tMin, float tMax,
                              Intersection* intersection) const;
};

#endif

        

The Implementation

cppexamples/graphics3d/CompositeShape3D.cpp

        #include "CompositeShape3D.h"

CompositeShape3D::CompositeShape3D() {
}

CompositeShape3D::CompositeShape3D(Shape3D** s, int n) {
  shapes = s;
  length = n;
}

bool CompositeShape3D::intersectsWith(const Ray& r,
                             float tMin, float tMax,
                             Intersection* intersection) const {
  Intersection temp;
  bool intersects = false;
  double closest = tMax;

  for (int i = 0; i < length; i++) {
    if (shapes[i]->intersectsWith(r, tMin, closest, &temp)) {
      intersects = true;
      closest = temp.t;
      intersection->shape = temp.shape;
      intersection->t = temp.t;
      intersection->p = temp.p;
      intersection->n = temp.n;
      intersection->material = temp.material;
    }
  }
  return intersects;
}
        

The Specification

cppexamples/graphics3d/Light.h

        #ifndef edu_jmu_cs_Light_h
#define edu_jmu_cs_Light_h

#include <glm/glm.hpp>

/**
 * An encapsulation of a Light.
 *
 * @author Prof. David Bernstein, James Madison University
 */
class Light {
 public:
  glm::vec3 location;
  glm::vec3 color;

  /**
   * Explicit Value Constructor.
   *
   * @param xyz  The location of the Light
   * @param rgb  The color/intensity of the Light
   */
  Light(const glm::vec3 &xyz, const glm::vec3 &rgb);
};

#endif
        

The Implementation

cppexamples/graphics3d/Light.cpp

        #include "Light.h"

Light::Light(const glm::vec3 &xyz, const glm::vec3 &rgb):
    location(xyz), color(rgb) {
}