C++ OpenGL: Ray Trace Shading Isn't Properly Shading

Question

I'm a CS student and for our final we were told to construct the reflections on multiple spheres via ray tracing. That's almost literally what we got for directions except a picture for how it should look when finished. So I need spheres, with they're reflections (using ray tracing) mapped on them with the proper shading from a light.

Well I have all of it working, except having multiple spheres and the fact that it doesn't look like the picture he gave us for a rubric.

The multiple spheres thing I'm not too sure how to do, but I'd say I need to store them in a 2D array and modify a few sections of code.

What I thought was modifying the sphere_intersect and find_reflect to include which sphere is being analyzed. Next, modify find_reflect so that when the new vector u is calculated its starting point (P0) is also updated. Then if the ray hits a sphere it will have to count how many times the ray has been reflected. At some point terminate (after 10 times maybe) and then I'll just draw the pixel. For an added touch I'd like to add solid colors to the spheres which would call for finding the normal of a sphere I believe.

Anyways I'm going to attach a picture of his, a picture of mine, and the source code. Hopefully someone can help me out on this one.

Thanks in advance!

Professor's spheres

My spheres

#include "stdafx.h"
#include <stdio.h>
#include <stdlib.h>
#include <GL/glut.h>
#include <math.h>
#include <string>

#define screen_width 750
#define screen_height 750
#define true 1
#define false 0
#define perpendicular 0

int gridXsize = 20;
int gridZsize = 20;
float plane[] = {0.0, 1.0, 0.0, -50.0,};
float sphere[] = {250.0, 270.0, -100.0, 100.0};
float eye[] = {0.0, 400.0, 550.0};
float light[] = {250.0, 550.0, -200.0};

float dot(float *u, float *v)
{
   return u[0]*v[0] + u[1]*v[1] + u[2]*v[2];
}

void norm(float *u)
{
   float norm = sqrt(abs(dot(u,u)));

   for (int i =0; i <3; i++)
   {
      u[i] = u[i]/norm;
   }

}

float plane_intersect(float *u, float *pO)
{
   float normt[3] = {plane[0], plane[1], plane[2]};

   float s;

   if (dot(u,normt) == 0)
   {
      s = -10;
   }

   else
   {
      s = (plane[3]-(dot(pO,normt)))/(dot(u,normt));
   }

   return s;
}

float sphere_intersect(float *u, float *pO)
{

   float deltaP[3] = {sphere[0]-pO[0],sphere[1]-pO[1],sphere[2]-pO[2]};
   float deltLen = sqrt(abs(dot(deltaP,deltaP)));
   float t=0;
   float answer;
   float det;

   if ((det =(abs(dot(u,deltaP)*dot(u,deltaP))- (deltLen*deltLen)+sphere[3]*sphere[3])) < 0)
   {
      answer = -10;
   }

   else
   {
      t =-1*dot(u,deltaP)- sqrt(det) ;

          if (t>0)
      {
         answer = t;
      }

      else
      {
         answer = -10;
      }
   }

   return answer;
}

void find_reflect(float *u, float s, float *pO)
{
   float n[3] = {pO[0]+s *u[0]-sphere[0],pO[1]+s *u[1]-sphere[1],pO[2]+s *u[2]- sphere[2]};
   float l[3] = {s *u[0],s *u[1],s *u[2]};
   u[0] =(2*dot(l,n)*n[0])-l[0];
   u[1] = (2*dot(l,n)*n[1])-l[1];
   u[2] = (2*dot(l,n)*n[2])-l[2];
}

float find_shade(float *u,float s, float *pO)
{
   float answer;
   float lightVec[3] = {light[0]-(pO[0]+s *u[0]), light[1]-(pO[1]+s *u[1]), light[2]-(pO[2]+s *u[2])};
   float n[3] = {pO[0]+s *u[0]-sphere[0],pO[1]+s *u[1]-sphere[1],pO[2]+s *u[2]-sphere[2]};
   answer = -1*dot(lightVec,n)/(sqrt(abs(dot(lightVec,lightVec)))*sqrt(abs(dot(n,n))));
   return answer;
}

void init()
{
   glMatrixMode(GL_PROJECTION);
   glLoadIdentity();
   gluOrtho2D(0,screen_width,0,screen_height);
}

void display()
{
   glClear(GL_COLOR_BUFFER_BIT| GL_DEPTH_BUFFER_BIT);
   glMatrixMode(GL_MODELVIEW);
   glLoadIdentity();

   for (int i=0; i < screen_width; i++)
   {
      for (int j=0; j < screen_height; j++)
      {
         float ray[3] = {1*(eye[0]-i),-1*(eye[1]-j),1*eye[2]};
         float point[3] = {i,j,0};
         norm(ray);
         int plotted = false;

         while (!plotted)
         {
            float s_plane = plane_intersect(ray, point);
            float s_sphere = sphere_intersect(ray, point);

            if (s_plane <= 0 && s_sphere <=0)
            {
               glColor3f(0,0,0);
               glBegin(GL_POINTS);
               glVertex3f(i,j,0);
               glEnd();
               plotted = true;
            }

            else if (s_sphere >= 0  && (s_plane <=0 || s_sphere <= s_plane))
            {
               find_reflect(ray, s_sphere, point);
            }

            else if (s_plane >=0 && (s_sphere <=0 ||s_plane <= s_sphere))
            {
               float shade = find_shade(ray, s_plane, point);
               float xx = s_plane*ray[0] + eye[0];
               float z = s_plane*ray[2] + eye[2];

               if (abs((int)xx/gridXsize)%2 == abs((int)z/gridZsize)%2)
               {
                  glColor3f(shade,0,0);
               }

               else
               {
                  glColor3f(shade,shade,shade);
               }

               glBegin(GL_POINTS);
               glVertex3f(i,j,0);
               glEnd();
               plotted = true;
            }
         }
      }
   }

   glFlush();
}

int main(int argc, char **argv)
{
   glutInit(&argc, argv);
   glutCreateWindow("Ray Trace with Sphere.");
   glutInitWindowSize(screen_width,screen_height);
   glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
   glutDisplayFunc(display);
   init();
   glutMainLoop();
   return 0;
}

Answer 1

The professor did not tell you too much, because such a topic is covered thousands of time over the web, just check-out "Whitted Raytracing" ;) It's homework, and 5mn of googling around would solve the issue... Some clues to help without doing your homework for you

Do it step by step, don't try to reproduce the picture in one step

• Get one sphere working, if hit the plane green pixel, the sphere red pixel, nothing, black. It's enough to get the intersections computing right. It looks like, from your picture, that you don't have the intersections right, for a start
• Same as previous, with several spheres. Same as one sphere : check intersection for all objects, keep the closest intersection from the point of view.
• Same as previous, but also compute the amount of light received for each intersection found, to have shade of red for spheres, and shade of green for the plane. (hint: dot product ^^)
• Texture for the plane
• Reflection for the spheres. Protip: a mirror don't reflect 100% of the light, just a fraction of it.