/* draw a sphere and use raytracing on the sphere in OpenGL glut. */ #include #include #include #include #include #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(.

1. /* draw a sphere and use raytracing on the sphere in OpenGL glut. */
#include
#include
#include
#include
#include
#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)
{

2. 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]};

3. 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);

4. 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();
}

5. 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;
}
Solution
/* draw a sphere and use raytracing on the sphere in OpenGL glut. */
#include
#include
#include
#include
#include
#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)

6. {
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)

7. {
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);

8. 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

9. {
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;
}