struct maybe_point sphere_intersection_point(struct ray r, struct sphere s){
struct maybe_point p;
double A = dot_vector(r.dir,r.dir);
double B = 2 * dot_vector(difference_point(r.p,s.center), r.dir);
double C = dot_vector(difference_point(r.p,s.center),
difference_point(r.p, s.center)) - s.radius*s.radius;
double E = (-B+sqrt(B*B-4*A*C))/2/A;
double F = (-B-sqrt(B*B-4*A*C))/2/A;
if((E>0&& F>0)){
p.isPoint = 1;
if(E>F)
p.p = translate_point(r.p, scale_vector(r.dir,F));
else
p.p = translate_point(r.p, scale_vector(r.dir,E));
}else if((E>0||F>0)){
p.isPoint = 1;
if(E>0)
p.p = translate_point(r.p, scale_vector(r.dir,E));
else
p.p = translate_point(r.p, scale_vector(r.dir,F));
}else{
p.isPoint =0;
p.p = create_point(0,0,0);
}
return p;
}
struct maybe_point sphere_intersection_point(struct ray r, struct sphere s)
{
double a = dot_vector(r.dir, r.dir);
double b = 2 * dot_vector(difference_point(r.p, s.center), r.dir);
double c = dot_vector(difference_point(r.p, s.center),
difference_point(r.p, s.center)) - (s.radius * s.radius);
double disc = discriminant(a, b, c);
double pos_result = pos_quadratic(a, b, c);
double neg_result = neg_quadratic(a, b, c);
double result;
if (disc < 0)
{
return create_maybe_point(0, create_point(0.0, 0.0, 0.0));
}
if (pos_result > 0 && neg_result > 0)
{
if (pos_result < neg_result)
{
result = pos_result;
}
else
{
result = neg_result;
}
}
else if (pos_result > 0)
{
result = pos_result;
}
else if (neg_result > 0)
{
result = neg_result;
}
else
{
result = -1;
}
if (result > 0)
{ /*point is valid*/
return create_maybe_point(1, translate_point(r.p, scale_vector(r.dir, result)));
}
else
{ /* point is invalid*/
return create_maybe_point(0, translate_point(r.p, scale_vector(r.dir, result)));
}
}
struct maybe_point sphere_intersection_point(struct ray r, struct sphere s)
{
double a = dot_vector(r.dir,r.dir);
struct vector v=difference_point(r.p,s.center);
double b = 2*dot_vector(v,r.dir);
double c = dot_vector(v,v) - (s.radius*s.radius);
if( (b*b-4*a*c)>0) //two real roots
{
double t1 = ( (-b+sqrt((b*b)-(4*a*c)))/(2*a));
double t2 = ( (-b-sqrt((b*b)-(4*a*c)))/(2*a));
if(t1>0 && t2>0) // ray hits sphere twice, need lower t value
{
if(t1<=t2)
{
struct maybe_point mp5;
mp5.isPoint=1;
mp5.p=translate_point(r.p,scale_vector(r.dir,t1));
return mp5;
}
else
{
struct maybe_point mp6;
mp6.isPoint=1;
mp6.p=translate_point(r.p,scale_vector(r.dir,t2));
return mp6;
}
}
else if( (t1>0&&t2<0) || (t1<0&&t2>0) ) //t is positive and negative,need positive t value
{
if(t1>0)
{
struct maybe_point mp7;
mp7.isPoint=1;
mp7.p=translate_point(r.p,scale_vector(r.dir,t1));
return mp7;
}
else
{
struct maybe_point mp8;
mp8.isPoint=1;
mp8.p=translate_point(r.p,scale_vector(r.dir,t2));
return mp8;
}
}
else //no intersection, both t's negative
{
struct maybe_point mp1;
mp1.isPoint=0;
mp1.p.x=0;
mp1.p.y=0;
mp1.p.z=0;
return mp1;
}
}
else if( (b*b-4*a*c)==0)//one real root
{
printf("oneroot!");
double t3 = -b/2*a;
if(t3>0)//t is positive, so the ray intersects sphere tangentially
{
struct maybe_point mp2;
mp2.isPoint=1;
mp2.p=translate_point(r.p,scale_vector(r.dir,t3));
return mp2;
}
else //t is negative, so ray does not intersect sphere.
//also includes the case where t==0, where the ray starting
//point is on the sphere. am going to treat like non-intersection
{
struct maybe_point mp3;
mp3.isPoint=0;
mp3.p.x=0;
mp3.p.y=0;
mp3.p.z=0;
return mp3;
}
}
else // no real roots
{
struct maybe_point mp;
mp.isPoint=0;
mp.p.x=0;
mp.p.y=0;
mp.p.z=0;
return mp;
}
}
struct vector sphere_normal_at_point(struct sphere s, struct point p)
{
return normalize_vector(difference_point(p, s.center));
}
