问题
I am developing a Ray Tracing system and it is working, now I am trying to support more primitives (for now it supports: spheres, boxes, planes and triangles), and I am having problems with cylinders.
I know to intersect ray with cylinder I need to do two check, the first is with the body (with that I get an Infinite Cylinder), for this I assume circle in two dimensions, in the plane xz (x² + z² = r, where r is the radius) then I need check that Y coordinate is between 0 and height and finally I need to check if the intersection is in the caps (x²+z²<=r, where r is the radius).
My code is the follow (see the comments for more explanations)
Intersection Cylinder::hit(Ray ray)
{
ray.setOrigin(vec3(getInverseTransform() * vec4(ray.getOrigin(),1)));
ray.setDirection(glm::normalize(vec3(getInverseTransform() * vec4(ray.getDirection(),0))));
// R(t) = o + td
// x² + z² = r²
// (ox+tdx)² + (oz+tdz)² = r²
// (ox)² + 2oxtdx + (tdx)² + (oz)² + 2oztdz + (tdz)² = r²
// t²(dx + dz) + 2t(oxdx + ozdz) + (ox)² + (oz)² - r² = 0
// a=(dx + dz); b = 2(oxdx + ozdz); c = (ox)² + (oz)² - r²
float a = ray.getDirection().x*ray.getDirection().x + ray.getDirection().z*ray.getDirection().z;
float b = 2*(ray.getOrigin().x*ray.getDirection().x + ray.getOrigin().z*ray.getDirection().z);
float c = ray.getOrigin().x*ray.getOrigin().x + ray.getOrigin().z*ray.getOrigin().z - m_radius*m_radius;
float discr = b*b - 4*a*c;
if (discr < 0)
{
return Intersection(false);
}
float x1 = (-b+sqrt(discr))/(2*a);
float x2 = (-b-sqrt(discr))/(2*a);
float t;
//choose the smallest and >=0 t
if (x1 > x2)
{
t=x2;
}
if (t < 0)
{
t=x1;
}
// if both solution are <0 => NO INTERSECTION!
if (t<0)
{
return Intersection(false);
}
// normal calculation
// f(x,y) = x² + z² - r² = 0
// T = (dx/dt, y, dz/dt)
// 0 = df/dt = (df/dx, y, df/dz) · T
// N = (2x, 0, 2z)
vec3 point = ray.getOrigin() + ray.getDirection()*t;
vec3 normal = vec3(2*point.x, 0.0f, 2*point.z);
// If the y-component from point computed is smaller than 0 or bigger than height => NO INTERSECTION!
if (point.y < 0 || point.y > m_height)
{
return Intersection(false);
}
//If ray direction is not pararel to Y Plane
if (ray.getDirection().y != 0.0f) //Paralel
{
//Compute t's for point intersection in the Y Plane
float t3 = (0-ray.getOrigin().y)/ray.getDirection().y;
float t4 = (m_height-ray.getOrigin().y)/ray.getDirection().y;
float t2;
//choose the smallest and >=0 t
t2 = std::min(t3,t4);
if (t2 < 0)
{
t2 = std::max(t3,t4);
}
if (t2 >= 0)
{
// If there is a t >= 0 compute de point and check if the point is inside the cap
vec3 point1 = ray.getOrigin() + ray.getDirection()*t2;
std::cout << "point " << point1.y << " hipo " << point1.x*point1.x + point1.z*point1.z << " radio " << m_radius*m_radius << std::endl;
if (point1.x*point1.x + point1.z*point1.z <= m_radius*m_radius+0.9f)
{
// Intersection point is inside cap but, Which t is the smallest? t from cap or t from body cylinder?
// I choose the smallest t and check if the t is from cap and compute normal and return intersection.
t = std::min(t,t2);
if (t == t3)
{
normal = vec3(0.0f,-1.0f,0.0f);
return Intersection(true, point1, normal);
}
else if (t == t4)
{
normal = vec3(0.0f,1.0f,0.0f);
return Intersection(true, point1, normal);
}
}
}
}
// Intersection in the body cylinder, compute the point and return the intersection
point = ray.getOrigin() + ray.getDirection()*t;
return Intersection(true, point, normal);
}
this code result in the following image
(As you can see the top cap is not rendering, and I want to render the caps also)
I have been researching and the problem look like here:
point1.x*point1.x + point1.z*point1.z <= m_radius*m_radius
The code never enter here, here is the output text (generated by std::cout << "point " << point1.y << " hipo " << point1.x*point1.x + point1.z*point1.z << " radio " << m_radius*m_radius << std::endl;) from the firsts pixeles (that should enter in that condition because the first pixeles corresponds with the top cap)
point 0.5 hipo 0.0900812 radio 0.09
point 0.5 hipo 0.0900206 radio 0.09
point 0.5 hipo 0.0900812 radio 0.09
point 0.5 hipo 0.0900206 radio 0.09
Pixel: y: 280
point 0.5 hipo 0.0913921 radio 0.09
point 0.5 hipo 0.120013 radio 0.09
point 0.5 hipo 0.0913921 radio 0.09
point 0.5 hipo 0.120013 radio 0.09
Pixel: y: 281
point 0.5 hipo 0.0930369 radio 0.09
point 0.5 hipo 0.183345 radio 0.09
point 0.5 hipo 0.0930369 radio 0.09
point 0.5 hipo 0.183345 radio 0.09
Pixel: y: 282
point 0.5 hipo 0.0950108 radio 0.09
point 0.5 hipo 0.261889 radio 0.09
point 0.5 hipo 0.0903952 radio 0.09
point 0.5 hipo 0.0903952 radio 0.09
point 0.5 hipo 0.0950108 radio 0.09
point 0.5 hipo 0.261889 radio 0.09
Pixel: y: 283
point 0.5 hipo 0.0973093 radio 0.09
point 0.5 hipo 0.347767 radio 0.09
point 0.5 hipo 0.0927148 radio 0.09
point 0.5 hipo 0.0927148 radio 0.09
point 0.5 hipo 0.0973093 radio 0.09
point 0.5 hipo 0.347767 radio 0.09
As you can see never hipo is < than radio
I want to render the whole cylinder with caps. Can anybody guide me to render the whole cylinder? (body and caps)
Thanks
回答1:
I assume that you are able to find the intersection points between the ray and the cylinder surface, obtained as t values along the ray. Do a similar computation to find the intersections with the planes of the two basis.
You will get two pairs [tc0, tc1], [tp0, tp1]. If these intervals do not overlap, the ray doesn't hit the cylinder. Otherwise, the largest of tc0 and tp0 tells you what surface is actually hit, and this t value tells you where.
来源：https://stackoverflow.com/questions/35164707/ray-cylinder-intersection