我正在开发一个光线追踪系统并且它正在工作,现在我正在尝试支持更多基元(目前它支持:球体、盒子、平面和三角形),并且我在圆柱体方面遇到了问题。
我知道要使射线与圆柱体相交,我需要进行两项检查,第一个是与主体(通过它我得到一个无限圆柱体),为此我假设在平面 xz 中的二维圆(x² + z² = r,其中 r 是半径)然后我需要检查 Y 坐标是否在 0 和高度之间,最后我需要检查交点是否在大写字母中(x²+z²
我的代码如下(更多解释请参阅评论)
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);
}
此代码产生下图
(正如你所看到的,顶盖没有渲染,我也想渲染顶盖)
我一直在研究,问题如下:
point1.x*point1.x + point1.z*point1.z <= m_radius*m_radius
代码永远不会在这里输入,这里是输出文本(由std::cout << "point " << point1.y << " hipo " << point1.x*point1.x + point1.z*point1.z << " radio " << m_radius*m_radius << std::endl;
)来自第一个像素(应该进入该条件,因为第一个像素对应于顶盖)
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
正如你所看到的,永远不会hipo
是 radio
我想用盖子渲染整个圆柱体。有人可以指导我渲染整个圆柱体吗? (主体和盖子)
Thanks