我正在编写一个简单的光线追踪器，为了保持简单，我决定在我的场景中只使用球体。我现在处于一个阶段，我只想确认我的光线是否正确地与场景中的球体相交，仅此而已。我创建了一个 Ray 和 Sphere 类，然后在我的主文件中创建了一个函数，该函数遍历每个像素以查看是否存在交叉点（相关代码将在下面发布）。问题是与球体的整个交叉点表现得相当奇怪。如果我创建一个中心为 (0, 0, -20) 且半径为 1 的球体，那么我只会得到一个交点，该交点始终位于我的图像的第一个像素（左上角）。一旦我到达 15 的半径，我会突然在左上角区域看到三个交叉点。
我怀疑我的射线球相交代码在这里可能有问题，但是通过查看它并通过网络查看更多信息，大多数解决方案都描述了我使用的相同方法，所以我认为它不应该（！）有问题这里。所以......我不确定我做错了什么，它可能是我的交集代码，也可能是其他导致问题的东西。我似乎无法找到它。给球体和光线赋值时，我想错了吗？下面是相关代码
球体类：
Sphere::Sphere(glm::vec3 center, float radius)
: m_center(center), m_radius(radius), m_radiusSquared(radius*radius)
{
}
//Sphere-ray intersection. Equation: (P-C)^2 - R^2 = 0, P = o+t*d
//(P-C)^2 - R^2 => (o+t*d-C)^2-R^2 => o^2+(td)^2+C^2+2td(o-C)-2oC-R^2
//=> at^2+bt+c, a = d*d, b = 2d(o-C), c = (o-C)^2-R^2
//o = ray origin, d = ray direction, C = sphere center, R = sphere radius
bool Sphere::intersection(Ray& ray) const
{
//Squared distance between ray origin and sphere center
float squaredDist = glm::dot(ray.origin()-m_center, ray.origin()-m_center);
//If the distance is less than the squared radius of the sphere...
if(squaredDist <= m_radiusSquared)
{
//Point is in sphere, consider as no intersection existing
//std::cout << "Point inside sphere..." << std::endl;
return false;
}
//Will hold solution to quadratic equation
float t0, t1;
//Calculating the coefficients of the quadratic equation
float a = glm::dot(ray.direction(),ray.direction()); // a = d*d
float b = 2.0f*glm::dot(ray.direction(),ray.origin()-m_center); // b = 2d(o-C)
float c = glm::dot(ray.origin()-m_center, ray.origin()-m_center) - m_radiusSquared; // c = (o-C)^2-R^2
//Calculate discriminant
float disc = (b*b)-(4.0f*a*c);
if(disc < 0) //If discriminant is negative no intersection happens
{
//std::cout << "No intersection with sphere..." << std::endl;
return false;
}
else //If discriminant is positive one or two intersections (two solutions) exists
{
float sqrt_disc = glm::sqrt(disc);
t0 = (-b - sqrt_disc) / (2.0f * a);
t1 = (-b + sqrt_disc) / (2.0f * a);
}
//If the second intersection has a negative value then the intersections
//happen behind the ray origin which is not considered. Otherwise t0 is
//the intersection to be considered
if(t1<0)
{
//std::cout << "No intersection with sphere..." << std::endl;
return false;
}
else
{
//std::cout << "Intersection with sphere..." << std::endl;
return true;
}
}
程序：
#include "Sphere.h"
#include "Ray.h"
void renderScene(const Sphere& s);
const int imageWidth = 400;
const int imageHeight = 400;
int main()
{
//Create sphere with center in (0, 0, -20) and with radius 10
Sphere testSphere(glm::vec3(0.0f, 0.0f, -20.0f), 10.0f);
renderScene(testSphere);
return 0;
}
//Shoots rays through each pixel and check if there's an intersection with
//a given sphere. If an intersection exists then the counter is increased.
void renderScene(const Sphere& s)
{
//Ray r(origin, direction)
Ray r(glm::vec3(0.0f), glm::vec3(0.0f));
//Will hold the total amount of intersections
int counter = 0;
//Loops through each pixel...
for(int y=0; y<imageHeight; y++)
{
for(int x=0; x<imageWidth; x++)
{
//Change ray direction for each pixel being processed
r.setDirection(glm::vec3(((x-imageWidth/2)/(float)imageWidth), ((imageHeight/2-y)/(float)imageHeight), -1.0f));
//If current ray intersects sphere...
if(s.intersection(r))
{
//Increase counter
counter++;
}
}
}
std::cout << counter << std::endl;
}