对于学校，我最近开始创建自己的光线追踪器。但是，我在计算观察光线或检查三角形和光线之间的交点时遇到了障碍。据我所知，计算似乎执行正确，因为我将相机放在原点并让它面向 -z 轴朝向它前面的对象，从而允许手动进行简单的矢量数学运算。一切似乎都检查出来了，但屏幕上什么也没有画出来。
我将发布我正在使用计算观察光线的代码。
public Ray generateRay(float nX, float nY , Point2f coordinates)
{
// Compute l, r, b and t.
Vector3f temp = VectorHelper.multiply(u, nX/2.0f);
float r = temp.x + Position.x;
temp = VectorHelper.multiply(u, -nX/2.0f);
float l = temp.x + Position.x;
temp = VectorHelper.multiply(v, nY/2.0f);
float t = temp.y + Position.y;
temp = VectorHelper.multiply(v, -nY/2.0f);
float b = temp.y + Position.y;
// Compute the u and v coordinates.
float uCo = (l + (r - l) * (coordinates.x + 0.5f)/nX);
float vCo = (b + (t - b) * (coordinates.y + 0.5f)/nY);
// Compute the ray's direction.
Vector3f rayDirection = VectorHelper.multiply(w, -FocalLength);
temp = VectorHelper.add(VectorHelper.multiply(u, uCo), VectorHelper.multiply(v, vCo));
rayDirection = VectorHelper.add(rayDirection, temp);
rayDirection = VectorHelper.add(rayDirection, Position);
rayDirection = VectorHelper.normalize(VectorHelper.add(rayDirection, temp));
// Create and return the ray.
return new Ray(Position, rayDirection);
}
以下代码是我用来计算交点的代码。它使用克莱默法则来求解矩阵方程。
public static Point3f rayTriangleIntersection(
Ray ray, Point3f vertexA, Point3f vertexB, Point3f vertexC)
{
// Solve the linear system formed by the ray and the parametric surface
// formed by the points of the triangle.
// | a d g | | B | | j |
// | b e h | * | Y | = | k |
// | c f i | * | t | = | l |
// The following uses Cramer's rule to that effect.
float a = vertexA.x - vertexB.x; float d = vertexA.x - vertexC.x; float g = ray.getDirection().x;
float b = vertexA.y - vertexB.y; float e = vertexA.y - vertexC.y; float h = ray.getDirection().y;
float c = vertexA.z - vertexB.z; float f = vertexA.z - vertexC.z; float i = ray.getDirection().z;
float j = vertexA.x - ray.getOrigin().x;
float k = vertexA.y - ray.getOrigin().y;
float l = vertexA.z - ray.getOrigin().z;
// Compute some subterms in advance.
float eihf = (e * i) - (h * f);
float gfdi = (g * f) - (d * i);
float dheg = (d * h) - (e * g);
float akjb = (a * k) - (j * b);
float jcal = (j * c) - (a * l);
float blkc = (b * l) - (k * c);
// Compute common division number.
float m = (a * eihf) + (b * gfdi) + (c * dheg);
// Compute unknown t and check whether the point is within the given
// depth interval.
float t = -((f * akjb) + (e * jcal) + (d * blkc)) / m;
if (t < 0)
return null;
// Compute unknown gamma and check whether the point intersects the
// triangle.
float gamma = ((i * akjb) + (h * jcal) + (g * blkc)) / m;
if (gamma < 0 || gamma > 1)
return null;
// Compute unknown beta and check whether the point intersects the
// triangle.
float beta = ((j * eihf) + (k * gfdi) + (l * dheg)) / m;
if (beta < 0 || beta > (1 - gamma))
return null;
// Else, compute the intersection point and return it.
Point3f result = new Point3f();
result.x = ray.getOrigin().x + t * ray.getDirection().x;
result.y = ray.getOrigin().y + t * ray.getDirection().y;
result.z = ray.getOrigin().z + t * ray.getDirection().z;
return result;
}
我的问题很简单。我究竟做错了什么？我已经查看并调试了这段代码，但无法找出错误，谷歌提供的只是我正在使用的书中已有的理论。此外，代码仍然相当粗糙，因为我只是专注于在清理它之前让它工作。
提前致谢，
凯文