drawing a cube with perspective - math

Question

I am trying to draw the Mandelbox using my own ray marching on the CPU.
I have a width*height bitmap to render to.
For each pixel, I want to march towards the cube:
static float eye = 0.0f; eye = glm::clamp(eye+0.005f,0.0f,1.0f); // animate
const glm::mat4 projection = glm::perspective(35.0f, (float)width/height, 0.1f, 10.0f),
modelview = glm::lookAt(glm::vec3(cos(eye),sin(eye),-1),glm::vec3(0,0,0),glm::vec3(0,0,1));
const float epsilon = sqrt(1.0f/std::max(width,height))/2.0f;
for(int y=0; y<height; y++) {
for(int x=0; x<width; x++) {
glm::vec3 p = glm::unProject(glm::vec3(x,y,0),modelview,projection,glm::vec4(0,0,width,height)),
dir = glm::unProject(glm::vec3(x,y,1),modelview,projection,glm::vec4(0,0,width,height))-p,
P0 = p;
//std::cout << x << "," << y << " " << p.x << "," << p.y << "," << p.z << " " << dir.x << "," << dir.y << "," << dir.z << std::endl;
float D = 0;
for(int i=0; i<MAX_ITER; i++) {
const float d = DE(p);
D += d;
if(d<epsilon) {
depth_bmp[y*width+x] = 255.0f/i;
break;
}
p = dir*D + P0;
}
}
}
My distance estimator function is a very literal translation and looks like this:
float DE(glm::vec3 p) {
const float Scale = -1.77f, fixedRadius2 = 1.0f, minRadius2 = (0.5f*0.5f);
const glm::vec3 p0 = p;
float dr = 1.0f;
for(int n = 0; n < 13; n++) {
// Reflect
p = (glm::clamp(p,-1.0f,1.0f) * 2.0f) - p;
// Sphere Inversion
const float r2 = glm::dot(p,p);
if(r2<minRadius2) {
const float t = (fixedRadius2/minRadius2);
p *= t;
dr *= t;
} else if(r2<fixedRadius2) {
const float t = (fixedRadius2/r2);
p *= t;
dr *= t;
}
// Scale & Translate
p = p * Scale + p0;
dr = dr * abs(Scale) + 1.0f;
}
return glm::length(p)/abs(dr);
}
And the output looks completely unbox-like:
How do I set the eye transform up so I see the cube properly?

Answer 1

The issue is that the length of the ray must be normalised:
glm::vec3 p = glm::unProject(glm::vec3(x,y,0),modelview,projection,glm::vec4(0,0,width,height)),
dir = glm::unProject(glm::vec3(x,y,1),modelview,projection,glm::vec4(0,0,width,height))-p;
const float len = glm::length(dir);
dir = glm::normalise(dir);
float D = 0;
for(int i=0; i<MAX_ITER; i++) {
const float d = DE(p + dir*D);
D += d;
if(D > len) break;
...

Answer 2

You can use the method outlined here to generate the correct rays (and their lengths).