Ray-Marching: Rendering a Voxel Grid with Proper Normals

Question

Dear Computer Graphics SE,

I have a RAYMARCHING renderer, that looks up voxel data from a 3D texture. Each cell in the texture can be 0 or 1.

I have a very simple algorithm for calculating the signed distance at a given point p in space. Here is some pseudocode

Let p be some vec3(x,y,z)
Let v = value of the 3D texture at point p (0 or 1)
If v == 1:
    sdf=0.0
If v == 0:
    sdf = cell_width/2.0

This works fine to find the intersection point between the ray and the voxel grid for raymarching, but this totally messes with the normals. More specifically, normals in +x, +y, +z direction work fine, but normals that should be in the -x, -y, -z directions show up as vec3(0.0) instead.

Here is my normal algorithm (glsl):

vec3 get_normal(vec3 intersection){


    vec3 axis1 = intersection+vec3(1.0,0.0,0.0)*normal_epsilon;
    vec3 axis2 = intersection+vec3(0.0,1.0,0.0)*normal_epsilon;
    vec3 axis3 = intersection+vec3(0.0,0.0,1.0)*normal_epsilon;

    float d1 = primary_sdf(axis1);
    float d2 = primary_sdf(axis2);
    float d3 = primary_sdf(axis3);


    vec3 n = normalize(vec3(d1,d2,d3));

    return n;



}

What is the best way to get a good sdf for my voxel field, that won't break the normals?

Answer 1

To estimate the normal at a point, you need to find the gradient of the distance field in the immediate vicinity of the point. You need the rate of change, not the actual values.

vec3 getNormal(vec3 p) {
   return normalize(vec3(
       getSDF(vec3(p.x + EPSILON, p.y, p.z)) - getSDF(vec3(p.x - EPSILON, p.y, p.z)),
       getSDF(vec3(p.x, p.y + EPSILON, p.z)) - getSDF(vec3(p.x, p.y - EPSILON, p.z)),
       getSDF(vec3(p.x, p.y, p.z + EPSILON)) - getSDF(vec3(p.x, p.y, p.z - EPSILON))
   ));
}

However, a set of 1 and 0 values is not a proper signed distance field, so it's not clear if this will work.