The SDF gradient estimated by finite differences gives the surface normal needed for lighting

Lighting requires knowing which direction a surface faces (its normal). For an SDF scene the normal is the gradient of the distance field at the hit point, approximated by sampling the SDF at six nearby points (±epsilon in x, y, z) and taking finite differences. If the SDF is smaller to the left than to the right, the normal’s x-component points right (towards the outside). This tetrahedral or central-difference gradient is equivalent to the analytic surface normal for exact SDFs and remains a good approximation for blended or displaced geometry.

Examples

vec3 calcNormal(vec3 p){ vec2 e=vec2(0.001,0); return normalize(vec3(map(p+e.xyy)-map(p-e.xyy), map(p+e.yxy)-map(p-e.yxy), map(p+e.yyx)-map(p-e.yyx))); }

Assessment

Describe what happens to the estimated normal when the epsilon value is too large vs too small, and why this matters for lighting quality.