SDF Shapes¶

Besides analytic spheres, rectangles and triangles, RayON renders ten shapes defined by signed distance functions (SDFs). They are intersected by sphere tracing in the GPU kernel, on both back-ends, from one shared source file (gpu_renderers/sdf_primitives.cuh). The distance functions are Íñigo Quilez's.

18_sdf_shapes.yaml: gold mandelbulb, ceramic death star, brass cut hollow sphere, torus, glass octahedron, pyramid, capsule, box, cylinder and sphere, lit by a hidden soft box and two bulbs. OptiX, 384 spp, 720p.

What is an SDF?¶

A signed distance function returns the distance from a point \(\mathbf{p}\) to the nearest surface of a shape, negative inside:

For a sphere of radius \(r\): \(f(\mathbf{p}) = |\mathbf{p}| - r\). For a box of half extents \(\mathbf{b}\), with \(\mathbf{q} = |\mathbf{p}| - \mathbf{b}\): \(f = |\max(\mathbf{q}, 0)| + \min(\max(q_x, q_y, q_z), 0)\). For a torus of radii \(R, r\): \(f = \left|\left(\sqrt{p_x^2 + p_z^2} - R,\; p_y\right)\right| - r\).

Shapes compose with unions, intersections and smooth minima, which is how the death star (a sphere minus a sphere) and the cut hollow sphere are built.

Ray marching¶

An SDF is intersected by sphere tracing: from the ray origin, step forward by the distance the function returns, which is the largest step that cannot overshoot the surface, until the distance falls under a threshold.

t = t_enter                     # the ray is first clipped to the shape's bounding sphere
repeat up to 320 times:
    d = sdf(origin + t * dir)
    if |d| < eps(t):  hit        # eps = 1e-4 * max(1, 0.1 t): looser far from the camera
    t += d                       # or at least 2 eps once inside the band, to keep moving
    if t > t_exit:   miss

Two details matter for a path tracer, where rays also start on the shapes:

• A hit only counts after the march has been at least 1.5 ε away from the surface once ("arming"), so a refracted ray leaving a glass octahedron is not caught by the surface it starts on.
• The normal is the gradient of the SDF by central differences with a step of 2·10⁻⁴.

On OptiX each SDF is a custom primitive: its axis-aligned bounding box goes into the acceleration structure and __intersection__sdf runs the marcher when a ray enters the box. On CUDA the same marcher is called from intersect_geometry() through the BVH, which wraps the shape in its bounding sphere.

YAML syntax¶

  - type: "sdf"
    material: "steel"
    shape: "death_star"
    center: [-3.5, 1.2, -4.5]
    radius: 0.8
    cutout_radius: 0.5
    cutout_distance: 1.0
    rotation: [0, 54, 0]          # degrees, applied in X, Y, Z order

params: [a, b, c] sets the same three values positionally when you prefer. A plane shape also exists for infinite ground planes. Rotations are Euler angles in degrees; the inverse rotation is applied to the ray, which is equivalent to rotating the shape about its centre.

Materials on SDFs¶

Any material works: the gallery scene puts glass on the octahedron, a clear-coat lacquer on the death star and anisotropic gold on the mandelbulb. The sdf_material type exists for the built-in demos but is not required.

Cost¶

A sphere intersection is one formula; a march is 20 to 80 evaluations of the distance function, and the mandelbulb evaluates a fractal at each of them. The bounding box or sphere keeps the marcher from running on rays that miss the shape, so a few SDFs among analytic geometry cost little; a scene made of mandelbulbs is slow. The gallery scene uses settings.samples_per_batch: 2 to stay responsive in interactive mode.