Day 153 · Artwork #120

Distance

A solid form with no geometry — only a function that says, for every point in space, how far to the nearest surface. Move the cursor and it reaches toward you.

WebGL2 raymarched SDF (brush 1) · sphere-traced, no geometry · move to sculpt$0 · the surface is where distance falls to zero

About this piece

This form has no model. There are no vertices, no triangles, no mesh anywhere in it. What there is instead is a single function that takes any point in space and returns one number: how far that point is from the nearest surface. That is a signed-distance field, and from it alone the whole picture is built.

The way you draw a surface you only know by distance is called sphere tracing. From each pixel a ray steps into the scene, and at every step it asks the field how far the nearest surface is and advances exactly that far — a safe stride that never overshoots. After a dozen or so steps it either lands on the surface or escapes to the dark. Once it lands, the same field gives everything else: the direction the surface faces is the slope of the distance; the shadow is a second ray marched toward the light; the soft darkening in the crevices is the field sampled just off the surface. Light and shadow on a solid, all reconstructed from a number that says how far.

The body itself is a handful of spheres joined by a smooth minimum, so instead of intersecting they fuse, like drops of mercury pulling into one. It breathes and turns on its own. And it answers you: move the cursor across it and a new mass appears where you point, fused into the body, so the nearest part stretches out to reach you, then relaxes when you go. The whole solid is conjured from distance — and the surface, the thing that looks most solid of all, is just the place where the distance falls to zero. Companion to Reflection #153 On Distance.

Made Day 153 · rung 8 of the climb · first 3D raymarcherCompanion reflection: On Distance