Marching Cubes Isosurface

Marching Cubes samples a scalar field on a finite 3D grid and joins points where that field equals the chosen isovalue. The mesh approximates that contour; increasing resolution adds samples and triangles, but should not move the underlying surface.

For the sphere preset, the isovalue is the radius in displayed coordinates: f = r² − x² − y² − z², so the surface f = 0 has radius r. Metaballs add three inverse-distance contributions; the gyroid is a periodic trigonometric field; and the torus is defined by distance from a ring. The grid is limited to 12–40 points per edge and the cube spans −0.55 to +0.55 in each coordinate.

The field is sampled only on that finite box. Marching Cubes can produce grid-dependent topology near thin features or ambiguous cells. Normals are estimated from the generated triangle mesh; this view is not a volume renderer or a proof of a smooth surface.