opOnion: Shell Creation Operation

Hollow Interior Transform for Distance Fields

The opOnion operation creates hollow shells from solid SDF shapes by applying an absolute value transformation to the distance field. This operation converts any solid shape into a hollow version with controllable wall thickness.

Mathematical Foundation

The onion operation transforms the distance field using:

$$\text{opOnion}(d, h) = |d| - h$$

where:

• $d$ is the input distance from the base SDF function
• $h$ is the shell thickness parameter

This transformation creates a shell around the zero isosurface of the original shape. The absolute value ensures that both interior and exterior distances contribute to the shell formation, effectively creating walls of thickness $2h$ around the original surface.

Function Signature

Parameter	Type	Description
d	float	Input distance from base SDF
h	float	Shell thickness (half-thickness)

Implementation Demonstration

ライブエディター

const fragment = () => {
      const up = vec3(0, 1, 0)
      const eps = vec3(0.01, 0, 0)
      const eye = rotate3dY(iTime).mul(vec3(5))
      const sdf = Fn(([p]: [Vec3]) => {
              const sphere = sphereSDF(p)
              const box = cubeSDF(p, 0.8)
              const base = sphere.min(box)
              return opOnion(base, 0.15)
      })
      const march = Fn(([eye, dir]: [Vec3, Vec3]) => {
              const p = eye.toVar()
              const d = sdf(p).toVar()
              Loop(16, ({ i }) => {
                      If(d.lessThanEqual(eps.x), () => {
                              const dx = sdf(p.add(eps.xyy)).sub(d)
                              const dy = sdf(p.add(eps.yxy)).sub(d)
                              const dz = sdf(p.add(eps.yyx)).sub(d)
                              const normal = vec3(dx, dy, dz).normalize()
                              const light = vec3(2, 4, 3).sub(p).normalize()
                              const diffuse = normal.dot(light).max(0.1)
                              return vec4(vec3(diffuse.mul(0.8).add(0.2)), 1)
                      })
                      p.addAssign(d.mul(dir))
                      d.assign(sdf(p))
              })
              return vec4(0)
      })
      const z = eye.negate().normalize()
      const x = z.cross(up)
      const y = x.cross(z)
      const scr = vec3(uv.sub(0.5), 2)
      const dir = mat3(x, y, z).mul(scr).normalize()
      return march(eye, dir)
}