cubeSDF: Uniform Cubic Distance Field

Simplified Box Geometry with Equal Dimensions

The cubeSDF function generates a signed distance field for a cube with uniform dimensions. This function is a convenience wrapper around boxSDFSize, automatically creating a cube by applying the same size value to all three dimensions.

Mathematical Foundation

A cube is defined as a box where all dimensions are equal:

$$d_{\text{cube}}(p, s) = d_{\text{box}}(p, \vec{s})$$

where $\vec{s} = (s, s, s)$ represents the uniform size vector.

The distance calculation follows the standard box SDF formula:

$$d = \max(0, |\vec{p}| - \vec{s}) + \min(0, \max(|p_x| - s, |p_y| - s, |p_z| - s))$$

Function Signature

Parameter	Type	Description
p	vec3	Sample point position
s	float	Cube half-size (radius from center to face)

Implementation Demonstrations

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 args = [1]
      const march = Fn(([eye, dir]: [Vec3, Vec3]) => {
              const p = eye.toVar()
              const d = cubeSDF(p, ...args).toVar()
              Loop(16, ({ i }) => {
                      If(d.lessThanEqual(eps.x), () => {
                              const dx = cubeSDF(p.add(eps.xyy), ...args).sub(d)
                              const dy = cubeSDF(p.add(eps.yxy), ...args).sub(d)
                              const dz = cubeSDF(p.add(eps.yyx), ...args).sub(d)
                              return vec4(vec3(dx, dy, dz).normalize().mul(0.5).add(0.5), 1)
                      })
                      p.addAssign(d.mul(dir))
                      d.assign(cubeSDF(p, ...args))
              })
              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)
}