coneSDF: Parametric Cone Distance Field System

Multi-Form Conical Geometry Distance Computation

The coneSDF family provides three distinct parameterization methods for cone distance field calculation. Each function addresses different geometric requirements through vector parameters, radius specifications, and height-width ratios.

Mathematical Foundation

Cone distance fields utilize cylindrical coordinate transformations and linear interpolation between circular cross-sections:

$$d_{\text{cone}} = \sqrt{\min(|a|^2, |b|^2)} \cdot \text{sign}(s)$$

where projection vectors $a$ and $b$ represent optimal distance candidates from the sample point to the cone surface.

Function Variants

Function	Parameters	Description
coneSDF	p, c	Vector-based cone with direction parameter
coneSDFVec2Height	p, c, h	2D angle parameter with explicit height
coneSDFRadii	p, r1, r2, h	Truncated cone with dual radius specification

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 = [0.8, 0.2, 1.5]
      const march = Fn(([eye, dir]: [Vec3, Vec3]) => {
              const p = eye.toVar()
              const d = coneSDFRadii(p, ...args).toVar()
              Loop(16, ({ i }) => {
                      If(d.lessThanEqual(eps.x), () => {
                              const dx = coneSDFRadii(p.add(eps.xyy), ...args).sub(d)
                              const dy = coneSDFRadii(p.add(eps.yxy), ...args).sub(d)
                              const dz = coneSDFRadii(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(coneSDFRadii(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)
}