cylinderSDF: Cylindrical Distance Field Variations

Versatile Tube Geometry with Multiple Parameterization Methods

The cylinderSDF function family generates signed distance fields for cylindrical geometries with various parameterization options. These functions support standard cylinders, uniform height cylinders, height-radius specification, and arbitrary orientation with caps.

Mathematical Foundation

The basic cylinder distance function operates on radial and axial components:

$$d_{\text{cylinder}} = \min(\max(d_x, d_y), 0) + |\max(\vec{d}, 0)|$$

where $\vec{d} = |\vec{q}| - \vec{h}$ and $\vec{q} = (|\vec{p}_{xz}|, p_y)$ represents the radial-axial projection.

For arbitrary orientation cylinders with caps, the distance involves projection calculations:

$$x = |\vec{pa} \cdot ba_{ba} - \vec{ba} \cdot pa_{ba}| - r \cdot ba_{ba}$$ $$y = |pa_{ba} - \frac{ba_{ba}}{2}| - \frac{ba_{ba}}{2}$$

Function Variants

Function	Parameters	Description
cylinderSDF	p, h	Vector height parameter (radius, height)
cylinderSDFHeight	p, h	Uniform radius with height specification
cylinderSDFHeightRadius	p, h, r	Explicit height and radius parameters
cylinderSDFCaps	p, a, b, r	Arbitrary orientation with endpoint caps

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