triPrismSDF: Triangular Prism Distance Field

Extruded Triangle Geometry

The triPrismSDF function computes the signed distance from any 3D point to a triangular prism. This primitive represents a triangular base extruded along the Z-axis, creating a three-sided prism with flat triangular ends.

Mathematical Foundation

The triangular prism SDF combines triangular cross-section constraints with height bounds:

$$d_{\text{tri}} = \max(|q_x| \cdot \sqrt{3}/2 + p_y \cdot 0.5, -p_y) - h_x \cdot 0.5$$ $$d_{\text{height}} = |q_z| - h_y$$ $$d_{\text{prism}} = \max(d_{\text{height}}, d_{\text{tri}})$$

where $\vec{q} = |p|$ represents absolute coordinates and $\sqrt{3}/2 \approx 0.866025$ is the geometric coefficient for the triangular profile.

Function Signature

Parameter	Type	Description
p	vec3	Sample point position
h	vec2	Prism dimensions (width, height)

The h.x parameter controls the triangular base size, while h.y controls the extrusion height along the Z-axis.

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(4))
      const args = [vec2(0.8, 0.9)]
      const march = Fn(([eye, dir]: [Vec3, Vec3]) => {
              const p = eye.toVar()
              const d = triPrismSDF(p, ...args).toVar()
              Loop(16, ({ i }) => {
                      If(d.lessThanEqual(eps.x), () => {
                              const dx = triPrismSDF(p.add(eps.xyy), ...args).sub(d)
                              const dy = triPrismSDF(p.add(eps.yxy), ...args).sub(d)
                              const dz = triPrismSDF(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(triPrismSDF(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)
}

結果

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