Smooth Curves from Curvature-Driven Subdivision

arXiv cs.GR details an interpolatory subdivision scheme that builds each new point from a curvature-profile model rather than a weighted average of neighboring control points. The paper says the construction works in both the plane and on the sphere, with inserted points placed at half arc length after Frenet integration and geodesic shooting.

For game and graphics teams, the practical angle is curve quality: the scheme reproduces geodesics and circles exactly, and the authors prove convergence to a regular limit curve with continuous tangent direction and curvature, twice continuously differentiable in arc length. That makes it relevant anywhere smooth, stable curve refinement matters, from path generation to procedural shape tools.

A unique curvature prefilter turns the planar linearisation into the six-point Deslauriers-Dubuc scheme, which helps connect the method to familiar subdivision theory. The paper also notes that the straightening condition of Ewald, Reif, and Sabin fails here, so the regularity argument is adjusted to depend only on the normal component of relative distortion.

The broader takeaway is that curvature can drive subdivision directly without losing the guarantees developers usually want from classic affine schemes. That could be useful for toolchains that need predictable smoothness on both flat and curved domains, especially when exact reproduction of canonical curves is more valuable than simple control-point interpolation.