# Guided subdivision surfaces: modeling, shape and refinability

## TL;DR

This paper introduces a guided subdivision method for converting quad meshes into smooth, refinable surfaces, combining highlight line quality with shape control, and provides algorithms with proven eigen-structure properties.

## Contribution

It presents new C2 subdivision algorithms of degrees bi-6 and bi-5 with adjustable eigenspectrum, enhancing shape refinement and curvature control in surface modeling.

## Key findings

- The algorithms achieve smooth, high-quality surface representations.
- Eigen-structure can be tuned without shape distortion.
- The methods effectively combine highlight line distribution with refinability.

## Abstract

Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2 subdivision algorithm of polynomial degree bi-6 and a curvature bounded algorithm of degree bi-5. We prove that the common eigen-structure of this class of subdivision algorithms is determined by their guide and demonstrate that the eigenspectrum (speed of contraction) can be adjusted without harming the shape.