Guided subdivision surfaces: modeling, shape and refinability
Kestutis Karciauskas, J\"org Peters
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.
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.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Tribology and Lubrication Engineering · Advanced machining processes and optimization
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Construction and comparison of guided subdivision: (a) input net defining in (c) the irregular subdivision region and a regular (green) bi-3 region; (b) guide surface that does not match the bi-3 spline but defines the shape; (c) six subdivision rings (alternating gold and cyan) capped by a finite polynomial (red) surface cap; (d) embossing exploiting the degrees of freedom in the subdivision rings. (e) Catmull-Clark vs (f) guided subdivision: improvement of the highlight line distribution.
Guided subdivision surfaces: modeling, shape and refinability
Kȩstutis Karčiauskasa and Jörg Petersb
a Vilnius University b University of Florida
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 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. classification
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