Abstract
We present a novel framework for creating Möbius-invariant subdivision operators with a simple conversion of existing linear subdivision operators. By doing so, we create a wide variety of subdivision surfaces that have properties derived from Möbius geometry; namely, reproducing spheres, circular arcs, and Möbius regularity. Our method is based on establishing a canonical form for each 1-ring in the mesh, representing the class of all 1-rings that are Möbius equivalent to that 1-ring.We perform a chosen linear subdivision operation on these canonical forms, and blend the positions contributed from adjacent 1-rings, using two novel Möbius-invariant operators, into new face and edge points. The generality of the method allows for easy coarse-to-fine mesh editing with diverse polygonal patterns, and with exact reproduction of circular and spherical features. Our operators are in closed-form and their computation is as local as the computation of the linear operators they correspond to, allowing for efficient subdivision mesh editing and optimization.
Original language | English |
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Article number | 227 |
Journal | ACM Transactions on Graphics |
Volume | 37 |
Issue number | 6 |
DOIs | |
State | Published - Nov 2018 |
Bibliographical note
Publisher Copyright:© 2018 Association for Computing Machinery.
Funding
This research was partially funded by the Austrian Science Fund (FWF) (projects P 29981 and I 2978-N35) and by the Israel Science Foundation (grants No. 1869/15 and 2102/15). We thank Ron Van-derfeesten for the stylistic rendering of Figure 2.
Funders | Funder number |
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Austrian Science Fund | I 2978-N35, P 29981 |
Israel Science Foundation | 2102/15, 1869/15 |
Keywords
- Architectural geometry
- Conformal transformations
- Mesh subdivision
- Möbius transformations
- Regular meshes