Abstract
We establish a framework to design triangular and circular polygonal meshes by using face-based compatible Möbius transformations. Embracing the viewpoint of surfaces from circles, we characterize discrete conformality for such meshes, in which the invariants are circles, cross-ratios, and mutual intersection angles. Such transformations are important in practice for editing meshes without distortions or loss of details. In addition, they are of substantial theoretical interest in discrete differential geometry. Our framework allows for handle-based deformations, and interpolation between given meshes with controlled conformal error.
Original language | English |
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Article number | 55 |
Pages (from-to) | 1-11 |
Number of pages | 11 |
Journal | ACM Transactions on Graphics |
Volume | 34 |
Issue number | 4 |
DOIs | |
Publication status | Published - 27 Jul 2015 |
Externally published | Yes |
Keywords
- Circular meshes
- Discrete conformal transformations
- Handle-based editing
- Interpolation
- Möbius transformations