Quad-mesh based isometric mappings and developable surfaces
| Autor: | Helmut Pottmann, Florian Rist, Johannes Wallner, Caigui Jiang, Cheng Wang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Developable surface
Pure mathematics Gauss map Discretization Computer science 020207 software engineering Conformal map 02 engineering and technology Computer Graphics and Computer-Aided Design Spline (mathematics) 0202 electrical engineering electronic engineering information engineering Isometry Shape optimization Polygon mesh Discrete differential geometry Geometric modeling |
| Zdroj: | ACM Transactions on Graphics. 39 |
| ISSN: | 1557-7368 0730-0301 |
| DOI: | 10.1145/3386569.3392430 |
| Popis: | We discretize isometric mappings between surfaces as correspondences between checkerboard patterns derived from quad meshes. This method captures the degrees of freedom inherent in smooth isometries and enables a natural definition of discrete developable surfaces. This definition, which is remarkably simple, leads to a class of discrete developables which is much more flexible in applications than previous concepts of discrete developables. In this paper, we employ optimization to efficiently compute isometric mappings, conformal mappings and isometric bending of surfaces. We perform geometric modeling of developables, including cutting, gluing and folding. The discrete mappings presented here have applications in both theory and practice: We propose a theory of curvatures derived from a discrete Gauss map as well as a construction of watertight CAD models consisting of developable spline surfaces. |
| Databáze: | OpenAIRE |
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