Abstract
We study piecewise linear approximation of quadratic functions defined on Rn. Invariance properties and canonical Caley/Klein metrics that help in understanding this problem can be handled in arbitrary dimensions. However, the problem of optimal approximants in the sense that their linear pieces are of maximal size by keeping a given error tolerance, is a di±cult one. We present a detailled discussion of the case n = 2, where we can partially use results from convex geometry and discrete geometry. The case n = 3 is considerably harder, and thus just a few results can be formulated so far.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 31-53 |
| Number of pages | 23 |
| Journal | Journal for Geometry and Graphics |
| Volume | 4 |
| Issue number | 1 |
| State | Published - 2000 |
Keywords
- Cayley-Klein geometry
- Convex geometry
- Data--dependent triangulation
- Delone triangulation
- Discrete geometry
- Optimal polygon meshes
- Piecewise linear approximation
- Power diagram
- Voronoi tessellation
ASJC Scopus subject areas
- Applied Psychology
- Geometry and Topology
- Applied Mathematics