|Title||On Piecewise Linear Approximation of Quadratic Functions
|in||Journal for Geometry and Graphics|
Helmut Pottmann, R. Krasauskas, Bernd Hamann, Ken Joy, Wolfgang Seibold |
|Keyword(s)||optimal polygon meshes, piecewise linear approximation, data-dependent triangulation, Voronoi tessellation, power diagram, Delone triangulation. convex geometry, discrete geometry, Cayley-Klein geometry|
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 difficult one. We present a detailed discussion of the case n=2, where we can partially use results from convex geometry and discrete geomerty. The case n=3 is considerably harder, and thus just a few results can be formulated so far.