filename     : /home/mbotsch/dy/eg05/eg05.pdf
entry        : article
conference   : Eurographics, Dublin, Ireland, Aug 29th - Sep 2nd, 2005
pages        : 611-621
year         : 2005
month        : September
title        : Real-Time Shape Editing using Radial Basis Functions
subtitle     : 
author       : Mario Botsch, Leif Kobbelt
booktitle    : Computer Graphics Forum
ISSN/ISBN    : 
editor       : 
publisher    : 
publ.place   : 
volume       : 24
issue        : 3
language     : english
keywords     : geometric modeling
abstract     : 

Current surface-based methods for interactive freeform editing of high
resolution 3D models are very powerful, but at the same time require a
certain minimum tessellation or sampling quality in order to guarantee
sufficient robustness. In contrast to this, space deformation
techniques do not depend on the underlying surface representation and
hence are affected neither by its complexity nor by its quality
aspects. However, while analogously to surface-based methods high
quality deformations can be derived from variational optimization, the
major drawback lies in the computation and evaluation, which is
considerably more expensive for volumetric space deformations. In this
paper we present techniques which allow us to use triharmonic radial
basis functions for real-time freeform shape editing. An incremental
least-squares method enables us to approximately solve the involved
linear systems in a robust and efficient manner and by precomputing a
special set of deformation basis functions we are able to
significantly reduce the per-frame costs. Moreover, evaluating these
linear basis functions on the GPU finally allows us to deform highly
complex polygon meshes or point-based models at a rate of 30M vertices
or 13M splats per second, respectively.