Premium
Positional, Metric, and Curvature Control for Constraint‐Based Surface Deformation
Author(s) -
Eigensatz Michael,
Pauly Mark
Publication year - 2009
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01395.x
Subject(s) - curvature , surface (topology) , constraint (computer aided design) , principal curvature , geometry processing , metric (unit) , computer science , distortion (music) , point (geometry) , geometry , mathematics , mean curvature , polygon mesh , amplifier , computer network , operations management , bandwidth (computing) , economics
We present a geometry processing framework that allows direct manipulation or preservation of positional, metric, and curvature constraints anywhere on the surface of a geometric model. Target values for these properties can be specified point‐wise or as integrated quantities over curves and surface patches embedded in the shape. For example, the user can draw several curves on the surface and specify desired target lengths, manipulate the normal curvature along these curves, or modify the area or principal curvature distribution of arbitrary surface patches. This user input is converted into a set of non‐linear constraints. A global optimization finds the new deformed surface that best satisfies the constraints, while minimizing adaptable measures for metric and curvature distortion that provide explicit control of the deformation semantics. We illustrate how this approach enables flexible surface processing and shape editing operations not available in current systems.