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2008

Manifold-valued Thin-Plate Splines with Applications in Computer Graphics

9 years 2 months ago
Manifold-valued Thin-Plate Splines with Applications in Computer Graphics
We present a generalization of thin-plate splines for interpolation and approximation of manifold-valued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings between two Riemannian manifolds which is independent of parametrization and respects the geometry of both manifolds. If the manifolds are Euclidean, the energy functional reduces to the classical thin-plate spline energy. We show how the resulting optimization problems can be solved efficiently in many cases. Our example applications range from orientation interpolation and motion planning in animation over geometric modelling tasks to color interpolation. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling, Splines
Florian Steinke, Matthias Hein, Jan Peters, Bernha
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CGF
Authors Florian Steinke, Matthias Hein, Jan Peters, Bernhard Schölkopf
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