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Abstract:
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.
