Efficient computation of constrained parameterizations on parallel platforms

• Establishes the relation between mesh smoothing and parameterization techniques.
• Derives a simplified formulation for the isometric parameterization problem.
• Presents an efficient parallel implementation of a non-linear solver.
• Presents an iterative topological untangling process for constrained parameterization.
• Demonstrates the applicability of our approach on feature cut-and-paste design.

Constrained isometric planar parameterizations are central to a broad spectrum of applications. In this work, we present a non linear solver developed on OpenCL that is efficiently parallelizable on modern massively parallel architectures. We establish how parameterization relates to mesh smoothing and show how to efficiently and robustly solve the planar mesh parameterization problem with constraints. Furthermore, we demonstrate the applicability of our approach to real-time cut-and-paste editing and interactive mesh deformation.

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