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Journal Articles ACM Transactions on Graphics Year : 2011

Displacement interpolation using Lagrangian mass transport

Michiel van de Panne
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  • PersonId : 902100
Sylvain Paris
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Wolfgang Heidrich
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  • PersonId : 836035

Abstract

Interpolation between pairs of values, typically vectors, is a fundamental operation in many computer graphics applications. In some cases simple linear interpolation yields meaningful results without requiring domain knowledge. However, interpolation between pairs of distributions or pairs of functions often demands more care because features may exhibit translational motion between exemplars. This property is not captured by linear interpolation. This paper develops the use of displacement interpolation for this class of problem, which provides a generic method for interpolating between distributions or functions based on advection instead of blending. The functions can be non-uniformly sampled, high-dimensional, and defined on non-Euclidean manifolds, e.g., spheres and tori. Our method decomposes distributions or functions into sums of radial basis functions (RBFs). We solve a mass transport problem to pair the RBFs and apply partial transport to obtain the interpolated function. We describe practical methods for computing the RBF decomposition and solving the transport problem. We demonstrate the interpolation approach on synthetic examples, BRDFs, color distributions, environment maps, stipple patterns, and value functions.
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Dates and versions

hal-00763270 , version 1 (10-12-2012)

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Nicolas Bonneel, Michiel van de Panne, Sylvain Paris, Wolfgang Heidrich. Displacement interpolation using Lagrangian mass transport. ACM Transactions on Graphics, 2011, Proceedings of ACM SIGGRAPH Asia 2011, 30 (6), pp.Article n°158. ⟨10.1145/2070781.2024192⟩. ⟨hal-00763270⟩
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