Extrapolating curvature lines in rough concept sketches using mixed-integer nonlinear optimization

Abstract : We present several mathematical-optimization formulations for a problem that commonly occurs in geometry processing and specifically in the design of so-called smooth direction fields on surfaces. This problem has direct applications in 3D shape parameterization, texture mapping, and shape design via rough concept sketches, among many others. A key challenge in this setting is to design a set of unit-norm directions, on a given surface, that satisfy some prescribed constraints and vary smoothly. This naturally leads to mixed-integer optimization formulations, because the smoothness needs to be formulated with respect to angle-valued variables, which to compare one needs to fix the discrete jump between nearby points. Previous works have primarily attacked this problem via a greedy ad-hoc strategy with a specialized solver. We demonstrate how the problem can be cast in a standard mathematical-optimization form, and we suggest several relaxations that are especially adapted to modern mathematical-optimization solvers.
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Submitted on : Wednesday, November 6, 2019 - 5:18:54 AM
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Claudia D’ambrosio, Jon Lee, Leo Liberti, Maks Ovsjanikov. Extrapolating curvature lines in rough concept sketches using mixed-integer nonlinear optimization. Optimization and Engineering, Springer Verlag, 2019, 20 (2), pp.337-347. ⟨10.1007/s11081-018-9405-6⟩. ⟨hal-02350272⟩

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