Papers by Mathieu Desbrun


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Optimal Voronoi Tessellations with Hessian-based Anisotropy

Max Budninskiy, Beibei Liu, Fernando de Goes, Yiying Tong, Pierre Alliez, Mathieu Desbrun
December 2016

This paper presents a variational method to generate cell complexes with local anisotropy conforming to the Hessian of any given convex function and for any given local mesh density. Our formulation builds upon approximation theory to offer an anisotropic extension of Centroidal Voronoi Tessellations which can be seen as a ... more

Additional materials: [BLdG+16_SuppMat.pdf]


Subdivision Exterior Calculus for Geometry Processing

Fernando de Goes, Mathieu Desbrun, Mark Meyer, Tony DeRose
April 2016

This paper introduces a new computational method to solve differential equations on subdivision surfaces. Our approach adapts the numerical framework of Discrete Exterior Calculus (DEC) from the polygonal to the subdivision setting by exploiting the refinability of subdivision basis functions. The resulting Subdivision Exterior Calculus (SEC) provides significant improvements in ... more

Additional materials: [supplementalFigs.pdf], [supplemental.pdf]

Available as Pixar Technical Memo #16-01


Vector Field Processing on Triangle Meshes

Fernando de Goes, Mathieu Desbrun, Yiying Tong
August 2015

While scalar fields on surfaces have been staples of geometry processing, the use of tangent vector fields has steadily grown in geometry processing over the last two decades: they are crucial to encoding directions and sizing on surfaces as commonly required in tasks such as texture synthesis, non-photorealistic rendering, digital ... more