Browsing by Author "Alliez, P."

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    Selective Padding for Polycube‐Based Hexahedral Meshing
    (© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Cherchi, G.; Alliez, P.; Scateni, R.; Lyon, M.; Bommes, D.; Chen, Min and Benes, Bedrich
    Hexahedral meshes generated from polycube mapping often exhibit a low number of singularities but also poor‐quality elements located near the surface. It is thus necessary to improve the overall mesh quality, in terms of the minimum scaled Jacobian (MSJ) or average SJ (ASJ). Improving the quality may be obtained via global padding (or pillowing), which pushes the singularities inside by adding an extra layer of hexahedra on the entire domain boundary. Such a global padding operation suffers from a large increase of complexity, with unnecessary hexahedra added. In addition, the quality of elements near the boundary may decrease. We propose a novel optimization method which inserts sheets of hexahedra so as to perform selective padding, where it is most needed for improving the mesh quality. A sheet can pad part of the domain boundary, traverse the domain and form singularities. Our global formulation, based on solving a binary problem, enables us to control the balance between quality improvement, increase of complexity and number of singularities. We show in a series of experiments that our approach increases the MSJ value and preserves (or even improves) the ASJ, while adding fewer hexahedra than global padding.
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    Simplification of 2D Polygonal Partitions via Point‐line Projective Duality, and Application to Urban Reconstruction
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2022) Vuillamy, J.; Lieutier, A.; Lafarge, F.; Alliez, P.; Hauser, Helwig and Alliez, Pierre
    We address the problem of simplifying two‐dimensional polygonal partitions that exhibit strong regularities. Such partitions are relevant for reconstructing urban scenes in a concise way. Preserving long linear structures spanning several partition cells motivates a point‐line projective duality approach in which points represent line intersections, and lines possibly carry multiple points. We propose a simplification algorithm that seeks a balance between the fidelity to the input partition, the enforcement of canonical relationships between lines (orthogonality or parallelism) and a low complexity output. Our methodology alternates continuous optimization by Riemannian gradient descent with combinatorial reduction, resulting in a progressive simplification scheme. Our experiments show that preserving canonical relationships helps gracefully degrade partitions of urban scenes, and yields more concise and regularity‐preserving meshes than common mesh‐based simplification approaches.