Geodesic
Lagrangian evolution approach to surface-patch quadrangulation
Applications of Mathematics, Tome 66 (2021) no. 4, pp. 509-551 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present a method for the generation of a pure quad mesh approximating a discrete manifold of arbitrary topology that preserves the patch layout characterizing the intrinsic object structure. A three-step procedure constitutes the core of our approach which first extracts the patch layout of the object by a topological partitioning of the digital shape, then computes the minimal surface given by the boundaries of the patch layout (basic quad layout) and then evolves it towards the object boundaries. The Lagrangian evolution of the initial surface (basic quad layout) in the direction of the gradient of the signed distance function is smoothed by a mean curvature term. The direct control over the global quality of the generated quad mesh is provided by two types of tangential redistributions: area-based, to equally distribute the size of the quads, and angle-based, to preserve quad corner angles. Experimental results showed that the proposed method generates pure quad meshes of arbitrary topology objects, composed of well-shaped evenly distributed elements with few extraordinary vertices.
We present a method for the generation of a pure quad mesh approximating a discrete manifold of arbitrary topology that preserves the patch layout characterizing the intrinsic object structure. A three-step procedure constitutes the core of our approach which first extracts the patch layout of the object by a topological partitioning of the digital shape, then computes the minimal surface given by the boundaries of the patch layout (basic quad layout) and then evolves it towards the object boundaries. The Lagrangian evolution of the initial surface (basic quad layout) in the direction of the gradient of the signed distance function is smoothed by a mean curvature term. The direct control over the global quality of the generated quad mesh is provided by two types of tangential redistributions: area-based, to equally distribute the size of the quads, and angle-based, to preserve quad corner angles. Experimental results showed that the proposed method generates pure quad meshes of arbitrary topology objects, composed of well-shaped evenly distributed elements with few extraordinary vertices.
DOI : 10.21136/AM.2021.0366-19
Classification : 35K55, 35K93, 65M08
Keywords: Lagrangian evolution; patch layout; non-conforming mesh; mesh partitioning 
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     title = {Lagrangian evolution approach to surface-patch quadrangulation},
     journal = {Applications of Mathematics},
     pages = {509--551},
     year = {2021},
     volume = {66},
     number = {4},
     doi = {10.21136/AM.2021.0366-19},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0366-19/}
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Húska, Martin; Medl'a, Matej; Mikula, Karol; Morigi, Serena. Lagrangian evolution approach to surface-patch quadrangulation. Applications of Mathematics, Tome 66 (2021) no. 4, pp. 509-551. doi: 10.21136/AM.2021.0366-19

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