Quad Mesh Quantization Without a T‐Mesh

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Date
2024
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© 2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.
Abstract
Grid preserving maps of triangulated surfaces were introduced for quad meshing because the 2D unit grid in such maps corresponds to a sub‐division of the surface into quad‐shaped charts. These maps can be obtained by solving a mixed integer optimization problem: Real variables define the geometry of the charts and integer variables define the combinatorial structure of the decomposition. To make this optimization problem tractable, a common strategy is to ignore integer constraints at first, then to enforce them in a so‐called quantization step. Actual quantization algorithms exploit the geometric interpretation of integer variables to solve an equivalent problem: They consider that the final quad mesh is a sub‐division of a T‐mesh embedded in the surface, and optimize the number of sub‐divisions for each edge of this T‐mesh. We propose to operate on a decimated version of the original surface instead of the T‐mesh. It is easier to implement and to adapt to constraints such as free boundaries, complex feature curves network .
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@article{
10.1111:cgf.14928
, journal = {Computer Graphics Forum}, title = {{
Quad Mesh Quantization Without a T‐Mesh
}}, author = {
Coudert‐Osmont, Yoann
and
Desobry, David
and
Heistermann, Martin
and
Bommes, David
and
Ray, Nicolas
and
Sokolov, Dmitry
}, year = {
2024
}, publisher = {
© 2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.14928
} }
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