43-Issue 1

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/3606942

Browse

Browsing 43-Issue 1 by Subject "mesh generation"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Quad Mesh Quantization Without a T‐Mesh
    (© 2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2024) Coudert‐Osmont, Yoann; Desobry, David; Heistermann, Martin; Bommes, David; Ray, Nicolas; Sokolov, Dmitry; Alliez, Pierre; Wimmer, Michael
    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 .
  • Thumbnail Image
    Item
    A Robust Grid‐Based Meshing Algorithm for Embedding Self‐Intersecting Surfaces
    (© 2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2024) Gagniere, S.; Han, Y.; Chen, Y.; Hyde, D.; Marquez‐Razon, A.; Teran, J.; Fedkiw, R.; Alliez, Pierre; Wimmer, Michael
    The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self‐intersecting. However, due to numerical and/or user error, input surfaces are commonly self‐intersecting to some degree. The removal of self‐intersection is a burdensome task that complicates workflow and generally slows down the process of creating simulation‐ready digital assets. We present a method for the creation of a volumetric embedding hexahedron mesh from a self‐intersecting input triangle mesh. Our method is designed for efficiency by minimizing use of computationally expensive exact/adaptive precision arithmetic. Although our approach allows for nearly no limit on the degree of self‐intersection in the input surface, our focus is on efficiency in the most common case: many minimal self‐intersections. The embedding hexahedron mesh is created from a uniform background grid and consists of hexahedron elements that are geometrical copies of grid cells. Multiple copies of a single grid cell are used to resolve regions of self‐intersection/overlap. Lastly, we develop a novel topology‐aware embedding mesh coarsening technique to allow for user‐specified mesh resolution as well as a topology‐aware tetrahedralization of the hexahedron mesh.