Welcome



Welcome to the Computer Graphics Group at University of Bern!

For the previous Computer Graphics Group website led by Professor Zwicker click here.

The research and teaching activities at our institute

Results are published

Selective Padding for Polycube-based Hexahedral Meshing

The paper "Selective Padding for Polycube-based Hexahedral Meshing" was accepted to Computer Graphics Forum.

Dec. 21, 2018

SIGGRAPH 2019 technical committee

David Bommes will serve on the technical papers committee for SIGGRAPH2019, which will take place in Los Angeles, USA. SIGGRAPH is the premiere international conference for computer graphics and interactive techniques.

Nov. 1, 2018

New Siggraph paper

The paper "Singularity-Constrained Octahedral Fields for Hexahedral Meshing" was accepted for publication and is to be presented in SIGGRAPH 2018 Conference.

May 15, 2018

David Bommes on SIGGRAPH2018 technical papers commitee

David Bommes will serve on the technical papers committee for SIGGRAPH2018, which will take place in Vancouver, Canada. SIGGRAPH is the premiere international conference for computer graphics and interactive techniques.

Sept. 9, 2017

SIGGRAPH course

The course Directional Field Synthesis, Design, and Processing was taught at SIGGRAPH 2017.

Aug. 3, 2017

Octahedral Fields paper

Our paper Octaherdral Fields was presented at SIGGRAPH 2017.

Aug. 3, 2017

Recent Publications

Singularity-Constrained Octahedral Fields for Hexahedral Meshing

SIGGRAPH 2018

Despite high practical demand, algorithmic hexahedral meshing with guarantees on robustness and quality remains unsolved. A promising direction follows the idea of integer-grid maps, which pull back the Cartesian hexahedral grid formed by integer isoplanes from a parametric domain to a surface-conforming hexahedral mesh of the input object. Since directly optimizing for a high-quality integer-grid map is mathematically challenging, the construction is usually split into two steps: (1) generation of a surface-aligned octahedral field and (2) generation of an integer-grid map that best aligns to the octahedral field. The main robustness issue stems from the fact that smooth octahedral fields frequently exhibit singularity graphs that are not appropriate for hexahedral meshing and induce heavily degenerate integer-grid maps. The first contribution of this work is an enumeration of all local configurations that exist in hex meshes with bounded edge valence, and a generalization of the Hopf-Poincaré formula to octahedral fields, leading to necessary local and global conditions for the hex-meshability of an octahedral field in terms of its singularity graph. The second contribution is a novel algorithm to generate octahedral fields with prescribed hex-meshable singularity graphs, which requires the solution of a large non-linear mixed-integer algebraic system. This algorithm is an important step toward robust automatic hexahedral meshing since it enables the generation of a hex-meshable octahedral field.

 

Selective Padding for Polycube-based Hexahedral Meshing

Computer Graphics Forum

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 Scaled Jacobian (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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