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Welcome to the MGO Group at RWTH Aachen University!

The research and teaching activities at our institute

Results are published

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

David Bommes obtained habilitation equivalence through the positive evaluation of his junior professorship.

July 1, 2017

David Bommes was elected as one of the newly established Eurographics Junior Fellows.

April 26, 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.

 

A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes

Geometry Meets Deep Learning ECCV 2018 Workshop

The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art methods rely on patch-based or mapping-based techniques that introduce resampling operations in order to encode neighborhood information in a structured and regular manner. We investigate whether such resampling can be avoided, and propose a simple and direct encoding approach. It does not only increase processing efficiency due to its simplicity - its direct nature also avoids any loss in data fidelity. To evaluate the proposed method, we perform a number of experiments in the challenging domain of intrinsic, non-rigid shape correspondence estimation. In comparisons to current methods we observe that our approach is able to achieve highly competitive results.

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