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


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


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.


Directional Field Synthesis, Design, and Processing

SIGGRAPH '17 Courses, July 30 - August 03, 2017, Los Angeles, CA, USA

Direction fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector-set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This course provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges.


Boundary Element Octahedral Fields in Volumes

ACM Transactions on Graphics

The computation of smooth fields of orthogonal directions within a volume is a critical step in hexahedral mesh generation, used to guide placement of edges and singularities. While this problem shares high-level structure with surface-based frame field problems, critical aspects are lost when extending to volumes, while new structure from the flat Euclidean metric emerges. Taking these considerations into account, this paper presents an algorithm for computing such “octahedral” fields. Unlike existing approaches, our formulation achieves infinite resolution in the interior of the volume via the boundary element method (BEM), continuously assigning frames to points in the interior from only a triangle mesh discretization of the boundary. The end result is an orthogonal direction field that can be sampled anywhere inside the mesh, with smooth variation and singular structure in the interior even with a coarse boundary. We illustrate our computed frames on a number of challenging test geometries. Since the octahedral frame field problem is relatively new, we also contribute a thorough discussion of theoretical and practical challenges unique to this problem.

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