Year: Author:

Amir Vaxman, Marcel Campen, Olga Diamanti, David Bommes, Klaus Hildebrandt, Mirela Ben-Chen, Daniele Panozzo
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.

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@inproceedings{Vaxman:2017:DFS:3084873.3084921, author = {Vaxman, Amir and Campen, Marcel and Diamanti, Olga and Bommes, David and Hildebrandt, Klaus and Technion, Mirela Ben-Chen and Panozzo, Daniele}, title = {Directional Field Synthesis, Design, and Processing}, booktitle = {ACM SIGGRAPH 2017 Courses}, series = {SIGGRAPH '17}, year = {2017}, isbn = {978-1-4503-5014-3}, location = {Los Angeles, California}, pages = {12:1--12:30}, articleno = {12}, numpages = {30}, url = {}, doi = {10.1145/3084873.3084921}, acmid = {3084921}, publisher = {ACM}, address = {New York, NY, USA}, }

Justin Solomon, Amir Vaxman, David Bommes
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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@article{Solomon:2017:BEO:3087678.3065254, author = {Solomon, Justin and Vaxman, Amir and Bommes, David}, title = {Boundary Element Octahedral Fields in Volumes}, journal = {ACM Trans. Graph.}, issue_date = {June 2017}, volume = {36}, number = {3}, month = may, year = {2017}, issn = {0730-0301}, pages = {28:1--28:16}, articleno = {28}, numpages = {16}, url = {}, doi = {10.1145/3065254}, acmid = {3065254}, publisher = {ACM}, address = {New York, NY, USA}, keywords = {Octahedral fields, boundary element method, frames, singularity graph}, }

Maximilian Harmel, Roger Sauer, David Bommes
Computer-Aided Design

A new approach to obtain a volumetric discretization from a T-spline surface representation is presented. A T-spline boundary zone is created beneath the surface, while the core of the model is discretized with Lagrangian elements. T-spline enriched elements are used as an interface between isogeometric and Lagrangian finite elements. The thickness of the T-spline zone and thereby the isogeometric volume fraction can be chosen arbitrarily large such that pure Lagrangian and pure isogeometric discretizations are included. The presented approach combines the advantages of isogeometric elements (accuracy and smoothness) and classical finite elements (simplicity and efficiency). Different heat transfer problems are solved with the finite element method using the presented discretization approach with different isogeometric volume fractions. For suitable applications, the approach leads to a substantial accuracy gain.

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@article{harmel2017volumetric, title={Volumetric mesh generation from T-spline surface representations}, author={Harmel, Maximilian and Sauer, Roger A and Bommes, David}, journal={Computer-Aided Design}, volume={82}, pages={13--28}, year={2017}, publisher={Elsevier} }

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