Interactive Planarization and Optimization of 3D Meshes

• Published in: Computer graphics forum 2013-02, Vol.32 (1), p.152-163
• Main Authors: Poranne, Roi, Ovreiu, Elena, Gotsman, Craig
• Format: Article
• Language: English
• Subjects: 3-D graphics; Analysis; Computation; Constraining; Editing; I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling; Image processing systems; Interactive; Least squares method; Mathematical models; Optimization; planarization; Polyhedra; polyhedral meshes; shape optimization; Studies; Three dimensional; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12005

Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes—those having planar faces—are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least‐squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints. Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes ‐ those having planar faces ‐ are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least‐squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints.