Interactive Planarization and Optimization of 3D Meshes

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 ge...

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Bibliographic Details
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
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Summary: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.
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12005