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Exploring Local Modifications for Constrained Meshes
Author(s) -
Deng Bailin,
Bouaziz Sofien,
Deuss Mario,
Zhang Juyong,
Schwartzburg Yuliy,
Pauly Mark
Publication year - 2013
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12021
Subject(s) - polygon mesh , computer science , constraint (computer aided design) , set (abstract data type) , subspace topology , mathematical optimization , a priori and a posteriori , theoretical computer science , algorithm , mathematics , artificial intelligence , computer graphics (images) , philosophy , geometry , programming language , epistemology
Mesh editing under constraints is a challenging task with numerous applications in geometric modeling, industrial design, and architectural form finding. Recent methods support constraint‐based exploration of meshes with fixed connectivity, but commonly lack local control. Because constraints are often globally coupled, a local modification by the user can have global effects on the surface, making iterative design exploration and refinement difficult. Simply fixing a local region of interest a priori is problematic, as it is not clear in advance which parts of the mesh need to be modified to obtain an aesthetically pleasing solution that satisfies all constraints. We propose a novel framework for exploring local modifications of constrained meshes. Our solution consists of three steps. First, a user specifies target positions for one or more vertices. Our algorithm computes a sparse set of displacement vectors that satisfies the constraints and yields a smooth deformation. Then we build a linear subspace to allow realtime exploration of local variations that satisfy the constraints approximately. Finally, after interactive exploration, the result is optimized to fully satisfy the set of constraints. We evaluate our framework on meshes where each face is constrained to be planar.