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    Shape space exploration of constrained meshes

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    Type
    Article
    Authors
    Yang, Yongliang
    Yang, Yijun
    Pottmann, Helmut cc
    Mitra, Niloy J. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2012-10-19
    Online Publication Date
    2012-10-19
    Print Publication Date
    2011
    Permanent link to this record
    http://hdl.handle.net/10754/575912
    
    Metadata
    Show full item record
    Abstract
    We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of non-linear constraints. We computationally access such manifolds, typically of high dimension and co-dimension, through first and second order approximants, namely tangent spaces and quadratically parameterized osculant surfaces. Exploration and navigation of desirable subspaces of the shape space with regard to application specific quality measures are enabled using approximants that are intrinsic to the underlying manifold and directly computable in the parameter space of the osculant surface. We demonstrate our framework on shape spaces of planar quad (PQ) meshes, where each mesh face is constrained to be (nearly) planar, and circular meshes, where each face has a circumcircle. We evaluate our framework for navigation and design exploration on a variety of inputs, while keeping context specific properties such as fairness, proximity to a reference surface, etc. © 2011 ACM.
    Citation
    Yang, Y.-L., Yang, Y.-J., Pottmann, H., & Mitra, N. J. (2011). Shape space exploration of constrained meshes. Proceedings of the 2011 SIGGRAPH Asia Conference on - SA ’11. doi:10.1145/2024156.2024158
    Sponsors
    We thank Daniel Piker for providing the starting "rheotomic" mesh used as the input mesh in Figure 1 and for the starting flat meshes in the upper two rows of Figure 18. We thank Johannes Wallner for his many useful comments and suggestions, Alexander Schiftner, Mathias Hobinger and Michael Eigensatz for their help and valuable comments, and the anonymous reviewers for their feedback. We are grateful to Heinz Schmiedhofer for the final renderings. The work has been partially supported by Austrian Science Fund (FWF) grant P23735-N13 and Austrian Science Promotion Agency (FFG) grant 813391.
    Publisher
    Association for Computing Machinery (ACM)
    Journal
    Proceedings of the 2011 SIGGRAPH Asia Conference on - SA '11
    DOI
    10.1145/2024156.2024158
    10.1145/2070752.2024158
    10.1145/2070781.2024158
    ae974a485f413a2113503eed53cd6c53
    10.1145/2024156.2024158
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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