SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping

  • Authors:

  • Shenghua Wan;Zhao Yin;Kang Zhang;Hongchao Zhang;Xin Li

  • Affiliations:

  • Department of Electrical and Computer Engineering, and Center for Computation and Technology, Louisiana State University, Baton Rouge, 70803, USA;Department of Automation, Xiamen University, Xiamen 361005, China;Department of Electrical and Computer Engineering, and Center for Computation and Technology, Louisiana State University, Baton Rouge, 70803, USA;Department of Mathematics, Louisiana State University, Baton Rouge, 70803, USA;Department of Electrical and Computer Engineering, and Center for Computation and Technology, Louisiana State University, Baton Rouge, 70803, USA

  • Venue:
  • Computers and Graphics
  • Year:
  • 2011

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Abstract

We present an effective optimization framework to compute polycube mapping. Composed of a set of small cubes, a polycube well approximates the geometry of the free-form model yet possesses great regularity; therefore, it can serve as a nice parametric domain for free-form shape modeling and analysis. Generally, the more cubes are used to construct the polycube, the better the shape can be approximated and parameterized with less distortion. However, corner points of a polycube domain are singularities of this parametric representation, so a polycube domain having too many corners is undesirable. We develop an iterative algorithm to seek for the optimal polycube domain and mapping, with the constraint on using a restricted number of cubes (therefore restricted number of corner points). We also use our polycube mapping framework to compute an optimal common polycube domain for multiple objects simultaneously for lowly distorted consistent parameterization.