Foldover-Free Mesh Warping for Constrained Texture Mapping

Mapping texture onto 3D meshes with positional constraints is a popular technique that can effectively enhance the visual realism of geometric models. Such a process usually requires constructing a valid mesh embedding satisfying a set of positional constraints, which is known to be a challenging problem. This paper presents a novel algorithm for computing a foldover-free piecewise linear mapping with exact positional constraints. The algorithm begins with an unconstrained planar embedding, followed by iterative constrained mesh transformations. At the heart of the algorithm are radial basis function (RBF)-based warping and the longest edge bisection (LEB)-based refinement. A delicate integration of the RBF-based warping and the LEB-based refinement provides a provably-foldover-free, smooth constrained mesh warping, which can handle a large number of constraints and output a visually pleasing mapping result without extra smoothing optimization. The experiments demonstrate the effectiveness of the proposed algorithm.

[1]  Teseo Schneider,et al.  Bijective Composite Mean Value Mappings , 2013, SGP '13.

[2]  Ayellet Tal,et al.  FlexiStickers: photogrammetric texture mapping using casual images , 2009, ACM Trans. Graph..

[3]  Bruno Lévy,et al.  Least squares conformal maps for automatic texture atlas generation , 2002, ACM Trans. Graph..

[4]  Kikuo Fujimura,et al.  Foldover-Free Image Warping , 1998, Graph. Model. Image Process..

[5]  Wenjing Zhang,et al.  Inversion Free and Topology Compatible Tetrahedral Mesh Warping Driven by Boundary Surface Deformation , 2013, 2013 International Conference on Computer-Aided Design and Computer Graphics.

[6]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[7]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..

[8]  S. Korotov,et al.  Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm , 2008 .

[9]  Ligang Liu,et al.  Embedding a triangular graph within a given boundary , 2011, Comput. Aided Geom. Des..

[10]  Mark Meyer,et al.  Intrinsic Parameterizations of Surface Meshes , 2002, Comput. Graph. Forum.

[11]  Hyewon Seo,et al.  Constrained Texture Mapping using Image Warping , 2010, Comput. Graph. Forum.

[12]  Alan Saalfeld Joint triangulations and triangulation maps , 1987, SCG '87.

[13]  Denis Zorin,et al.  Locally injective parametrization with arbitrary fixed boundaries , 2014, ACM Trans. Graph..

[14]  Yaron Lipman,et al.  Bounded distortion mapping spaces for triangular meshes , 2012, ACM Trans. Graph..

[15]  Alla Sheffer,et al.  Matchmaker: constructing constrained texture maps , 2003, ACM Trans. Graph..

[16]  Craig Gotsman,et al.  Controllable morphing of compatible planar triangulations , 2001, TOGS.

[17]  Michael S. Floater,et al.  Mean value coordinates , 2003, Comput. Aided Geom. Des..

[18]  Hujun Bao,et al.  RBF-based constrained texture mapping , 2003, Comput. Graph..

[19]  Tong-Yee Lee,et al.  An RBF-Based Reparameterization Method for Constrained Texture Mapping , 2012, IEEE Transactions on Visualization and Computer Graphics.

[20]  Bernard Tiddeman,et al.  A general method for overlap control in image warping , 2001, Comput. Graph..

[21]  Tong-Yee Lee,et al.  Fast and Intuitive Metamorphosis of 3D Polyhedral Models Using SMCC Mesh Merging Scheme , 2003, IEEE Trans. Vis. Comput. Graph..

[22]  Diane L. Souvaine,et al.  Constructing piecewise linear homeomorphisms , 1994 .

[23]  Bruno Lévy,et al.  ABF++: fast and robust angle based flattening , 2005, TOGS.

[24]  Matthias Zwicker,et al.  Ieee Transactions on Visualization and Computer Graphics Ewa Splatting , 2002 .

[25]  Hugues Hoppe,et al.  Inter-surface mapping , 2004, ACM Trans. Graph..

[26]  Craig Gotsman,et al.  Texture Mapping with Hard Constraints , 2001, Comput. Graph. Forum.

[27]  Tong-Yee Lee,et al.  Texture Mapping with Hard Constraints Using Warping Scheme , 2008, IEEE Transactions on Visualization and Computer Graphics.

[28]  Yotam I. Gingold,et al.  A direct texture placement and editing interface , 2006, UIST.

[29]  Kai Hormann,et al.  Surface Parameterization: a Tutorial and Survey , 2005, Advances in Multiresolution for Geometric Modelling.

[30]  Pedro V. Sander,et al.  Texture mapping progressive meshes , 2001, SIGGRAPH.

[31]  Bruno Lévy,et al.  Constrained texture mapping for polygonal meshes , 2001, SIGGRAPH.