Shape isophotic error netric controllable re-sampling for point-sampled surfaces

Shape simplification and re-sampling of underlying point-sampled surfaces under user-defined error bounds is an important and challenging issue. Based on the regular triangulation of the Gaussian sphere and the surface normals mapping onto the Gaussian sphere, a Gaussian sphere based re-sampling scheme is presented that generates a non-uniformly curvature-aware simplification of the given point-sampled model. Owing to the theoretical analysis of shape isophotic error metric for did that Gaussian sphere based sampling, the proposed simplification scheme provides a convenient way to control the re-sampling results under a user-specified error metric bound. The novel algorithm has been implemented and demonstrated on several examples.

[1]  Hugues Hoppe,et al.  New quadric metric for simplifying meshes with appearance attributes , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[2]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[3]  Michael Garland,et al.  Simplifying surfaces with color and texture using quadric error metrics , 1998, IEEE Visualization.

[4]  Matthias Zwicker,et al.  Pointshop 3D: an interactive system for point-based surface editing , 2002, SIGGRAPH.

[5]  Marc Alexa,et al.  Computing and Rendering Point Set Surfaces , 2003, IEEE Trans. Vis. Comput. Graph..

[6]  Tim Weyrich,et al.  Post-processing of Scanned 3D Surface Data , 2004, PBG.

[7]  Shi-Min Hu,et al.  Robust Feature Classification and Editing , 2007, IEEE Transactions on Visualization and Computer Graphics.

[8]  Pablo Diaz-Gutierrez.  Gaussian Sphere sampling based Surface Approximation , 2007 .

[9]  Markus H. Gross,et al.  Efficient simplification of point-sampled surfaces , 2002, IEEE Visualization, 2002. VIS 2002..

[10]  Kenneth L. Clarkson,et al.  Building triangulations using ε-nets , 2006, STOC '06.

[11]  Pierre Alliez,et al.  Variational shape approximation , 2004, ACM Trans. Graph..

[12]  Leif Kobbelt,et al.  Optimized Sub‐Sampling of Point Sets for Surface Splatting , 2004, Comput. Graph. Forum.

[13]  Markus Gross,et al.  Point-Based Graphics , 2007 .

[14]  Pierre Alliez,et al.  Geometric Modeling Based on Polygonal Meshes , 2008, Eurographics.

[15]  Marc Alexa,et al.  Point set surfaces , 2001, Proceedings Visualization, 2001. VIS '01..

[16]  Christian Rössl,et al.  Geometric modeling based on polygonal meshes Video files associated with this course are available from the citation page , 2007, SIGGRAPH Courses.

[17]  Jack Snoeyink,et al.  Theory and practice of sampling and reconstruction for manifolds with boundaries , 2001 .

[18]  Paul S. Heckbert,et al.  Survey of Polygonal Surface Simplification Algorithms , 1997 .

[19]  Marc Alexa,et al.  On Normals and Projection Operators for Surfaces Defined by Point Sets , 2004, PBG.

[20]  Meenakshisundaram Gopi,et al.  Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation , 2000, Comput. Graph. Forum.

[21]  Paolo Cignoni,et al.  Metro: Measuring Error on Simplified Surfaces , 1998, Comput. Graph. Forum.

[22]  Helmut Pottmann,et al.  The Isophotic Metric and Its Application to Feature Sensitive Morphology on Surfaces , 2004, ECCV.