Mesh blending

A new method for smoothly connecting different patches on triangle meshes with arbitrary connectivity, called mesh blending, is presented. A major feature of mesh blending is to move vertices of the blending region to a virtual blending surface by choosing an appropriate parameterization of those vertices. Once blending is completed, the parameterization optimization is performed to perfect the final meshes. Combining mesh blending with multiresolution techniques, an effective blending technique for meshes is obtained. Our method has several advantages: (1) the user can intuitively control the blending result using different blending radii, (2) the shape of cross-section curves can be adjusted to flexibly design complex models, and (3) the resulting mesh has the same connectivity as the original mesh. In this paper, some examples about smoothing, sharpening, and mesh editing show the efficiency of the method.

[1]  Leif Kobbelt,et al.  Geometric fairing of irregular meshes for free-form surface design , 2001, Comput. Aided Geom. Des..

[2]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, SIGGRAPH 2004.

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

[4]  A. Requicha,et al.  CONSTANT-RADIUS BLENDING IN SOLID MODELLING , 1984 .

[5]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[6]  Ralph R. Martin,et al.  Survey A survey of blending methods that use parametric surfaces , 2002 .

[7]  David E. Breen,et al.  Level set surface editing operators , 2002, ACM Trans. Graph..

[8]  Ayellet Tal,et al.  Metamorphosis of Polyhedral Surfaces using Decomposition , 2002, Comput. Graph. Forum.

[9]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[10]  Bruno Lévy.  Dual domain extrapolation , 2003, ACM Trans. Graph..

[11]  Ralph R. Martin,et al.  Parametric Blending in a Boundary Representation Solid Modeller , 1988, IMA Conference on the Mathematics of Surfaces.

[12]  Bongsik Choi,et al.  Constant-radius blending in surface modelling , 1989 .

[13]  Yutaka Ohtake,et al.  Mesh regularization and adaptive smoothing , 2001, Comput. Aided Des..

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

[15]  Gábor Lukács.  Differential geometry of G1 variable radius rolling ball blend surfaces , 1998, Comput. Aided Geom. Des..

[16]  Henning Biermann,et al.  Approximate Boolean operations on free-form solids , 2001, SIGGRAPH.

[17]  Thomas Hermann.  Rolling ball blends and self-intersection , 1992 .

[18]  Takashi Maekawa,et al.  An overview of offset curves and surfaces , 1999, Comput. Aided Des..

[19]  Qian Chen,et al.  Constant-Radius Blending of Parametric Surfaces , 1992, Geometric Modelling.

[20]  Adi Levin.  Combined subdivision schemes for the design of surfaces satisfying boundary conditions , 1999, Comput. Aided Geom. Des..

[21]  Nozomu Hamada,et al.  Feature edge extraction from 3D triangular meshes using a thinning algorithm , 2001, SPIE Optics + Photonics.

[22]  Frédo Durand,et al.  Non-iterative, feature-preserving mesh smoothing , 2003, ACM Trans. Graph..

[23]  Mark Meyer,et al.  Interactive geometry remeshing , 2002, SIGGRAPH.

[24]  Tomas Akenine-Möller,et al.  A Fast Triangle-Triangle Intersection Test , 1997, J. Graphics, GPU, & Game Tools.

[25]  Leif Kobbelt,et al.  Resampling Feature and Blend Regions in Polygonal Meshes for Surface Anti‐Aliasing , 2001, Comput. Graph. Forum.

[26]  Mark Meyer,et al.  Anisotropic Feature-Preserving Denoising of Height Fields and Bivariate Data , 2000, Graphics Interface.

[27]  Martin Rumpf,et al.  Anisotropic geometric diffusion in surface processing , 2000 .

[28]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[29]  Leif Kobbelt,et al.  An Interactive Approach to Point Cloud Triangulation , 2000, Comput. Graph. Forum.

[30]  Yun-shi Zhou,et al.  On blending of several quadratic algebraic surfaces , 2000, Comput. Aided Geom. Des..

[31]  Hyungjun Park,et al.  A method for approximate NURBS curve compatibility based on multiple curve refitting , 2000, Comput. Aided Des..

[32]  Gabriel Taubin,et al.  The ball-pivoting algorithm for surface reconstruction , 1999, IEEE Transactions on Visualization and Computer Graphics.

[33]  Peter Schröder,et al.  Multiresolution signal processing for meshes , 1999, SIGGRAPH.

[34]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[35]  Erich Hartmann,et al.  Parametric Gn blending of curves and surfaces , 2001, The Visual Computer.

[36]  M. Floater.  Mean value coordinates , 2003, Computer Aided Geometric Design.