Adaptive patch-based mesh fitting for reverse engineering

In this paper, we propose a novel adaptive mesh fitting algorithm that fits a triangular model with G^1 smoothly stitching bi-quintic Bezier patches. Our algorithm first segments the input mesh into a set of quadrilateral patches, whose boundaries form a quadrangle mesh. For each boundary of each quadrilateral patch, we construct a normal curve and a boundary-fitting curve, which fit the normal and position of its boundary vertices respectively. By interpolating the normal and boundary-fitting curves of each quadrilateral patch with a Bezier patch, an initial G^1 smoothly stitching Bezier patches is generated. We perform this patch-based fitting scheme in an adaptive fashion by recursively subdividing the underlying quadrilateral into four sub-patches. The experimental results show that our algorithm achieves precision-ensured Bezier patches with G^1 continuity and meets the requirements of reverse engineering.

[1]  Jean-Pierre Kruth,et al.  Reverse engineering modelling of free-form surfaces from point clouds subject to boundary conditions , 1998 .

[2]  Stefanie Hahmann,et al.  Smooth adaptive fitting of 3D models using hierarchical triangular splines , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[3]  Yan Zhao,et al.  G1 CONTINUOUS CONDITIONS OF BICUBIC B-SPLINE SURFACES , 2000 .

[4]  Carlos Gonzalez-Ochoa,et al.  Localized-hierarchy surface splines (LeSS) , 1999, SI3D.

[5]  Marc Levoy,et al.  Fitting smooth surfaces to dense polygon meshes , 1996, SIGGRAPH.

[6]  J. Peters.  Smooth interpolation of a mesh of curves , 1991 .

[7]  Jarke J. van Wijk,et al.  Bicubic patches for approximating non-rectangular control-point meshes , 1986, Comput. Aided Geom. Des..

[8]  Carlo H. Séquin,et al.  Local surface interpolation with Bézier patches: errata and improvements , 1991, Comput. Aided Geom. Des..

[9]  Xiuzi Ye,et al.  G1-Interpolation of Rectangular Unrestricted Cubic Curve Meshes Using Biquintic Bézier Patches , 1994, IMA Conference on the Mathematics of Surfaces.

[10]  Carlo H. Séquin,et al.  Local surface interpolation with Bézier patches , 1987, Comput. Aided Geom. Des..

[11]  Ligang Liu,et al.  Parameterization for fitting triangular mesh , 2006 .

[12]  Matthias Eck,et al.  Automatic reconstruction of B-spline surfaces of arbitrary topological type , 1996, SIGGRAPH.

[13]  Xiuzi Ye,et al.  Curvature continuous interpolation of curve meshes , 1997, Comput. Aided Geom. Des..

[14]  Fengshan Liu,et al.  Reconstruction of convergent G1 smooth B-spline surfaces , 2004, Comput. Aided Geom. Des..

[15]  Valerio Pascucci,et al.  Spectral surface quadrangulation , 2006, SIGGRAPH 2006.

[16]  Jörg Peters,et al.  Biquartic C1-surface splines over irregular meshes , 1995, Comput. Aided Des..

[17]  Fujio Yamaguchi,et al.  Computer-Aided Geometric Design , 2002, Springer Japan.

[18]  Richard F. Riesenfeld,et al.  A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Xiquan Shi,et al.  G 1 continuous conditions of biquartic B-spline surfaces , 2002 .

[20]  Ulrich Reif,et al.  Biquadratic G-spline surfaces , 1995, Comput. Aided Geom. Des..

[21]  Lizhuang Ma,et al.  Smoothing of free-form surfaces with Bézier patches , 1995, Comput. Aided Geom. Des..

[22]  Xiquan Shi,et al.  A practical construction of G1 smooth biquintic B-spline surfaces over arbitrary topology , 2004, Comput. Aided Des..

[23]  Jörg Peters,et al.  Patching Catmull-Clark meshes , 2000, SIGGRAPH.

[24]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[25]  Shi Xi-quan,et al.  G~1 Continuous Condition of B-Spline Surfaces with Double Knots , 2005 .

[26]  Tom Lyche,et al.  T-spline Simplication and Local Renement , 2004 .

[27]  Colin Bradley,et al.  G1 continuity of B-spline surface patches in reverse engineering , 1995, Comput. Aided Des..