Surface Approximation to Scattered Lines

A global weighted-mean approximation to scattered lines is introduced. Rational Gaussian weights are stretched along lines and standard deviations of Gaussians are selected in such a way as to produce surfaces that closely follow data along lines. When the lengths of the lines approach zero, the proposed formulation converges to that of global weighted mean approximation to scattered points. Therefore, the traditional weighted mean approximation becomes a special case of the proposed approximation. Implementation strategies are presented and examples of surface approximation using range data and polygon meshes are given.

[1]  A. Ardeshir Goshtasby,et al.  Parametric circles and spheres , 2003, Comput. Aided Des..

[2]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[3]  Peter Oswald,et al.  Designing composite triangular subdivision schemes , 2005, Comput. Aided Geom. Des..

[4]  A. Ardeshir Goshtasby,et al.  Geometric modelling using rational Gaussian curves and surfaces , 1995, Comput. Aided Des..

[5]  Scott Schaefer,et al.  On C2 triangle/quad subdivision , 2005, TOGS.

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

[7]  E. Grosse.  A catalogue of algorithms for approximation , 1990 .

[8]  Tony DeRose,et al.  Subdivision surfaces in character animation , 1998, SIGGRAPH.

[9]  Hugues Hoppe,et al.  Spherical parametrization and remeshing , 2003, ACM Trans. Graph..

[10]  A. Ardeshir Goshtasby,et al.  Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces , 1993, International Journal of Computer 11263on.

[11]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[12]  Luc Van Gool,et al.  Wide-baseline stereo matching with line segments , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[13]  James F. O'Brien,et al.  Interpolating and approximating implicit surfaces from polygon soup , 2005, SIGGRAPH Courses.

[14]  A. Ardeshir Goshtasby,et al.  Approximating Digital 3D Shapes by Rational Gaussian Surfaces , 2003, IEEE Trans. Vis. Comput. Graph..

[15]  E. Catmull,et al.  A CLASS OF LOCAL INTERPOLATING SPLINES , 1974 .

[16]  Weiyin Ma,et al.  Subdivision surfaces for CAD - an overview , 2005, Comput. Aided Des..

[17]  Peihua Qiu,et al.  Discontinuous regression surfaces fitting , 1998 .

[18]  J. Warren,et al.  Subdivision methods for geometric design , 1995 .

[19]  Larry L. Schumaker,et al.  A Bibliography of multivariate Approximation , 1987, Topics in Multivariate Approximation.

[20]  A. Ardeshir Goshtasby,et al.  A weighted mean approach to smooth parametric representation of polygon meshes , 2004, The Visual Computer.

[21]  Gábor Renner,et al.  Advanced surface fitting techniques , 2002, Comput. Aided Geom. Des..

[22]  Michael E. Mortenson.  Geometric modeling (2nd ed.) , 1997 .

[23]  Michael E. Mortenson,et al.  Geometric Modeling , 2008, Encyclopedia of GIS.