Review of surface representations and fitting for reverse engineering

The selection of an appropriate surface representation scheme for reverse engineering and inspection depends upon several criteria, including fitting schemes, data collection, intersection algorithms, surface extension and constraint management. A comparison is presented between algebraic and parametric surfaces based on these criteria. The results of the paper are useful in choosing surface representations for various reverse engineering applications.

[1]  Edwin Boender.  A survey of intersection algorithms for curved surfaces , 1991, Comput. Graph..

[2]  HoppeHugues,et al.  Surface Reconstruction from Unorganized Points , 1992 .

[3]  George Salmon.  A Treatise on the Analytic Geometry of Three Dimensions , 1912 .

[4]  Tony C. Woo,et al.  Dimensional measurement of surfaces and their sampling , 1993, Comput. Aided Des..

[5]  MurakiShigeru.  Volumetric shape description of range data using Blobby Model , 1991 .

[6]  E LorensenWilliam,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987 .

[7]  W. J. Gordon,et al.  B-SPLINE CURVES AND SURFACES , 1974 .

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

[9]  Joris S. M. Vergeest,et al.  Connecting arbitrary surfaces under geometric constraints , 1987 .

[10]  Pramod N. Chivate,et al.  Solid-model generation from measured point data , 1993, Comput. Aided Des..

[11]  Robert E. Barnhill,et al.  Surfaces in computer aided geometric design: a survey with new results , 1985, Comput. Aided Geom. Des..

[12]  Joe D. Warren,et al.  On computing the intersection of a pair of algebraic surfaces , 1989, Comput. Aided Geom. Des..

[13]  Ramon F. Sarraga,et al.  Algebraic methods for intersections of quadric surfaces in GMSOLID , 1983, Comput. Vis. Graph. Image Process..

[14]  Les A. Piegl.  Representation of rational Be´zier curves and surfaces by recursive algorithms , 1986 .

[15]  P. Rabinowitz.  Applications of Linear Programming to Numerical Analysis , 1968 .

[16]  James R. Miller,et al.  Analysis of quadric-surface-based solid models , 1988, IEEE Computer Graphics and Applications.

[17]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[18]  C. Chui,et al.  Approximation Theory II , 1976 .

[19]  Larry L. Schumaker,et al.  Topics in Multivariate Approximation , 1987 .

[20]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[21]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[22]  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.

[23]  Kai-ching Chu,et al.  B3-splines for interactive curve and surface fitting , 1990, Comput. Graph..

[24]  Joris S. M. Vergeest,et al.  Surface fitting for interactive shape design , 1989 .

[25]  G. Farin.  Algorithms for rational Bézier curves , 1983 .

[26]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling , 1989 .

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

[28]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[29]  Ron Goldman,et al.  Using multivariate resultants to find the intersection of three quadric surfaces , 1991, TOGS.

[30]  C. Balaras,et al.  A surface fitting method for three dimensional scattered data , 1990 .

[31]  Baba C. Vemuri,et al.  On Three-Dimensional Surface Reconstruction Methods , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  L. Schumaker.  Fitting surfaces to scattered data , 1976 .

[33]  J. M. Galm,et al.  The strategic design driven inspection of machined parts , 1988, [Proceedings] 1988 International Conference on Computer Integrated Manufacturing.

[34]  L. Piegl,et al.  Curve and surface constructions using rational B-splines , 1987 .

[35]  Brian G. Schunck,et al.  A Two-Stage Algorithm for Discontinuity-Preserving Surface Reconstruction , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  Robert E. Barnhill,et al.  A marching method for parametric surface/surface intersection , 1990, Comput. Aided Geom. Des..

[37]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[38]  Wayne Tiller,et al.  Rational B-Splines for Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.

[39]  Richard Franke,et al.  Recent Advances in the Approximation of surfaces from scattered Data , 1987, Topics in Multivariate Approximation.

[40]  Thomas W. Sederberg.  Piecewise algebraic surface patches , 1985, Comput. Aided Geom. Des..

[41]  Chia-Hsiang Menq,et al.  Smooth-surface approximation and reverse engineering , 1991, Comput. Aided Des..

[42]  Q. Peng,et al.  An algorithm for finding the intersection lines between two B-spline surfaces , 1984 .

[43]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[44]  Hans Hagen,et al.  Topics in Surface Modeling , 1992 .

[45]  Tomoyuki Nishita,et al.  Geometric hermite approximation of surface patch intersection curves , 1991, Comput. Aided Geom. Des..

[46]  Francis J. M. Schmitt,et al.  An adaptive subdivision method for surface-fitting from sampled data , 1986, SIGGRAPH.

[47]  Robert P. Markot,et al.  Procedural method for evaluating the intersection curves of two parametric surfaces , 1991, Comput. Aided Des..

[48]  Les A. Piegl,et al.  On NURBS: A Survey , 2004 .

[49]  M. Sabin,et al.  Behaviour of recursive division surfaces near extraordinary points , 1978 .

[50]  Joshua Z. Levin.  Mathematical models for determining the intersections of quadric surfaces , 1979 .

[51]  James V. Miller,et al.  Extracting geometric models through constraint minimization , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[52]  Faryar Etesami,et al.  Tolerance verification through manufactured part modeling , 1988 .

[53]  M SchmittFrancisJ,et al.  An adaptive subdivision method for surface-fitting from sampled data , 1986 .

[54]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[55]  M. R. Irving,et al.  Power System State Estimation Using Linear Programming , 1978 .

[56]  C. D. Boor,et al.  Bicubic Spline Interpolation , 1962 .

[57]  David F. Rogers,et al.  Mathematical elements for computer graphics , 1976 .

[58]  J. G. Hayes,et al.  The Least-squares Fitting of Cubic Spline Surfaces to General Data Sets , 1974 .

[59]  Uniform rational approximation of functions of several variables , 1975 .

[60]  Malcolm A. Sabin,et al.  Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[61]  Nadim M. Aziz,et al.  Bezier surface/surface intersection , 1990, IEEE Computer Graphics and Applications.

[62]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[63]  James R. Miller,et al.  Geometric approaches to nonplanar quadric surface intersection curves , 1987, TOGS.

[64]  Nirant V. Puntambekar,et al.  Unified review of 3D model generation for reverse engineering , 1994 .

[65]  J. Neter,et al.  Applied Linear Regression Models , 1983 .

[66]  Shigeru Muraki,et al.  Volumetric shape description of range data using “Blobby Model” , 1991, SIGGRAPH.

[67]  E CarlsonWayne.  An algorithm and data structure for 3D object synthesis using surface patch intersections , 1982 .

[68]  A. Robin Forrest,et al.  Curves and surfaces for computer-aided design , 1968 .

[69]  C. Bajaj.  Surface fitting using implicit algebraic surface patches , 1992 .