Geometric method of intersecting natural quadrics represented in trimmed surface form

Abstract A purely geometric method for intersecting natural quadrics (plane, cone, cylinder and sphere) is presented in this paper, which supports the Boolean algorithm to intersect trimmed surfaces given in rational B-spline form. The advantages of the geometric approach are emphasized and all the important issues of the intersection process are described in detail.

[1]  Spencer W. Thomas Modelling volumes bounded by b-spline surfaces , 1984 .

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

[3]  R. J. Walker Algebraic curves , 1950 .

[4]  Paul G. Comba,et al.  A Procedure for Detecting Intersections of Three-Dimensional Objects , 1968, JACM.

[5]  R. Farouki Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations , 1987 .

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

[7]  K. Cheng Using plane vector fields to obtain all the intersection curves of two general surfaces , 1989 .

[8]  Mark B. Phillips,et al.  An Algorithm for Locating and Displaying the Intersection of Two Arbitrary Surfaces , 1984, IEEE Computer Graphics and Applications.

[9]  Rida T. Farouki,et al.  The characterization of parametric surface sections , 1986, Comput. Vis. Graph. Image Process..

[10]  Chaman L. Sabharwal,et al.  Implementation of a divide-and-conquer method for intersection of parametric surfaces , 1985, Comput. Aided Geom. Des..

[11]  Michael I. Jordan,et al.  Surface/surface intersection , 1987, Comput. Aided Geom. Des..

[12]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[13]  Joshua Levin,et al.  A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces , 1976, CACM.

[14]  Hans-Ulrich Pfeifer Methods used for intersecting geometrical entities in the GPM module for volume geometry , 1985 .

[15]  Les A. Piegl,et al.  A technique for smoothing scattered data with conic sections , 1987 .

[16]  Malcolm S. Casale,et al.  Free-Form Solid Modeling with Trimmed Surface Patches , 1987, IEEE Computer Graphics and Applications.

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

[18]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

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

[20]  James R. Miller,et al.  Sculptured Surfaces in Solid Models: Issues and Alternative Approaches , 1986, IEEE Computer Graphics and Applications.

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

[22]  J. Y. S. Luh,et al.  Mathematical model for mechanical part description , 1965, Commun. ACM.

[23]  Dieter Lasser,et al.  Intersection of parametric surfaces in the Bernstein—Be´zier representation , 1986 .

[24]  Thomas Powers,et al.  The Computer Graphics Virtual Device Interface , 1986, IEEE Computer Graphics and Applications.

[25]  Donald Greenberg,et al.  Intersection of parametric surfaces by means of look-up tables , 1983, IEEE Computer Graphics and Applications.

[26]  Tor Dokken Finding intersections of B-spline represented geometries using recursive subdivision techniques , 1985, Comput. Aided Geom. Des..

[27]  S. Mudur,et al.  A new class of algorithms for the processing of parametric curves , 1983 .

[28]  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.

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

[30]  I. C. Braid,et al.  Designing with volumes , 1973 .

[31]  Sudhir P. Mudur,et al.  Computational techniques for processing parametric surfaces , 1984, Comput. Vis. Graph. Image Process..

[32]  Ruth A. Weiss BE VISION, A Package of IBM 7090 FORTRAN Programs to Draw Orthographic Views of Combinations of Plane and Quadric Surfaces , 1966, J. ACM.