COMPUTER AIDED GEOMETRIC DESIGN

iii Preface This semester is the 24 th time I have taught a course at Brigham Young University titled, " Computer Aided Geometric Design. " When I first taught such a course in 1983, the field was young enough that no textbook covered everything that I wanted to teach, and so these notes evolved. The field now has matured to the point that several semesters worth of valuable material could be compiled. These notes, admittedly biased towards my own interests, reflect my personal preferences as to which of that material is most beneficial to students in an introductory course. I welcome anyone who has an interest in studying this fascinating topic to make free use of these notes. I invite feedback on typos and on material that could be written more clearly.

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

[2]  T. Sakkalis,et al.  Pythagorean hodographs , 1990 .

[3]  Tomoyuki Nishita,et al.  Curve intersection using Bézier clipping , 1990, Comput. Aided Des..

[4]  T. Sederberg.  Algorithm for algebraic curve intersection , 1989 .

[5]  Lyle Ramshaw,et al.  Blossoms are polar forms , 1989, Comput. Aided Geom. Des..

[6]  Thomas W. Sederberg,et al.  Fat arcs: A bounding region with cubic convergence , 1989, Comput. Aided Geom. Des..

[7]  Lyle Ramshaw,et al.  Béziers and B-splines as Multiaffine Maps , 1988 .

[8]  Michael S. Floater,et al.  Derivatives of rational Bézier curves , 1992, Comput. Aided Geom. Des..

[9]  Malcolm A. Sabin,et al.  Non-uniform recursive subdivision surfaces , 1998, SIGGRAPH.

[10]  P. Revesz.  Interpolation and Approximation , 2010 .

[11]  Michael A. Lachance,et al.  Chebyshev economization for parametric surfaces , 1988, Comput. Aided Geom. Des..

[12]  H. Timmer,et al.  Alternative representation for parametric cubic curves and surfaces , 1980 .

[13]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[14]  Xuguang Wang,et al.  Rational hodographs , 1987, Comput. Aided Geom. Des..

[15]  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.

[16]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

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

[18]  Jon G. Rokne.  Reducing the degree of an interval polynomial , 2005, Computing.

[19]  Ron Goldman,et al.  Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves , 1984, Comput. Aided Geom. Des..

[20]  Dana H. Ballard,et al.  Strip trees: a hierarchical representation for curves , 1981, CACM.

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

[22]  Rida T. Farouki,et al.  Algorithms for polynomials in Bernstein form , 1988, Comput. Aided Geom. Des..

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

[24]  N. Bose.  Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory , 1995 .

[25]  Tomoyuki Nishita,et al.  Ray tracing trimmed rational surface patches , 1990, SIGGRAPH.

[26]  W. Mccrea.  Analytical Geometry of Three Dimensions , 1943, Nature.

[27]  W. Böhm,et al.  Generating the Bézier points of B-spline curves and surfaces , 1981 .

[28]  A. W. Overhauser,et al.  Analytic Definition of Curves and Surfaces by Parabolic Blending , 2005, ArXiv.

[29]  Heinz Kredel,et al.  Gröbner Bases: A Computational Approach to Commutative Algebra , 1993 .

[30]  Eldon Hansen,et al.  A globally convergent interval method for computing and bounding real roots , 1978 .

[31]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[32]  M. Sabin.  Envelope curves and surfaces , 1987 .

[33]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[34]  Nicholas M. PATRIKALAKIS.  Approximate conversion of rational splines , 1989, Comput. Aided Geom. Des..

[35]  Thomas W. Sederberg,et al.  Curve implicitization using moving lines , 1994, Comput. Aided Geom. Des..

[36]  Horst Nowacki,et al.  Fairing Bézier curves with constraints , 1990, Comput. Aided Geom. Des..

[37]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[38]  Melvin R. Spencer.  Polynomial real root finding in Bernstein form , 1994 .

[39]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[40]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[41]  Rida T. Farouki,et al.  On the numerical condition of polynomials in Bernstein form , 1987, Comput. Aided Geom. Des..

[42]  Ralf Fröberg,et al.  An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[43]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..

[44]  Nicholas S. North,et al.  T-spline simplification and local refinement , 2004, SIGGRAPH 2004.

[45]  Sudhir P. Mudur,et al.  Interval Methods for Processing Geometric Objects , 1984, IEEE Computer Graphics and Applications.

[46]  T. Sederberg,et al.  Improved test for closed loops in surface intersections , 1989 .

[47]  Matthias Eck,et al.  Degree reduction of Bézier curves , 1993, Comput. Aided Geom. Des..

[48]  Josef Hoschek.  Approximate conversion of spline curves , 1987, Comput. Aided Geom. Des..

[49]  A. Z..  An Introduction to Projective Geometry , 1938, Nature.

[50]  Knut Mørken,et al.  Knot removal for parametric B-spline curves and surfaces , 1987, Comput. Aided Geom. Des..

[51]  Ron Goldman,et al.  Implicit representation of parametric curves and surfaces , 1984, Comput. Vis. Graph. Image Process..

[52]  P. Bézier.  MATHEMATICAL AND PRACTICAL POSSIBILITIES OF UNISURF , 1974 .