Free-form deformation of solid geometric models

A technique is presented for deforming solid geometric models in a free-form manner. The technique can be used with any solid modeling system, such as CSG or B-rep. It can deform surface primitives of any type or degree: planes, quadrics, parametric surface patches, or implicitly defined surfaces, for example. The deformation can be applied either globally or locally. Local deformations can be imposed with any desired degree of derivative continuity. It is also possible to deform a solid model in such a way that its volume is preserved.The scheme is based on trivariate Bernstein polynomials, and provides the designer with an intuitive appreciation for its effects.

[1]  A. Ricci,et al.  A Constructive Geometry for Computer Graphics , 1973, Computer/law journal.

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

[3]  J. A. Brewer,et al.  Visual interaction with overhauser curves and surfaces , 1977, SIGGRAPH '77.

[4]  Richard E. Parent.  A system for sculpting 3-D data , 1977, SIGGRAPH.

[5]  E. L. Stanton,et al.  A parametric cubic modelling system for general solids of composite material , 1977 .

[6]  Barr,et al.  Superquadrics and Angle-Preserving Transformations , 1981, IEEE Computer Graphics and Applications.

[7]  Yehuda E. Kalay,et al.  Modeling Polyhedral Solids Bounded by Multi-Curved Parametric Surfaces , 1983, 19th Design Automation Conference.

[8]  James F. Blinn,et al.  A Generalization of Algebraic Surface Drawing , 1982, TOGS.

[9]  Requicha,et al.  Solid Modeling: A Historical Summary and Contemporary Assessment , 1982, IEEE Computer Graphics and Applications.

[10]  Hiroaki Chiyokura,et al.  Design of solids with free-form surfaces , 1983, SIGGRAPH.

[11]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[12]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[13]  Herbert A. Steinberg.  A Smooth Surface Based on Biquadratic Patches , 1984, IEEE Computer Graphics and Applications.

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

[15]  Fumihiko Kimura,et al.  Geomap-III: Designing Solids With Free-Form Surfaces , 1984, IEEE Computer Graphics and Applications.

[16]  T. Varady,et al.  Synthesis of volume modelling and sculptured surfaces in BUILD , 1984 .

[17]  Tamás Várady,et al.  Design techniques for the definition of solid objects with free-form geometry , 1984, Comput. Aided Geom. Des..

[18]  Ramon F. Sarraga,et al.  Free-Form Surfaces in GMSolid: Goals and Issues , 1984 .

[19]  E. S. Cobb.  Design of sculptured surfaces using the b-spline representation , 1984 .

[20]  Rida T. Farouki,et al.  A Hierarchy of Geometric Forms , 1985, IEEE Computer Graphics and Applications.

[21]  Alan E. Middleditch,et al.  Blend surfaces for set theoretic volume modelling systems , 1985, SIGGRAPH '85.

[22]  Malcolm S. Casale,et al.  An Overview of Analytic Solid Modeling , 1985, IEEE Computer Graphics and Applications.

[23]  S. Parry.  Free-form deformation in a constructive solid geometry modeling system , 1986 .