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- W56873668 abstract "The tensor product B-spline surface, while regarded as a powerful boundary representation for computer aided geometric design (CAGD), still suffers restrictions because of its inherent rectangular nature. One manifestation of this problem is the difficulty of modelling nonrectangular regions. The need for three, five, and six-sided regions often arises naturally in CAGD. In recent years, the theory of univariate B-splines has been extended to multidimensional spaces. These multivariate splines provide generalizations of the univariate spline that preserve desirable features while providing more general domains.This thesis investigates the use of a parametric box spline surface representation over a three direction grid to define spline surfaces over three, four, five, and six-sided regions. Results are reported showing adaptive refinement of box spline surfaces and applications to display of shaded raster images and isoparametric curves. Modelling experiments which exploit the new capabilities provided by the box spline surface including nontensor product rectangular surfaces, nonrectangular surfaces, and hybrid nonrectangular regions composed of both box spline and tensor product surfaces are presented as well. Conditions for maintaining tangent plane continuity between nonuniform tensor product B-spline surfaces and box splines are developed." @default.
- W56873668 created "2016-06-24" @default.
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- W56873668 date "1986-06-30" @default.
- W56873668 modified "2023-09-27" @default.
- W56873668 title "Geometric modeling with multivariate box-splines" @default.
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