作者:
BARRY, PJUniversity of Minnesota
Computer Science Department 4-192 EE/CSci Bldg. 200 Union St. SE Minneapolis 55455 MN United States
Knot insertion is one of the most important tools for spline curves in computergraphics and geometric modeling. This paper is a survey of knot insertion. In particular, it lists certain knot insertion algorithms for ...
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The main goal of surface characterization addresses the reduction of a surface to a compact symbolic description that efficiently stores information about the morphological structure of the surface. In the context of ...
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ISBN:
(纸本)081940747X
The main goal of surface characterization addresses the reduction of a surface to a compact symbolic description that efficiently stores information about the morphological structure of the surface. In the context of polyhedral surfaces characteristic regions, i.e., regions with convex, concave, planar, and saddle shape, are proposed as structural surface components and are defined taking into account geometric relationships between triangles. Based on these areal features, a symbolic representation of the surface called characteristic region configuration graph is produced where the nodes correspond to the surface regions while the arcs and hyperarcs correspond to the surface characteristic lines and points.
We describe a new method for creating rectangular Bezier surface patches on an implicit cubic surface. Traditional techniques for representing surfaces have relied on parametric representations of surfaces, that, in g...
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ISBN:
(纸本)081940747X
We describe a new method for creating rectangular Bezier surface patches on an implicit cubic surface. Traditional techniques for representing surfaces have relied on parametric representations of surfaces, that, in general, generate surfaces of implicit degree eight in case of rectangular Bezier surfaces with rational biquadratic parametrization. Thus we have achieved low-degree algebraic surface patch construction by reducing the implicit degree from eight to three. The construction uses a rectangular biquadratic Bezier control polyhedron, embedded within a tetrahedron and satisfying a projective constraint. The control polyhedron and the resulting cubic surface patch satisfy all of the standard properties of parametric Bezier surfaces, including
We present a strategy for reducing the number of knots for the representation of a piecewise polynomial approximation of a function defined on scattered data, without perturbing the approximation more than a given tol...
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ISBN:
(纸本)081940747X
We present a strategy for reducing the number of knots for the representation of a piecewise polynomial approximation of a function defined on scattered data, without perturbing the approximation more than a given tolerance. The method removes some (or all) of the interior knots. The number and location of these knots are determined automatically. Applications are in approximation of data, data storage, and image reconstruction.
Thin-plate spline fitting is often applied to fitting smooth surfaces to a collection of data. However, discontinuities in the data are smoothed by this technique. This occurs because of several underlying assumptions...
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ISBN:
(纸本)081940747X
Thin-plate spline fitting is often applied to fitting smooth surfaces to a collection of data. However, discontinuities in the data are smoothed by this technique. This occurs because of several underlying assumptions of spline fitting that do not hold when discontinuities are present. The theory of robust statistics can be used to deal with these outliers. In this paper, we present one way to apply the theory of robust statistics to the problem of discontinuous surface fitting.
In this paper, we deal with the problem of associative memory synthesis via multivariate interpolation. We present an abstract yet simple formalism to address the possibility of detecting and eliminating redundant inp...
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ISBN:
(纸本)081940747X
In this paper, we deal with the problem of associative memory synthesis via multivariate interpolation. We present an abstract yet simple formalism to address the possibility of detecting and eliminating redundant input data from the set of exemplars. The remaining pairs are then stored in a way so as to introduce controlled redundancy by replication of the corresponding neurons. The redundancy is detected via orthogonalization carried out in a Reproducing Kernel Hilbert Space setting.
In this paper, we firstly construct a general Binary Subdivision Algorithm (BSA) for surfaces over uniform triangulations and then present a matrix approach of convergence analysis. In the analysis, the idea of "...
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Integer versions of subdivision and corner cutting algorithms of NURBS curves are presented here. The algorithms are used to render NURBS curves of any degree on a raster device by either computing a polygonal approxi...
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This paper describes the first results of a test implementation of the new multivariate B-splines as recently developed for quadratics and cubics. The surface scheme is based on blending functions and control points a...
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ISBN:
(纸本)081940747X
This paper describes the first results of a test implementation of the new multivariate B-splines as recently developed for quadratics and cubics. The surface scheme is based on blending functions and control points and allows us to model Ck-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations of the parameter plane. The surface scheme exhibits both affine invariance and the convex hull property, and the control points can be used to manipulate the shape of the surface locally. Additional degrees of freedom in the underlying knot net allow for the modeling of discontinuities. Explicit formulas are given for the representation of polynomials and piecewise polynomials as linear combinations of B-splines.
We present the foundations of a method to generate blend surfaces. The idea of this method is to consider functionals depending on parametrized surfaces and their partial derivatives up to order two. The blend surface...
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ISBN:
(纸本)0819410314
We present the foundations of a method to generate blend surfaces. The idea of this method is to consider functionals depending on parametrized surfaces and their partial derivatives up to order two. The blend surface then is the surface which minimizes the functional. In section 2 we briefly describe the mathematical foundation. We discuss the variational problem associated to certain bilinear functionals in the Sobolov space of order 2. In section 2 we outline in detail the procedure how to generate blend surfaces by this method. Starting with a primary parameter space and a primary bilinear functional, one has to determine the final bilinear functional. The blend surface then is chosen as the tensor spline surface which minimizes the quadratic form corresponding to this bilinear functional.
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