C++ classes for the building and prototyping of spline applications are described. Flexibility, extensibility, and maximal code reuse are achieved by separating the concept of a basis from the implementations of curve...
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ISBN:
(纸本)081940747X
C++ classes for the building and prototyping of spline applications are described. Flexibility, extensibility, and maximal code reuse are achieved by separating the concept of a basis from the implementations of curves, functions, and surfaces.
Elimination theory was originally developed in the 18th and 19th centuries to find solvability criteria for a system of polynomial equations. We present some new resolvent methods that are suitable to solve important ...
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ISBN:
(纸本)081940747X
Elimination theory was originally developed in the 18th and 19th centuries to find solvability criteria for a system of polynomial equations. We present some new resolvent methods that are suitable to solve important problems in computer aided geometric design (CAGD), including implicitization, inversion, intersection, computation of self intersection points, and detection of unfaithful parametrizations of rational curves and surfaces.
Methods for approximating sweep surfaces by tensor product NURBS are presented. Sweep surfaces are generated by sweeping a (possibly deforming) NURBS cross-section curve along a NURBS axis curve. A general form for NU...
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ISBN:
(纸本)081940747X
Methods for approximating sweep surfaces by tensor product NURBS are presented. Sweep surfaces are generated by sweeping a (possibly deforming) NURBS cross-section curve along a NURBS axis curve. A general form for NURBS approximation to sweep surfaces is derived and expressed in terms of the approximation to a set of offset curves of the axis curve. The actual algorithm used to construct the surface approximation depends on the nature of the desired deformation and change in orientation that the cross-section undergoes as it is swept along the axis.
We present results on optimal recovery of band- and energy-limited signals from their inaccurate samples or inner products involving prolate spheroidal wave functions.
ISBN:
(纸本)081940747X
We present results on optimal recovery of band- and energy-limited signals from their inaccurate samples or inner products involving prolate spheroidal wave functions.
The analysis of parametric curves for the presence of shape characteristics such as loops, cusps, and inflections is considered. In contrast to previous methods that use heavily algebraic techniques to study polynomia...
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ISBN:
(纸本)081940747X
The analysis of parametric curves for the presence of shape characteristics such as loops, cusps, and inflections is considered. In contrast to previous methods that use heavily algebraic techniques to study polynomial cubic curves, our approach, based on the classical notion of normal curves, is predominately geometric. The approach not only provides new insight into the cubic polynomial case, it can also be applied to rational curves and to curves of degree greater than three. We demonstrate the use of the technique to analyze planar cubic curves, planar rational cubic curves, and polynomial curves of degree four in the plane and in three- space.
We survey research in progress involving the hierarchical fitting of regular data to tensor product splines. The approach is suitable for data in any dimension and for splines in any number of variables.
ISBN:
(纸本)081940747X
We survey research in progress involving the hierarchical fitting of regular data to tensor product splines. The approach is suitable for data in any dimension and for splines in any number of variables.
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.
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