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Surface Fitting with Hierarchical Splines
 ACM Transactions on Graphics
, 1995
"... We consider the fitting of tensor product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor product splines are used with gridded data, the surface fitting problem decomposes into a sequence of curve fitting processes, making the c ..."
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Cited by 57 (1 self)
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We consider the fitting of tensor product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor product splines are used with gridded data, the surface fitting problem decomposes into a sequence of curve fitting processes, making
Regularization Theory and Neural Networks Architectures
 Neural Computation
, 1995
"... We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Ba ..."
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Cited by 395 (32 self)
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to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models
Polynomial Splines and Their Tensor Products in Extended Linear Modeling
 Ann. Statist
, 1997
"... ANOVA type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function, or spectral density function. Polynomial splines are used to m ..."
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Cited by 221 (16 self)
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to model the main effects, and their tensor products are used to model any interaction components that are included. In the special context of survival analysis, the baseline hazard function is modeled and nonproportionality is allowed. In general, the theory involves the L 2 rate of convergence
Convexity Conditions for Parametric TensorProduct Bspline Surfaces
, 1998
"... This paper provides four alternative sufficient conditionsets, ensuring that a patch of a parametric tensorproduct Bspline surface is locally convex. These conditions are at most triquadratic with respect to the control points of the surface. ..."
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Cited by 3 (1 self)
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This paper provides four alternative sufficient conditionsets, ensuring that a patch of a parametric tensorproduct Bspline surface is locally convex. These conditions are at most triquadratic with respect to the control points of the surface.
Automatic reconstruction of Bspline surfaces of arbitrary topological type
 SIGGRAPH'96
, 1996
"... Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisitionâ€”the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners in ..."
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Cited by 173 (0 self)
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into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product Bspline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single Bspline patch, our goal
Fitting Smooth Surfaces to Dense Polygon Meshes
 Proceedings of SIGGRAPH 96
, 1996
"... Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches with ..."
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Cited by 240 (5 self)
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Recent progress in acquiring shape from range data permits the acquisition of seamless millionpolygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product Bspline surface patches
TENSOR PRODUCT SPLINE SURFACE APPROXIMATION OF A DISCRETE POINT FIELD
"... Designing the appropriate surface that approximates a certain point vector is one of the most challenging engineering tasks. Some of the aero and hydrodynamic profiles, materials plastic deformation technological problems are to be approached through surface approximation. Usually, the discrete inpu ..."
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. It is known that a surface parametrization p(u,v), which polynomial degree is at most n in u and m in v, can be written as a tensor product Bezier surface [6]: n
Polycube splines
, 2008
"... This paper proposes a new concept of polycube splines and develops novel modeling techniques for using the polycube splines in solid modeling and shape computing. Polycube splines are essentially a novel variant of manifold splines which are built upon the polycube map, serving as its parametric dom ..."
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Cited by 22 (9 self)
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domain. Our rationale for defining spline surfaces over polycubes is that polycubes have rectangular structures everywhere over their domains, except a very small number of corner points. The boundary of polycubes can be naturally decomposed into a set of regular structures, which facilitate tensorproduct
Spherical DCBspline Surfaces with . . .
, 2011
"... This paper develops a novel surface fitting scheme for automatically reconstructing a genus0 object into a continuous parametric spline surface. A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration Bspline (D ..."
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This paper develops a novel surface fitting scheme for automatically reconstructing a genus0 object into a continuous parametric spline surface. A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration Bspline
Exact Evaluation Of CatmullClark Subdivision Surfaces At Arbitrary Parameter Values
 Proceedings of SIGGRAPH
, 1998
"... In this paper we disprove the belief widespread within the computer graphics community that CatmullClark subdivision surfaces cannot be evaluated directly without explicitly subdividing. We show that the surface and all its derivatives can be evaluated in terms of a set of eigenbasis functions whi ..."
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Cited by 225 (8 self)
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and easy to implement. We have used our implementation to compute high quality curvature plots of subdivision surfaces. The cost of our evaluation scheme is comparable to that of a bicubic spline. Therefore, our method allows many algorithms developed for parametric surfaces to be applied to Catmull
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