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13,047
Piecewisepolynomial regression trees
 Statistica Sinica
, 1994
"... A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data ..."
Abstract

Cited by 51 (8 self)
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A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion
Compactly supported tight affine spline frames
 Math. Comp
, 1998
"... Abstract. The theory of fiberization is applied to yield compactly supported tight affine frames (wavelets) in L2(Rd) from box splines. The wavelets obtained are smooth piecewisepolynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The ..."
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Cited by 43 (9 self)
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Abstract. The theory of fiberization is applied to yield compactly supported tight affine frames (wavelets) in L2(Rd) from box splines. The wavelets obtained are smooth piecewisepolynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support
SIGNIFICANCE AND EXPLANATION
, 1986
"... The lecture addresses topics in multivariate approximation which have caught the author’s interest in the last ten years. These include: the approximation by functions with fewer variables, correct points for polynomial interpolation, the B(ernstein,ézier,arycentric)form for polynomials and its u ..."
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use in understanding smooth piecewise polynomial (pp) functions, approximation order from spaces of pp functions, multivariate Bsplines, and surface generation by subdivision.
Design of Flows on Smooth Surfaces
"... Vector fields tangent to a 2D manifold surface have many applications in Computer Graphics, Scientific Visualization and Geometric Design. These Tangent Vector Fields (TVF) may be used for generating textures on a surface, computing expressive renderings of a surface, modeling and visualizing a shea ..."
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. Second we want to establish a new TVF design method targeted to smooth piecewise polynomial surfaces. Such surfaces are the standard model for manufactured objects, and can also be used to model arbitrary topology surfaces ([5]). We expect that a dedicated method for smooth polynomial surfaces will speed
Parallel Smoothing of Quad Meshes
 THE VISUAL COMPUTER
"... For use in realtime applications, we present a fast algorithm for converting a quad mesh to a smooth, piecewise polynomial surface on the Graphics Processing Unit (GPU). The surface has welldefined normals everywhere and closely mimics the shape of CatmullClark subdivision surfaces. It consists o ..."
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Cited by 1 (0 self)
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For use in realtime applications, we present a fast algorithm for converting a quad mesh to a smooth, piecewise polynomial surface on the Graphics Processing Unit (GPU). The surface has welldefined normals everywhere and closely mimics the shape of CatmullClark subdivision surfaces. It consists
The multivariate spline method for numerical solution of partial differential equations and scattered data fitting
"... Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of nsimplices in the Euclidean space R^n. We present a straightforward method for using these spline functions to numerically solve elliptic partial differential equations such as Poisson and bi ..."
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Cited by 18 (14 self)
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Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of nsimplices in the Euclidean space R^n. We present a straightforward method for using these spline functions to numerically solve elliptic partial differential equations such as Poisson
The Multivariate Spline Method for Scattered Data Fitting . . .
, 2005
"... Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of nsimplices in the Euclidean space IR n. A straightforward method for using these spline functions to fit given scattered data and numerically solve elliptic partial differential equations is p ..."
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Cited by 14 (7 self)
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Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of nsimplices in the Euclidean space IR n. A straightforward method for using these spline functions to fit given scattered data and numerically solve elliptic partial differential equations
Numerical Solution of Optimal Control Problems Using Splines
, 2003
"... This paper explores numerical solutions of optimal control problems using BSpline curves. It is aimed to give a general framework on how to use BSplines to formulate optimal control problems and to solve them numerically using Nonlinear Trajectory Generation software package. E#ects of the se ..."
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#ects of the selection of the BSpline parameters, such as, number of intervals, smoothness, piecewise polynomial orders, number of berak points, on the solution of an optimal control problem are investigated. Formulation of optimal control problems involving complex arbitrary shape obstacles and tabular data using
C¹ surface splines
 SIAM Journal of Numerical Analysis
, 1995
"... The construction of quadratic C¹
surfaces from Bspline control points is generalized to a wider class of control meshes capable of outlining arbitrary freeform surfaces in space. Irregular meshes with non quadrilateral cells and more or fewer than four cells meeting at a point are allowed so that ..."
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Cited by 34 (12 self)
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that arbitrary freeform surfaces with or without boundary can be modeled in the same conceptual frame work as tensorproduct Bsplines. That is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local, evaluates by averaging and obeys the convex hull
Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets
 SIAM J. Math. Anal
, 1999
"... Abstract. Orthogonal polynomials are used to construct families of C 0 and C 1 orthogonal, compactly supported spline multiwavelets. These families are indexed by an integer which represents the order of approximation. We indicate how to obtain from these multiwavelet bases for L 2 [0,1] and present ..."
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Cited by 18 (5 self)
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Abstract. Orthogonal polynomials are used to construct families of C 0 and C 1 orthogonal, compactly supported spline multiwavelets. These families are indexed by an integer which represents the order of approximation. We indicate how to obtain from these multiwavelet bases for L 2 [0
Results 1  10
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13,047