Results 181 to 190 of about 1,510 (211)

A fitting approach with dynamic algebraic spline curves

Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05), 2005
In computer aided geometric design and computer graphics, fitting point clouds with smooth curves (known as curve reconstruction) is a widely investigated problem. Dynamic implicit curve reconstruction is a new approach appearing in the curve reconstruction.
Changqi Hu, Zhouwang Yang
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Multivariate Splines and Algebraic Geometry

2015
Multivariate splines are effective tools in numerical analysis and approximation theory. Despite an extensive literature on the subject, there remain open questions in finding their dimension, constructing local bases, and determining their approximation power. Much of what is currently known was developed by numerical analysts, using classical methods,
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Algebras of spline approximation sequences

1995
The main goal of the present chapter is to establish stability criteria for the approximate solution of singular integral equations with piecewise continuous coefficients on the real axis. Based on our knowledge of the structure of approximation systems for the singular integral operator we shall construct a Banach algebra of approximation sequences ...
Roland Hagen, Steffen Roch, Bernd Silbermann   +2 more
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Algebraic properties of discrete box splines

Constructive Approximation, 1987
It is known that the discrete box splines play an important role in the theory of multivariate splines, subdivision algorithms for the computer generation of surfaces, as well as in the theory of partition of numbers. This paper continues the previous works on discrete box splines and subdivision algorithms of \textit{E. Cohen}, \textit{T.
Dahmen, Wolfgang, Micchelli, Charles A.
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A Class of Algebraic Trigonometric Interpolation Splines and Applications

2010 International Conference on Computational and Information Sciences, 2010
A new kind of interpolation splines with a shape parameter over the algebraic trigonometric function space Ω=span {1, t, sint, cost, sint2t, cos2t} is presented, which are called cubic algebraic trigonometric splines. The cubic algebraic trigonometric splines have many similar properties to cubic B-splines.
Yang Lian, Li Juncheng, Chen Guohua
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Simultaneous blending of convex polyhedra by algebraic splines

Computer-Aided Design, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mou, Haining, Zhao, Guohui, Wang, Zhirui, Su, Zhixun   +3 more
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The linear algebra of box spline spaces

1993
In this chapter, we consider the cardinal spline space $$S: = {S_M}: = span{\left( {M\left( { \cdot - j} \right)} \right)_{j{ \in ^s}}}$$ (1) i.e., the space spanned by the shifts, or integer translates, of the box spline \(M: = {M_\Xi }.\)
Carl de Boor, Klaus Höllig, Sherman Riemenschneider   +2 more
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Representation of piecewise continuous algebraic surfaces in terms of B-splines

The Visual Computer, 1989
A method for representing shape using portions of algebraic surfaces bounded by rectangular boxes defined in terms of triple product Bernstein polynomials is described and some of its properties are outlined. The method is extended to handle piecewise continuous algebraic surfaces within rectangular boxes defined in terms of triple products of B-spline
Nicholas M. Patrikalakis, George A. Kriezis   +1 more
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Algebraic Proof of the B-Spline Derivative Formula

2005
We prove a well known formula for the generalized derivatives of Chebyshev B--splines: \begin{; ; ; eqnarray*}; ; ; L_1B_i^k(x) & = & \frac{; ; ; B_i^{; ; ; k-1}; ; ; (x)}; ; ; {; ; ; C_{; ; ; k-1}; ; ; (i)}; ; ; - \frac{; ; ; B_{; ; ; i+1}; ; ; ^{; ; ; k-1}; ; ; (x)}; ; ; {; ; ; C_{; ; ; k-1}; ; ; (i+1)}; ; ; , \end{; ; ; eqnarray*}; ; ; where \begin{;
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Algebraic Spline Geometry: Some Remarks

2014
In this short note we discuss some aspects of what could be called algebraic spline geometry. We concentrate on the concept of generalized Stanley–Reisner rings, namely the rings C r (Δ) of piecewise polynomial r-smooth functions on a simplicial complex Δ in ℝ d .
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