2 edition of **Analysis of uniform binary subdivision schemes for curve design** found in the catalog.

Analysis of uniform binary subdivision schemes for curve design

N. Dyn

- 78 Want to read
- 23 Currently reading

Published
**1988**
by Department of Mathematics and Statistics,Brunel University in Uxbridge, Middx
.

Written in English

**Edition Notes**

Statement | N. Dyn, J. A. Gregory and D. Levin. |

Series | TR/06/88 |

Contributions | Gregory, John A., Levin, D. |

The Physical Object | |
---|---|

Pagination | 28p. |

Number of Pages | 28 |

ID Numbers | |

Open Library | OL14467998M |

[DynLevGre87] N. Dyn, D. Levin and J.A. Gregory, A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design, 4(4), Pages , [Chaikin74] G. Chaikin, An algorithm for high speed curve generation. Computer Graphics and Image Processing, 3, , [Riesen75] R. Riesenfeld, On Chaikin's algorithm. () Improved binary four point subdivision scheme and new corner cutting scheme. Computers & Mathematics with Applications , () Linear-Regression Model Based Wavelet Filter Evaluation for Image Compression.

The paper proposes, a five-point binary non-stationary approximating subdivision scheme, which can generate the family of C 4 limiting curves. The asymptotic equivalence method has been applied in order to determine the smoothness and convergence of that scheme. The proposed scheme can be considered as the non-stationary counter part of the first binary 5point approximating stationary scheme. † Warren()- Binary subdivision schemes for functions of irregular knot sequences. † Gregory,Qu()- Non-uniform corner cutting. † Sederberg,Sewell,Sabin()- Non-uniform recursive subdivision surfaces.

Computer-Aided Design, , Google Scholar Cross Ref; 9. N Dyn, D Levin, and J A Gregory. A 4-point Interpolatory Subdivision Scheme For Curve Design. Computer Aided Geometric Design, , Google Scholar Digital Library; G Farin. Designing C1 Surfaces Consisting Of Triangular Cubic Patches. Computer-Aided Design, Abstract: Subdivision schemes are acknowledged as an important tool in computer aided geometric design. The new binary non-stationary three-point approximating subdivision schemes have been proposed that generate wide variations of C1 and C2 contin uous curves using shape control parameter ξ0. The proposed schemes are the.

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Analysis of uniform binary subdivision schemes for curve design Article (PDF Available) in Constructive Approximation 7(1) January with Reads How we measure 'reads'. The convergence of the control polygons to aC° curve is analysed in terms of the convergence to zero of a derived scheme for the differencesf i+1 k −f i analysis of the smoothness of the limit curve is reduced to the convergence analysis of “differentiated” schemes which correspond to divided differences off i k ∶i∈ Z with respect to the diadic parametrizationt i k =i/2 by: BibTeX @MISC{Dyn88analysisof, author = {Nira Dyn and John A.

Gregory and David Levin}, title = {Analysis of uniform binary subdivision schemes for curve design }, year = {}}. A 4-point interpolatory subdivision scheme for curve design, ().

An alqorithm for high speed curve generation, (). Computing curves invariant under halving, Analysis of uniform binary subdivision schemes for curve : N Dyn, JA Gregory and D Levin.

ANALYSIS OF UNIFORM BINARY SUBDIVISION SCHEMES FOR CURVE DESIGN 1. Introduction Recursive subdivision is being used increasingly in approximation theory and computer aided geometric design as a method for the generation and definition of curves and. Binary Subdivision Schemes In application of BSS to CAGD, it is desired that the geometric properties of the limit curve be controlled by the geometric properties of the control polygon.

The following theorem shows, for a wide class of BSS, that the length of the limit curve, and the variation of its components, are controlled by those of.

4. Polynomial reproduction analysis. Polynomial reproduction is a desirable property for a subdivision scheme, because any convergent subdivision scheme that reproduces polynomials of degree d has approximation order d + is, if we take the values of any function f ∈ C d+1 with ∥f (d+1) ∥ ∞ uniform grids of width h, then the limit function generated by the scheme from.

We present a new variant of Lane-Riesenfeld algorithm for curves and surfaces both. Our refining operator is the modification of Chaikin/Doo-Sabin subdivision operator, while each smoothing operator is the weighted average of the four/sixteen adjacent points.

Our refining operator depends on two parameters (shape and smoothing parameters). So we get new families of univariate and bivariate.

Subdivision depth of 4-point binary subdivision curve. D k 0 / e × 10 − 5 × 10 − 6 × 10 − 6 D 1 14 21 29 36 44 51 Due to good properties of the 4-point binary and ternary subdivision schemes [4–9], much attention has been given to extend their ability in modelling curves and surfaces.

For example, the 4-point ternary interpolating subdivision scheme [ 8 ] can generate higher smoothness than the 4-point binary one [ 6 ] by using the same number of control.

A convergence analysis for studying the continuity and differentiability of limit curves generated by uniform subdivision algorithms is presented.

The analysis is based on the study of corresponding difference and divided difference algorithms. Analysis of uniform binary subdivision schemes for curve design, Analysis of uniform binary. nary subdivision schemes for curves with two sets of rules of the form pk+1 2i = ∑j αj p k j+i pk+1 2i+1 = ∑j β jp k +i where αj and βj are numerical coefﬁcients and ∑αj = ∑βj = 1.

For instance, uniform cubic B-splines have an as-sociated subdivision scheme with rules given in equation 4. Notice that these binary subdivision. The classical binary 4-point and 6-point interpolatery subdivision schemes are generalized to a-ary setting for any integer a ≥ 3.

These new a-ary subdivision schemes for curve design are derived easily from their corresponding two-scale scaling functions, a notion from the context of wavelets. the smoothness analysis of subdivision schemes and stimulate research development of the two communities.

One of the main objectives of this paper is to introduce two new families of nonlinear 3-point subdivision schemes for curve design, both planar and 3D. The ﬁrst family is ternary interpolatory while the second family is binary approximation. A general compact form of linear, uniform, and stationary binary -variate (=1,2)subdivision scheme whichmapsapolygon 1 ={ 1, Z} to a re ned polygon ={, Z} is de ned as = Z 2 1, Z.

e symbol of above subdivision scheme is given by the Laurentpolynomial () = Z, (C \ {0}), where ={, Z} is called the mask of subdivision scheme.e.

Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2),].

Subdivision started as a tool for eecient computation of spline functions, and is now an independent subject with many applications.

It is used for developing new methods for curve and surface design, for approximation, for generating wavelets and mul-tiresolution analysis and also for solving some classes of functional equations. This paper reviews recent new directions and new developments.

subdivision schemes variate in between or around the approximating and interpolatory curves. We also design few analytical algorithms to study the properties of the proposed schemes uniform and stationary binary univariate subdivision scheme S awhich maps a for the binary subdivision scheme (1) to be convergent is that its mask satis es.

Subdivision algorithms which generate curves and surfaces play an important role in the subject of computer aided geometric design. The basic idea is that a given initial "control polygon" is successively refined so that, in the limit, it approaches a smooth curve or surface.

We will consider uniform binary subdivision. tionary subdivision schemes reﬁning control points. It reviews univari-ate schemes generating curves and their analysis. Several well known schemes are discussed. The second part of the paper presents three types of nonlinear subdivi-sion schemes, which depend on the geometry of the data, and which are extensions of univariate linear schemes.

We also briefly review other classes of schemes, such as schemes on general nets, matrix schemes, non-uniform schemes and nonlinear schemes. Different representations of subdivision schemes, and several tools for the analysis of convergence, smoothness and approximation order are discussed, followed by explanatory examples.estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions.

In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modiﬁcation of .Dissertation Committee • Internal Members Evanthia Papadopoulou Università della Svizzera italiana, Switzerland Lourenco Beirao Da Veiga Università degli Studi Milano Bicocca.