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21 
Surface fitting by minimizing the root mean squares error and application of clamped cubic spline /Gagne, AnnMarie F., January 2006 (has links)
Thesis (M.A.)  Central Connecticut State University, 2006. / Thesis advisor: Yuanquian Chen. "... in partial fulfillment of the requirements for the degree of Master of Art in Mathematics." Includes bibliographical references (leaf 43). Also available via the World Wide Web.

22 
Interactive spline approximationMerchant, Marian January 1974 (has links)
The use of spline basis functions in solving least squares approximation problems is investigated. The question as to which are appropriate basis functions to use is discussed along with the reasons why the final choice was made. The Householder transformation method for solving the fixed knot spline approximation problem is examined. Descriptions of both an automatic procedure using function minimization and an interactive procedure using a graphics terminal for solving the variable knot spline approximation problem are given. In conclusion, numerical results using the interactive system are presented and analyzed. / Science, Faculty of / Computer Science, Department of / Graduate

23 
Approximation properties of subdivision surfaces /Arden, Greg. January 2001 (has links)
Thesis (Ph. D.)University of Washington, 2001. / Vita. Includes bibliographical references (leaves 136138).

24 
Projection methods for nonlinear boundary value problemsReddien, George William 05 1900 (has links)
No description available.

25 
Splines and local approximation of the earth's gravity fieldVan Gysen, Hermanus Gerhardus January 1988 (has links)
Bibliography: pages 214220. / The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotationinvariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multiconic functions, Hardy's multiquadric functions, pseudocubic splines, and thinplate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudocubic spline geoid for southern Africa is given, interpolating Dopplerderived geoid heights and astrogeodetic deflections of the vertical. Quadrature rules are derived for the thinplate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem.

26 
Estimation of the term structure of interest rates via cubic exponential spline functions /Chen, Eva T. January 1987 (has links)
No description available.

27 
Subdivision, interpolation and splinesGoosen, Karin M.(Karin Michelle) 03 1900 (has links)
Thesis (MSc)University of Stellenbosch, 2000. / ENGLISH ABSTRACT: In this thesis we study the underlying mathematical principles of stationary subdivision,
which can be regarded as an iterative recursion scheme for the generation of smooth curves
and surfaces in computer graphics. An important tool for our work is Fourier analysis, from
which we state some standard results, and give the proof of one nonstandard result. Next,
since cardinal spline functions have strong links with subdivision, we devote a chapter to this
subject, proving also that the cardinal Bsplines are refinable, and that the corresponding
EulerFrobenius polynomial has a certain zero structure which has important implications
in our eventual applications. The concepts of a stationary subdivision scheme and its convergence
are then introduced, with as motivating example the de RahmChaikin algorithm.
Standard results on convergence and regularity for the case of positive masks are quoted and
graphically illustrated.
Next, we introduce the concept of interpolatory stationary subdivision, in which case
the limit curve contains all the original control points. We prove a certain set of sufficient
conditions on the mask for convergence, at the same time also proving the existence and
other salient properties of the associated refinable function. Next, we show how the analysis
of a certain Bezout identity leads to the characterisation of a class of symmetric masks which
satisfy the abovementioned sufficient conditions. Finally, we show that specific special cases
of the Bezout identity yield convergent interpolatory symmetric subdivision schemes which
are identical to choosing the corresponding mask coefficients equal to certain point evaluations
of, respectively, a fundamental Lagrange interpolation polynomial and a fundamental
cardinal spline interpolant. The latter procedure, which is known as the DeslauriersDubuc
subdivision scheme in the case of a polynomial interpolant, has received attention in recent
work, and our approach provides a convergence result for such schemes in a more general
framework.
Throughout the thesis, numerical illustrations of our results are provided by means of
graphs. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die onderliggende wiskundige beginsels van stasionêre onderverdeling,
wat beskou kan word as 'n iteratiewe rekursiewe skema vir die generering van
gladde krommes en oppervlakke in rekenaargrafika. 'n Belangrike stuk gereedskap vir ons
werk is Fourieranalise, waaruit ons sekere standaardresuJtate formuleer, en die bewys gee van
een niestandaard resultaat. Daarna, aangesien kardinale latfunksies sterk bande het met
onderverdeling, wy ons 'n hoofstuk aan hierdie onderwerp, waarin ons ook bewys dat die
kardinale BIatfunksies verfynbaar is, en dat die ooreenkomstige EulerFrobenius polinoom
'n sekere nulpuntstruktuur het wat belangrike implikasies het in ons uiteindelike toepassings.
Die konsepte van 'n stasionêre onderverdelingskema en die konvergensie daarvan word
dan bekendgestel, met as motiverende voorbeeld die de RahmChaikin algoritme. Standaardresultate
oor konvergensie en regulariteit vir die geval van positiewe maskers word
aangehaal en grafies geïllustreer.
Vervolgens stelons die konsep van interpolerende stasionêre onderverdeling bekend, in
welke geval die limietkromme al die oorspronklike kontrolepunte bevat. Ons bewys 'n sekere
versameling van voldoende voorwaardes op die masker vir konvergensie, en bewys terselfdertyd
die bestaan en ander toepaslike eienskappe van die geassosieerde verfynbare funksie.
Daarna wys ons hoedat die analise van 'n sekere Bezout identiteit lei tot die karakterisering
van 'n klas simmetriese maskers wat die bovermelde voldoende voorwaardes bevredig. Laastens
wys ons dat spesifieke spesiale gevalle van die Bezout identiteit konvergente interpolerende
simmetriese onderverdelingskemas lewer wat identies is daaraan om die ooreenkomstige
maskerkoëffisientegelyk aan sekere puntevaluasies van, onderskeidelik, 'n fundamentele
Lagrange interpolasiepolinoom en 'n kardinale latfunksieinterpolant te kies. Laasgenoemde
prosedure, wat bekend staan as die DeslauriersDubuc onderverdelingskema in die geval van
'n polinoominterpolant, het aandag ontvang in onlangse werk, en ons benadering verskaf 'n
konvergensieresultaat vir sulke skemas in 'n meer algemene raamwerk.
Deurgaans in die tesis word numeriese illustrasies van ons resultate met behulp van
grafieke verskaf.

28 
DESIGN OF UNOBSCURED REFLECTIVE OPTICAL SYSTEMS WITH GENERAL SURFACES.STACY, JOHN ERIC. January 1983 (has links)
Unobscured reflective optical systems can be more transmissive and of higher diffraction quality than classical systems. Unobscured systems are generated by decentering symmetric systems, tilting elements to correct coma or astigmatism along a real ray, or by crosstilting elements to control astigmatism. Such a system of relatively high quality may be further corrected with a general spline surface. For spline surfaces, optical aberration coefficients are undefined. This study developed real ray analysis and design techniques for general optical systems. A decentered symmetric system with a field correcting spline surface was designed. The optical design program ACCOS V was used for most design and analysis tasks. Design and analysis of general systems are considered first. Basic system quantities of image location, scaling, and irradiation are defined with real rays. Spline surfaces are discussed with special emphasis on features important in optical design. Real ray analytical techniques of composite spot diagrams across the image, footprints on spline surfaces, wavefront aperture maps, and spline surface maps are described. The use of these tools in general system design procedures is discussed. Standard telescope objectives of f/8.5 were considered as base designs for systems with spline surfaces. A spline surface was added to the decentered SchmidtCassegrain. Optimization yielded diffractionlimited performance across a 0.85 degree square field. The spline system was compared to the Galileo spacecraft narrow angle lens and a threemirror decentered design. It had a far wider field than the Galileo but at a lower quality. Diffraction quality was better than that of the threemirror system. Simple tolerances were considered for the spline system. The allowable effect of a thermal gradient was estimated by bending the reference axis. Decentration and figure tolerances for the spline were commensurate with classical surfaces. Techniques presented were shown to be useful for design and analysis of general systems. Spline surfaces were found to be useful in optimization of such systems. This work was supported by the Director's Discretionary Fund, Jet Propulsion Laboratory, California Institute of Technology.

29 
Reconstruction of electrodes and pole pieces from randomly generated axial potential distributions of electron and ion optical systemsSarfaraz, Mohamad Ali, 1960 January 1988 (has links)
The purpose of this investigation is to examine synthesis for reconstruction of electrostatic lenses having an axial potential distribution four times continuously differentiable. The solution of the electrode and pole piece reconstruction is given. Spline functions are used to approximate a continuous function to fit a curve. The present method of synthesis is based on cubic spline functions, which have only two simultaneous continuous derivatives, and all the other higher derivatives are ignored. The fifthorder or quintic spline is introduced simply because it has four simultaneous continuous derivatives. So the reconstruction program would have three terms appearing in the series expansion of the offaxis potential distribution, with regard to two terms when using cubic functions.

30 
Application of the Bspline collocation method to a geometrically nonlinear beam problem /Magoon, Jason. January 2010 (has links)
Thesis (M.S.)Rochester Institute of Technology, 2010. / Typescript. Includes bibliographical references (leaves 9499).

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