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Fitting Splines to a Parametric Function (Paperback, 1st ed. 2019) Loot Price: R901
Discovery Miles 9 010
You Save: R201 (18%)
Fitting Splines to a Parametric Function (Paperback, 1st ed. 2019): Alvin Penner

Fitting Splines to a Parametric Function (Paperback, 1st ed. 2019)

Alvin Penner

Series: SpringerBriefs in Computer Science

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List price R1,102 Loot Price R901 Discovery Miles 9 010 | Repayment Terms: R84 pm x 12* You Save R201 (18%)

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This Brief investigates the intersections that occur between three different areas of study that normally would not touch each other: ODF, spline theory, and topology. The Least Squares Orthogonal Distance Fitting (ODF) method has become the standard technique used to develop mathematical models of the physical shapes of objects, due to the fact that it produces a fitted result that is invariant with respect to the size and orientation of the object. It is normally used to produce a single optimum fit to a specific object; this work focuses instead on the issue of whether the fit responds continuously as the shape of the object changes. The theory of splines develops user-friendly ways of manipulating six different splines to fit the shape of a simple family of epiTrochoid curves: two types of Bezier curve, two uniform B-splines, and two Beta-splines. This work will focus on issues that arise when mathematically optimizing the fit. There are typically multiple solutions to the ODF method, and the number of solutions can often change as the object changes shape, so two topological questions immediately arise: are there rules that can be applied concerning the relative number of local minima and saddle points, and are there different mechanisms available by which solutions can either merge and disappear, or cross over each other and interchange roles. The author proposes some simple rules which can be used to determine if a given set of solutions is internally consistent in the sense that it has the appropriate number of each type of solution.

General

Imprint: Springer Nature Switzerland AG
Country of origin: Switzerland
Series: SpringerBriefs in Computer Science
Release date: March 2019
First published: 2019
Authors: Alvin Penner
Dimensions: 235 x 155mm (L x W)
Format: Paperback
Pages: 79
Edition: 1st ed. 2019
ISBN-13: 978-3-03-012550-9
Categories: Books > Computing & IT > Computer programming
Books > Computing & IT > Applications of computing
Books > Computing & IT > Computer programming > General
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Books > Computing & IT > Applications of computing > Image processing > General
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LSN: 3-03-012550-5
Barcode: 9783030125509

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