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Fitting Splines to a Parametric Function

Af: Alvin Penner Engelsk Paperback
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kr 99

Fitting Splines to a Parametric Function

Af: Alvin Penner Engelsk Paperback
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 Bézier 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.
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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 Bézier 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.
Produktdetaljer
Sprog: Engelsk
Sider: 79
ISBN-13: 9783030125509
Indbinding: Paperback
Udgave:
ISBN-10: 3030125505
Kategori: Computer vision
Udg. Dato: 5 mar 2019
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 5 mar 2019
Forfatter(e): Alvin Penner
Forfatter(e) Alvin Penner


Kategori Computer vision


Sprog Engelsk


Indbinding Paperback


Sider 79


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm


Udg. Dato 5 mar 2019


Oplagsdato 5 mar 2019

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