عنوان

Fitting splines to a parametric function /

شابک

3030125513

شابک

3030125521

شابک

9783030125516

شابک

9783030125523

شابک اشتباه

3030125505

شابک اشتباه

9783030125509

عنوان اصلي

Fitting splines to a parametric function /

نام عام مواد

[Book]

نام نخستين پديدآور

Alvin Penner.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2019.

نام خاص و کميت اثر

1 online resource (xii, 79 pages) :

ساير جزييات

illustrations (some color)

عنوان فروست

SpringerBriefs in computer science,

شاپا ي ISSN فروست

2191-5768

متن يادداشت

Includes bibliographical references.

متن يادداشت

Intro; Preface; Contents; 1 Introduction; 2 Least Squares Orthogonal Distance Fitting; 2.1 Definition of Error Function; 2.2 Character of Solution; 2.3 Optimization of F(a, u); References; 3 General Properties of Splines; References; 4 ODF Using a Cubic Bézier; 4.1 Fitting a Function with a Double Inflection Point; 4.2 Initializing a Cubic Bézier; 4.3 Optimizing the Fit; 4.4 Continuity of the rms Error; 4.5 Character of Coalescing Solutions; References; 5 Topology of Merges/Crossovers; 5.1 Center of Mass Fit; 5.2 Example of Two Types of Merge/Crossover; 5.3 Response to Change in g(t)

متن يادداشت

5.4 Distinguishing Between Type 1 and Type 2 EventsReferences; 6 ODF Using a 5-Point B-Spline; 6.1 Initializing a 5-Point B-Spline; 6.2 Basis Functions of a 5-Point B-Spline; 6.3 Decomposition into Two Bézier Segments; 6.4 ODF Results for a 5-Point B-Spline; 7 ODF Using a 6-Point B-Spline; 7.1 Initializing a 6-Point B-Spline; 7.2 Basis Functions of a 6-Point B-Spline; 7.3 Decomposition into Three Bézier Segments; 7.4 ODF Results for a 6-Point B-Spline; 8 ODF Using a Quartic Bézier; 8.1 Initializing a Quartic Bézier; 8.2 ODF Results for a Quartic Bézier; 8.3 Enumeration of Solutions

بدون عنوان

0

بدون عنوان

8

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030125516

عنوان

Fitting splines to a parametric function.

شماره استاندارد بين المللي کتاب و موسيقي

9783030125509

موضوع مستند نشده

Spline theory.

موضوع مستند نشده

Computer Graphics.

موضوع مستند نشده

Image Processing and Computer Vision.

موضوع مستند نشده

Spline theory.

موضوع مستند نشده

COM012000

موضوع مستند نشده

UML

موضوع مستند نشده

UML

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Penner, Alvin

تاريخ عمليات

20200823082954.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y