Fitting Splines to a Parametric Function (Record no. 174192)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03623nam a22005055i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-030-12551-6 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240423125108.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 190223s2019 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783030125516 |
| -- | 978-3-030-12551-6 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-030-12551-6 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | T385 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | UML |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | COM012000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | UML |
| Source | thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 006.6 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Penner, Alvin. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 245 10 - TITLE STATEMENT | |
| Title | Fitting Splines to a Parametric Function |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Alvin Penner. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2019. |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XII, 79 p. 32 illus., 21 illus. in color. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | SpringerBriefs in Computer Science, |
| International Standard Serial Number | 2191-5776 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1 Introduction -- 2 Least Squares Orthogonal Distance -- 3 General Properties of Splines -- 4 ODF using a cubic Bézier -- 5 Topology of Merges/Crossovers -- 6 ODF using a 5-Point B-spline -- 7 ODF using a 6-Point B-spline -- 8 ODF using a quartic Bézier -- 9 ODF using a Beta2-spline -- 10 ODF using a Beta1-spline -- 11 Conclusions. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer graphics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer vision. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer Graphics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer Vision. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783030125509 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783030125523 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | SpringerBriefs in Computer Science, |
| -- | 2191-5776 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-030-12551-6">https://doi.org/10.1007/978-3-030-12551-6</a> |
| 912 ## - | |
| -- | ZDB-2-SCS |
| 912 ## - | |
| -- | ZDB-2-SXCS |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks-CSE-Springer |
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