1、April 2016 English price group 13No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 17.040.30!%Q4“2469717www.din.deDIN
2、 EN ISO 16610-22Geometrical product specifications (GPS) Filtration Part 22: Linear profile filters: Spline filters (ISO 1661022:2015);English version EN ISO 1661022:2015,English translation of DIN EN ISO 16610-22:2016-04Geometrische Produktspezifikation (GPS) Filterung Teil 22: Lineare Profilfilter
3、: SplineFilter (ISO 1661022:2015);Englische Fassung EN ISO 1661022:2015,Englische bersetzung von DIN EN ISO 16610-22:2016-04Spcification gomtrique des produits (GPS) Filtrage Partie 22: Filtres de profil linaires: Filtres splines (ISO 1661022:2015);Version anglaise EN ISO 1661022:2015,Traduction ang
4、laise de DIN EN ISO 16610-22:2016-04www.beuth.deDocument comprises 28 pagesDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be considered authoritative.04.16DIN EN ISO 16610-22:2016-04 2 A comma is used as the decimal marker. National foreword This document (EN
5、 ISO 16610-22:2015) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” (Secretariat: DS, Denmark) in collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” (Secretar
6、iat: AFNOR, France). The responsible German body involved in its preparation was DIN-Normenausschuss Technische Grundlagen (DIN Standards Committee Technical Fundamentals), Working Committee NA 152-03-03 AA Oberflchen. The DIN Standards corresponding to the International Standards referred to in thi
7、s document are as follows: ISO 16610-1 DIN EN ISO 16610-1 ISO 16610-20 DIN EN ISO 16610-20 ISO/IEC Guide 99 International vocabulary of metrology (VIM)*)*)Obtainable from: Beuth Verlag GmbH, 10772 Berlin, Order no. 22472, ISBN 978-3-410-22472-3. DIN EN ISO 16610-22:2016-04 3 National Annex NA (infor
8、mative) Bibliography DIN EN ISO 8015, Geometrical product specifications (GPS) Fundamentals Concepts, principles and rules DIN EN ISO 14406, Geometrical product specifications (GPS) Extraction DIN EN ISO 14638, Geometrical product specifications (GPS) Matrix model DIN EN ISO 16610-1, Geometrical pro
9、duct specifications (GPS) Filtration Part 1: Overview and basic concepts DIN EN ISO 16610-20, Geometrical product specifications (GPS) Filtration Part 20: Linear profile filters: Basic concepts DIN EN ISO 16610-21, Geometrical product specifications (GPS) Filtration Part 21: Linear profile filters:
10、Gaussian filters DIN V ENV 13005, Guide to the expression of uncertainty in measurement*)VIM, International vocabulary of metrology *) Withdrawn without replacement in 2014-10. DIN EN ISO 16610-22:2016-04 4 Page intentionally left blank EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-
11、22 July 2015 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO 16610-22:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 22: Filtres de profil linaires: Filtres splines (ISO 16610-22:2015) Thi
12、s European Standard was approved by CEN on 7 May 2015. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
13、concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN membe
14、r into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, Fran
15、ce, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN D E NORMALISATION EUROPISCHES K
16、OMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2015 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-22:2015 E Geometrische Produktspezifikation (GPS) Filterung Teil 22: Lineare Profilfi
17、lter: SplineFilter (ISO 16610-22:2015) Foreword .4Introduction 61 Scope . 72 Normative references 73 Terms and definitions . 74 Spline profile filters . 84.1 General .84.2 Weighting function 84.3 Filter equations 84.3.1 General 84.3.2 Filter equation for the non-periodic spline profile filter . 94.3
18、.3 Filter equation for the periodic spline profile filter . 104.4 Transmission characteristics . 104.4.1 General. 104.4.2 Transmission characteristic of the long-wave profile component 114.4.3 Transmission characteristic of the short-wave profile component 115 Recommendations . 125.1 Nesting index (
19、cut-off values) . 125.2 Tension parameter () . 125.3 Implementation . 126 Filter designation 13Annex A (informative) Influence of the sampling interval 14Annex B (informative) Comparison of spline profile filter and Gaussian filter . 15Annex C (informative) Illustrative examples.16Annex D (informati
20、ve) Concept diagram .20Annex E (informative) Relationship to the filtration matrix model 21Annex F (informative) Relationship to the GPS matrix model 22Bibliography .24Contents PageEuropean foreword 32 EN ISO 16610-22:2015 (E) DIN EN ISO 16610-22:2016-04European foreword This document (EN ISO 16610-
21、22:2015) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” in collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the secretariat of which is held by AFNOR. This
22、 European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by January 2016, and conflicting national standards shall be withdrawn at the latest by January 2016. Attention is drawn to the possibility that some of th
23、e elements of this document may be the subject of patent rights. CEN and/or CENELEC shall not be held responsible for identifying any or all such patent rights. According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement t
24、his European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slova
25、kia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-22:2015 has been approved by CEN as EN ISO 16610-22:2015 without any modification. 3EN ISO 16610-22:2015 (E)DIN EN ISO 16610-22:2016-04ForewordISO (the International Organization for St
26、andardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the rig
27、ht to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.The procedures
28、 used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rul
29、es of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identi
30、fied during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.For an explanation on
31、 the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary informationThe committee responsible for this document is IS
32、O/TC 213, Dimensional and geometrical product specifications and verification.This first edition of ISO 16610-22 cancels and replaces ISO/TS 16610-22:2006, which has been technically revised.ISO 16610 consists of the following parts, under the general title Geometrical product specifications (GPS) F
33、iltration : Part 1: Overview and basic concepts Part 20: Linear profile filters: Basic concepts Part 21: Linear profile filters: Gaussian filters Part 22: Linear profile filters: Spline filters Part 28: Profile filters: End effects Part 29: Linear profile filters: Spline wavelets Part 30: Robust pro
34、file filters: Basic concepts Part 31: Robust profile filters: Gaussian regression filters Part 32: Robust profile filters: Spline filters Part 40: Morphological profile filters: Basic concepts Part 41: Morphological profile filters: Disk and horizontal line-segment filters Part 49: Morphological pro
35、file filters: Scale space techniques Part 60: Linear areal filters: Basic concepts4 EN ISO 16610-22:2015 (E) DIN EN ISO 16610-22:2016-04 Part 61: Linear areal filters: Gaussian filters Part 71: Robust areal filters: Gaussian regression filters Part 85: Morphological areal filters: SegmentationThe fo
36、llowing parts are planned: Part 26: Linear profile filters: Filtration on nominally orthogonal grid planar data sets Part 27: Linear profile filters: Filtration on nominally orthogonal grid cylindrical data sets Part 45: Morphological profile filters: Segmentation Part 62: Linear areal filters: Spli
37、ne filters Part 69: Linear areal filters: Spline wavelets Part 70: Robust areal filters: Basic concepts Part 72: Robust areal filters: Spline filters Part 80: Morphological areal filters: Basic concepts Part 81: Morphological areal filters: Sphere and horizontal planar segment filters Part 89: Morph
38、ological areal filters: Scale space techniques5EN ISO 16610-22:2015 (E)DIN EN ISO 16610-22:2016-04IntroductionThis part of ISO 16610 is a geometrical product specification (GPS) standard and is to be regarded as a general GPS standard (see ISO/TR 14638). It influences the feature characteristics and
39、 measurement chain links 3 and 5 in the GPS matrix structure.The ISO/GPS Masterplan given in ISO/TR 14638 gives an overview of the ISO/GPS system of which this part of ISO 16610 is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this part of ISO 16610 and the default decision rul
40、es given in ISO 14253-1 apply to specifications made in accordance with this part of ISO 16610, unless otherwise indicated.For more detailed information about the relation of this part of ISO 16610 to the GPS matrix model, see Annex F.This part of ISO 16610 develops the terminology and concepts of s
41、pline filters.The spline filter has an advantage over a conventional phase correct filter in that for open profiles, the ends of the measured profile are still usable.6 EN ISO 16610-22:2015 (E) DIN EN ISO 16610-22:2016-041 ScopeThis part of ISO 16610 specifies spline filters for the filtration of pr
42、ofiles. It specifies in particular how to separate the long- and short-wave component of a profile.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited a
43、pplies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 16610-1:2015, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic terminologyISO 16610-20:2015, Geometrical product specifications (GPS) Filtration Part 20:
44、 Linear profile filters: Basic conceptsISO/IEC Guide 99:2007, International vocabulary of metrology Basic and general concepts and associated terms (VIM)ISO/IEC Guide 98-3:2008, Uncertainty of measurement Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)3 Terms and definitions
45、For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99:2007 (VIM), ISO 16610-1, and ISO 16610-20 and the following apply.3.1splinelinear combination of piecewise polynomials, with a smooth fit between the piecesNote 1 to entry: The degree of the spline is equal to the
46、 degree of the polynomial of the highest degree used, e.g. a cubic spline is made of cubic polynomials.3.2cardinal splinebasic function of the space of splines (3.1) with infinite support3.3natural splinespline (3.1) which is a straight line beyond the end points3.4spline profile filterlinear profil
47、e filter based on splines (3.1)Note 1 to entry: For the purposes of this part of ISO 16610, the result of the low-pass filtering is a spline.7EN ISO 16610-22:2015 (E)DIN EN ISO 16610-22:2016-044 Spline profile filters4.1 GeneralFor a spline filter to conform with this part of ISO 16610, it shall sat
48、isfy the filter equations given in 4.3.2, for open profiles, and 4.3.3, for closed profiles.NOTE A comparison with Gaussian filters is given in Annex B, and illustrative examples are given in Annex C. A concept diagram for the concepts of spline filters is given in Annex D, and the relationship to t
49、he filtration matrix model is given in Annex E.4.2 Weighting functionThe weighting function of a spline profile filter cannot be given by a simple closed formula. Filter equations are therefore used instead of weighting functions to describe the spline profile filters. However, where necessary, a numerical calculation of the weighting function for a spline profile filter is always possible. If the sampling interval x is small enough, and the spline profile filter is based on cardinal
