1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS EN ISO 14406:2010Geometrical productspecifications (GPS) Extraction (ISO 14406:2010)BS EN ISO 14406:2010 BRITISH STANDARDNational forewordThis British Standard is the UK imple
2、mentation of EN ISO14406:2010.The UK participation in its preparation was entrusted to TechnicalCommittee TDW/4, Technical Product Realization.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessa
3、ryprovisions of a contract. Users are responsible for its correctapplication. BSI 2011ISBN 978 0 580 64170 1ICS 17.040.01Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committ
4、ee on 31 January 2011.Amendments issued since publicationDate Text affectedEUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 14406 December 2010 ICS 17.040.01 English Version Geometrical product specifications (GPS) - Extraction (ISO 14406:2010) Spcification gomtrique des produits (GPS) - Ext
5、raction (ISO 14406:2010) Geometrische Produktspezifikation (GPS) - Erfassung (ISO 14406:2010) This European Standard was approved by CEN on 9 October 2010. CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the s
6、tatus of a national standard without any alteration. Up-to-date lists and bibliographical references 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,
7、 German). A version in any other language made by translation under the responsibility of a CEN member 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, Cr
8、oatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. EUROPEAN COMMITTEE FOR STANDAR
9、DIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG Management Centre: Avenue Marnix 17, B-1000 Brussels 2010 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 14406:2010: EBS EN ISO 14406:2010EN ISO 14406:2010
10、 (E) 3 Foreword This document (EN ISO 14406:2010) 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 se
11、cretariat of which is held by AFNOR. This 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 June 2011, and conflicting national standards shall be withdrawn at the latest by June 2011. Attention is drawn
12、 to the possibility that some of the 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
13、 countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia,
14、 Slovenia, Spain, Sweden, Switzerland and the United Kingdom. Endorsement notice The text of ISO 14406:2010 has been approved by CEN as a EN ISO 14406:2010 without any modification. BS EN ISO 14406:2010ISO 14406:2010(E) ISO 2010 All rights reserved iiiContents Page Foreword iv Introduction.v 1 Scope
15、1 2 Normative references1 3 Terms and definitions .1 4 Sampling and reconstruction for extraction.5 4.1 General .5 4.2 Wavelets: exact reconstruction .5 4.3 Morphological filters: zone of possible reconstruction 5 4.3.1 General .5 4.3.2 Circular disk structuring element6 4.3.3 Horizontal line struct
16、uring element.7 5 Sampling schemes7 5.1 General .7 5.2 Orthogonal grid .8 5.3 Orthogonal grid birdcage.8 5.4 Orthogonal grid polar grid .9 5.5 Specified grid.9 5.6 Stratified .10 5.7 Helix 10 5.8 Spiral.11 5.9 Spider web .11 5.10 Points method12 Annex A (informative) Concept diagram 13 Annex B (info
17、rmative) Relation to the GPS matrix model.14 Bibliography16 BS EN ISO 14406:2010ISO 14406:2010(E) iv ISO 2010 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing Interna
18、tional 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 right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with
19、ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical
20、committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to t
21、he 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. ISO 14406 was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product specifications and verificatio
22、n. BS EN ISO 14406:2010ISO 14406:2010(E) ISO 2010 All rights reserved vIntroduction This International Standard is a geometrical product specification (GPS) standard and is to be regarded as a general GPS standard (see ISO/TR 14638). It influences the chain links 3 and 5 of all chains of standards.
23、For more detailed information of the relation of this International Standard to the GPS matrix model, see Annex B. This International Standard develops the terminology and concepts for GPS extraction. It introduces the concept of sampling and reconstruction for extraction (see ISO 17450-1). BS EN IS
24、O 14406:2010BS EN ISO 14406:2010INTERNATIONAL STANDARD ISO 14406:2010(E) ISO 2010 All rights reserved 1Geometrical product specifications (GPS) Extraction 1 Scope This International Standard specifies the basic terminology for GPS extraction. It defines a framework for the fundamental operations use
25、d in GPS extraction and introduces the concepts of sampling and reconstruction for extraction, together with some principal sampling schemes on several basic geometries. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated refere
26、nces, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 14660-1:1999, Geometrical product specifications (GPS) Geometrical features Part 1: General terms and definitions ISO/TS 16610-1:2006, Geometrical produ
27、ct specifications (GPS) Filtration Part 1: Overview and basic concepts ISO/TS 16610-40:2006, Geometrical product specifications (GPS) Filtration Part 40: Morphological profile filters: Basic concepts ISO 17450-1:1), Geometrical product specifications (GPS) General concepts Part 1: Model for geometri
28、cal specification and verification ISO 17450-2:2 ), Geometrical product specifications (GPS) General concepts Part 2: Basic tenets, specifications, operators and uncertainties 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 14660-1, ISO/TS 16610-1, I
29、SO/TS 16610-40, ISO 17450-1, ISO 17450-2 and the following apply. 3.1 non-ideal surface model (of a workpiece) skin model (of a workpiece) model of the physical interface of the workpiece with its environment ISO 17450-1:, 3.27 1) To be published. (Revision of ISO/TS 17450-1:2005) 2) To be published
30、. (Revision of ISO/TS 17450-2:2002) BS EN ISO 14406:2010ISO 14406:2010(E) 2 ISO 2010 All rights reserved3.1.1 mechanical surface boundary of the erosion, by a sphere of radius r, of the locus of the centre of an ideal tactile sphere, also with radius r, rolled over the skin model of a workpiece (3.1
31、) NOTE 1 Erosion is a morphological operation (see ISO/TS 16610-40). NOTE 2 The mechanical surface is an essential characteristic of a skin model of a workpiece. 3.1.2 electromagnetic surface surface obtained by the electromagnetic interaction with the skin model of a workpiece (3.1) NOTE 1 Differen
32、t wavelengths give different surfaces. NOTE 2 The electromagnetic surface is an essential characteristic of a skin model of a workpiece. NOTE 3 Examples of electromagnetic surface include optical surfaces from coherence-scanning interferometers, optical stylus instruments and scanning confocal micro
33、scopes. 3.2 real surface of a workpiece set of features which physically exist and separate the entire workpiece from the surrounding medium ISO 14660-1:1999, 2.4.1 NOTE Real surfaces of workpieces have many potential functional uses, from bearing surfaces in roller bearings to visual appearance in
34、car body panels. At the atomic level, these different functions define different real surfaces, depending on the nature of the functional interaction with the surface. Since nanoscale measurement is becoming increasingly important economically, there is a requirement to differentiate between these d
35、ifferent functional surfaces. The mechanical surface and the electromagnetic surface, defined below, are two commonly used functional surfaces. 3.2.1 real mechanical surface boundary of the erosion, by a sphere of radius r, of the locus of the centre of an ideal tactile sphere, also with radius r, r
36、olled over the real surface of a workpiece (3.2) NOTE 1 Erosion is a morphological operation (see ISO/TS 16610- 40). NOTE 2 The real mechanical surface is a specific type of real surface of a workpiece. 3.2.2 real electromagnetic surface surface obtained by the electromagnetic interaction with the r
37、eal surface of a workpiece (3.2) NOTE 1 The locus of the effective ideal reflection point can be affected by both the topographical surface and the material properties of the workpiece. NOTE 2 Different wavelengths give different surfaces. NOTE 3 The real electromagnetic surface is a specific type o
38、f real surface of a workpiece. 3.3 integral feature surface or line on a surface NOTE An integral feature is intrinsically defined. ISO 14660-1:1999, 2.1.1 BS EN ISO 14406:2010ISO 14406:2010(E) ISO 2010 All rights reserved 33.3.1 real (integral) feature integral feature (3.3) part of a real surface
39、of a workpiece (3.2) limited by the adjacent real (integral) features ISO 14660-1:1999, 2.4.1 3.3.2 surface portion portion of a partitioned integral surface ISO/TS 16610-1:2006, 3.1.1 NOTE In practice, the integral surface will be either an integral feature (3.3) or a real (integral) feature (3.3.1
40、). 3.4 primary mathematical model set of nested mathematical representations of the surface portion (3.3.2), wherein each representation in the set can be described by a finite number of parameters ISO/TS 16610-1:2006, 3.2 3.4.1 nesting index NI number, or set of numbers, indicating the relative lev
41、el of nesting for a particular primary mathematical model (3.4) NOTE 1 Given a particular nesting index, models with lower indices contain more surface information, whereas models with higher nesting indices contain less surface information. NOTE 2 By convention, as the nesting index approaches zero
42、 (or a series of all zeros), there exists a primary mathematical model that approximates the real surface of a workpiece to within any given measure of closeness. ISO/TS 16610-1:2006, 3.2.1 3.4.2 degrees of freedom primary mathematical model number of independent parameters required to fully describ
43、e a particular primary mathematical model (3.4) ISO/TS 16610-1:2006, 3.2.2 3.5 primary surface PS surface portion (3.3.2) obtained when the latter is represented as a specified primary mathematical model (3.4) with specified nesting index (3.4.1) ISO/TS 16610-1:2006, 3.3 3.6 primary mapping PM( | NI
44、) mapping indexed by the nesting index (3.4.1), used to identify a particular primary surface (3.5) with the specified nesting index, in order to represent a surface portion (3.3.2) that satisfies the sieve and projection criteria NOTE The primary mapping is defined in terms of mathematical mappings
45、 as PS = PM(SP | NI) BS EN ISO 14406:2010ISO 14406:2010(E) 4 ISO 2010 All rights reservedwhere PS is the primary surface; SP is the surface portion. ISO/TS 16610-1:2006, 3.4 3.7 primary extracted surface finite set of data points sampled from the primary surface (3.5) NOTE 1 The primary extracted su
46、rface represents the basis for digital processing by means of surface filters and the calculation of characterization parameters. NOTE 2 Here, “extracted” is used only for objects containing a finite number of data points. Thus the primary surface is still a continuous surface and the primary extrac
47、ted surface contains a finite number of data points sampled from the primary surface. 3.7.1 reconstruction method of choosing a particular primary mathematical model (3.4), of a fixed nesting index (3.4.1), that passes exactly through the primary extracted surface (3.7) NOTE 1 The concept of “exact
48、reconstruction” is described in 4.2. NOTE 2 With many primary mathematical models, if the number of sampled points is greater than or equal to the number of degrees of freedom, there exists a sampling scheme by which the primary surface can be reconstructed without any loss of information from the p
49、rimary extracted surface (this generalizes the Nyquist criterion). 3.7.2 sampling aliasing two or more primary mathematical models (3.4), of a fixed nesting index (3.4.1), passing exactly through the primary extracted surface (3.7) NOTE 1 This can cause real problems if the two or more primary mathematical models are very different from each other. NOTE 2 The aliasing is the incorrect reconstruction of a signal due to the overlap of the transfer functions of the filter in a filter bank. 3.8 extraction
