kSIST FprEN ISO 16610-22:2025

Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO/FDIS 16610‑22:2025)

ISO 16610-22:2015 specifies spline filters for the filtration of profiles. It specifies in particular how to separate the long- and short-wave component of a profile.

Geometrische Produktspezifikation (GPS) - Filterung - Teil 22: Lineare Profilfilter: Spline‑Filter (ISO/FDIS 16610‑22:2025)

Dieses Dokument legt lineare Spline-Filter zur Filterung von Oberflächenprofilen fest. Es legt insbesondere fest, wie langwellige und kurzwellige Anteile von Oberflächenprofilen getrennt werden.
Die für geschlossene Profile dargestellten Konzepte sind für den Fall der Rundheitsfilterung anwendbar. Diese Konzepte können gegebenenfalls auf verallgemeinerte geschlossene Profile erweitert werden, insbesondere für Oberflächenprofile mit Wiederholungsmerkmalen.
Beispiele für die Anwendung des Spline-Filters sind in Anhang A angegeben. Der Einfluss der Spannungskenngröße β auf den langwelligen Anteil des Oberflächenprofils ist in Anhang B dargestellt.

Spécification géométrique des produits (GPS) - Filtrage - Partie 22: Filtres de profil linéaires: Filtres splines (ISO/FDIS 16610‑22:2025)

L'ISO 16610-22:2015 définit les filtres splines pour le filtrage des profils. Elle précise en particulier la méthode qui permet de séparer les composantes d'un profil à longueurs d'onde courte et longue.

Specifikacija geometrijskih veličin izdelka (GPS) - Filtriranje - 22. del: Filtri linearnih profilov: utorni filtri (ISO/FDIS 16610‑22:2025)

General Information

• Status: Not Published
• Public Enquiry End Date: 30-Jan-2025
• ICS: 17.040.20 - Properties of surfaces
• ICS: 17.040.40 - Geometrical Product Specification (GPS)
• Technical Committee: ISEL - Mechanical elements
• Current Stage: 5020 - Formal vote (FV) (Adopted Project)
• Start Date: 09-Dec-2025
• Due Date: 27-Jan-2026
• Completion Date: 10-Dec-2025
• Ref Project: FprEN ISO 16610-22 - Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO/FDIS 16610-22:2025)

Relations

• Revises: SIST EN ISO 16610-22:2015 - Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO 16610-22:2015)
• Effective Date: 04-Oct-2023

Standards Content (Sample)

SLOVENSKI STANDARD
oSIST prEN ISO 16610-22:2025
01-januar-2025
Specifikacija geometrijskih veličin izdelka (GPS) - Filtriranje - 22. del: Filtri
linearnih profilov: utorni filtri (ISO/DIS 16610-22:2024)
Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters:
Spline filters (ISO/DIS 16610-22:2024)
Geometrische Produktspezifikation (GPS) - Filterung - Teil 22: Lineare Profilfilter:
Spline‑Filter (ISO/DIS 16610-22:2024)
Spécification géométrique des produits (GPS) - Filtrage - Partie 22: Filtres de profil
linéaires: Filtres splines (ISO/DIS 16610-22:2024)
Ta slovenski standard je istoveten z: prEN ISO 16610-22
ICS:
17.040.20 Lastnosti površin Properties of surfaces
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
oSIST prEN ISO 16610-22:2025 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

oSIST prEN ISO 16610-22:2025
oSIST prEN ISO 16610-22:2025
DRAFT
International
Standard
ISO/DIS 16610-22
ISO/TC 213
Geometrical product specifications
Secretariat: BSI
(GPS) — Filtration —
Voting begins on:
Part 22: 2024-11-11
Linear profile filters: Spline filters
Voting terminates on:
2025-02-03
Spécification géométrique des produits (GPS) — Filtrage —
Partie 22: Filtres de profil linéaires: Filtres splines
ICS: 17.040.40
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
AND MAY NOT BE REFERRED TO AS AN
INTERNATIONAL STANDARD UNTIL
PUBLISHED AS SUCH.
This document is circulated as received from the committee secretariat.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
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USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
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POTENTIAL TO BECOME STANDARDS TO
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NATIONAL REGULATIONS.
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
PROVIDE SUPPORTING DOCUMENTATION.
Reference number
ISO/DIS 16610-22:2024(en)
oSIST prEN ISO 16610-22:2025
DRAFT
ISO/DIS 16610-22:2024(en)
International
Standard
ISO/DIS 16610-22
ISO/TC 213
Geometrical product specifications
Secretariat: BSI
(GPS) — Filtration —
Voting begins on:
Part 22:
Linear profile filters: Spline filters
Voting terminates on:
Spécification géométrique des produits (GPS) — Filtrage —
Partie 22: Filtres de profil linéaires: Filtres splines
ICS: 17.040.40
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
AND MAY NOT BE REFERRED TO AS AN
INTERNATIONAL STANDARD UNTIL
PUBLISHED AS SUCH.
This document is circulated as received from the committee secretariat.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
© ISO 2024
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
STANDARDS MAY ON OCCASION HAVE TO
ISO/CEN PARALLEL PROCESSING
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
BE CONSIDERED IN THE LIGHT OF THEIR
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TO SUBMIT, WITH THEIR COMMENTS,
CH-1214 Vernier, Geneva
NOTIFICATION OF ANY RELEVANT PATENT
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RIGHTS OF WHICH THEY ARE AWARE AND TO
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Email: [e-mail]
Website: www.iso.org
Published in Switzerland Reference number
ISO/DIS 16610-22:2024(en)
ii
oSIST prEN ISO 16610-22:2025
ISO/DIS 16610-22:2024(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Characteristics of the spline filter for open profiles . 3
4.1 General .3
4.2 Filter equations .3
4.2.1 Determination of the large-scale lateral component .3
4.2.2 Determination of the small-scale lateral component .4
4.3 Transmission characteristics .4
4.3.1 Transmission characteristic for the large-scale lateral component .4
4.3.2 Transmission characteristic for the small-scale lateral component .5
5 Characteristics of the spline filter for a closed profile . 6
5.1 General .6
5.2 Filter equations .6
5.3 Determination of the large-scale lateral component .6
5.4 Determination of the small-scale lateral component .7
5.5 Transmission characteristics .8
5.5.1 Transmission characteristic for the large-scale lateral component .8
5.5.2 Transmission characteristic of the small-scale lateral component .9
6 Series of nesting index values . 10
7 Tension parameter β .11
8 Implementation . .11
9 Filter designation .11
Annex A (informative) Examples for the application of the spline filter .12
Annex B (informative) Influence of the tension parameter ββ .
Annex C (informative) Relationship to the filtration matrix model .21
Annex D (informative) Relationship to the GPS matrix model .22
Bibliography .23

iii
oSIST prEN ISO 16610-22:2025
ISO/DIS 16610-22:2024(en)
Foreword
ISO (the International Organization for Standardization) 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 right 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 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 document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO’s adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product
specifications and verification, in collaboration with the European Committee for Standardization (CEN)
Technical Committee CEN/TC 290, Dimensional and geometrical product specification and verification, in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This second edition cancels and replaces the first edition (ISO 16610-22:2015), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— providing correction of the transfer characteristics and correction of examples.
— providing an informative annex for showing the influence of the tension parameter β .
A list of all parts in the ISO 16610 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
oSIST prEN ISO 16610-22:2025
ISO/DIS 16610-22:2024(en)
Introduction
This document is a geometrical product specification (GPS) standard and is to be regarded as a general GPS
standard (see ISO 14638). It influences chain links C and E in the GPS matrix structure.
The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this document
is a part. The fundamental rules of ISO GPS given in ISO 8015 apply to this document and the default decision
rules given in ISO 14253-1 apply to the specifications made in accordance with this document, unless
otherwise indicated.
For more information on the relationship of this document to the filtration matrix model, see Annex C.
For more detailed information on the relation of this document to other standards and the GPS matrix model,
see Annex D.
This document develops the terminology and concepts of linear spline filters for surface profiles. Linear
spline filters for surface profiles have a transmission of 50 % for sinusoidal surface profiles with wavelengths
equal to the cut-off wavelength. It separates the large- and small-scale lateral components of surface profiles
in such a way that the surface profiles can be reconstructed without altering. Depending on the selected
nesting index and tension parameter, linear spline filters offer one method for F-Operation.

v
oSIST prEN ISO 16610-22:2025
oSIST prEN ISO 16610-22:2025
DRAFT International Standard ISO/DIS 16610-22:2024(en)
Geometrical product specifications (GPS) — Filtration —
Part 22:
Linear profile filters: Spline filters
1 Scope
This document specifies linear spline filters for the filtration of surface profiles. It defines, in particular, how
to separate large- and small-scale lateral components of surface profiles.
The concept presented for closed profiles are applicable to the case of roundness filtration. Where
appropriate, these concept can be extended to generalized closed profiles, especially for surface profiles
with re-entrant features.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16610-1, ISO 16610-20,
ISO/IEC Guide 99 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
surface profile
line resulting from the intersection between a surface portion and an ideal plane
Note 1 to entry: The orientation of the ideal plane is usually perpendicular to the tangent plane of the surface portion.
Note 2 to entry: See ISO 17450-1:2011, 3.3 and 3.3.1, for the definition of an ideal plane.
[SOURCE: ISO 16610-1:2015, 3.1.2, modified — Note 2 to entry replaced.]
3.1.1
open profile
finite length surface profile (3.1) with two ends
Note 1 to entry: An open profile has a compact support, i.e. within a certain interval the height values of an open
profile can be equal to any real number. Outside the interval, the height values of an open profile are set to zero.
[SOURCE: ISO 16610-1:2015, 3.7, modified — Note 1 to entry replaced.]
3.1.2
unbounded open profile
infinite length surface profile (3.1) without ends
Note 1 to entry: In this document, the term “unbounded” refers to the x-axis.

oSIST prEN ISO 16610-22:2025
ISO/DIS 16610-22:2024(en)
Note 2 to entry: The concept of the unbounded open profile is ideal and do not apply to real surface profiles.
3.1.3
closed profile
connected finite length surface profile (3.1) without ends
Note 1 to entry: A closed profile is a closed curve which is periodic with the finite period length L.
Note 2 to entry: A typical example of a closed profile is one from a roundness measurement.
[SOURCE: ISO 16610-1:2015, 3.8, modified — Note 1 to entry replaced. Note 2 to entry added.]
3.2
linear profile filter
profile filter which separates surface profiles (3.1) into large- and small-scale lateral components and is also
a linear function
Note 1 to entry: If F is a function and X and Y are surface profiles, and if a and b are independent from X and Y, then F
being a linear function implies F (a X + b Y) = a F(X) + b F(Y).
[SOURCE: ISO 16610-20:2015, 3.1, modified — Definition and Note 1 to entry replaced.]
3.3
weighting function
function to calculate large-scale lateral components by convolution of the surface profile heights with this
function
Note 1 to entry: The convolution (see ISO 16610-20:2015, 4.1) performs a weighted moving average of the surface
profile heights. The weighting function, reflected at the x-axis, defines the weighting coefficients for the averaging
process.
3.4
transmission characteristic of a filter
characteristic that indicates the amount by which the amplitude of a sinusoidal surface profile is attenuated
as a function of its wavelength
Note 1 to entry: The transmission characteristic is the Fourier transformation of the weighting function (3.3).
3.5
cut-off wavelength
λ
c
wavelength of a sinusoidal surface profile of which 50 % of the amplitude is transmitted by the profile
Note 1 to entry: Linear profile filters are identified by the filter type and the cut-off wavelength value.
Note 2 to entry: The cut-off wavelength is the nesting index for linear profile filters.
[SOURCE: ISO 16610-20:2015, 3.5, modified — In Note 2 to entry “recommended” deleted.]
3.6
undulations per revolution
UPR
integer number of sinusoidal undulations contained in a closed profile (3.1.3)
Note 1 to entry: In this document, UPR is a frequency and is denoted by f.
3.7
cut-off frequency in undulations per revolution
f
c
frequency in UPR of a sinusoidal closed profile (3.1.3) of which 50 % of the amplitude is transmitted by the
profile filter
oSIST prEN ISO 16610-22:2025
ISO/DIS 16610-22:2024(en)
3.8
spline
linear combination of piecewise polynomials, with a smooth fit between the pieces
Note 1 to entry: The degree of the spline is equal to the degree of the polynomial of the highest degree used.
4 Characteristics of the spline filter for open profiles
4.1 General
In this clause, the filter equations and transfer characteristics of the spline filter for uniformly sampled open
profiles are considered.
4.2 Filter equations
4.2.1 Determination of the large-scale lateral component
For the determination of the large-scale lateral component of an open profile, the spline filter is defined by
Formula (1):
nn××24nn nn××nn11×
IP++βα 1−βα Qw =z (1)
()
()
where
12− 10  0
 
 
11− 00 −−25 41 
 
 


 
−−12 1  14−−64 1 
 
 
nn××  n nn
 
PQ= 00 , = 00 ,
 
 
 
 −−12 1   14−−64 1 
 
 
 
00 −11  14−−52
 
 
 
00 1 −22 1
 
and
n
is the number of uniformly sampled values of the open profile;
nn×
is the identity matrix of dimension nn× ;
I
n×1
is the vector of dimension n×1 of the uniformly sampled open profile;
z
n×1
is the vector of dimension n×1 of the large-scale lateral component of the open profile;
w
λ is the cut-off wavelength;
c
α
is the constant to provide 50 % transmission characteristic at the cut-off wavelength λ ;
c
β is the tension parameter with 01≤≤β .

The constant α is given by Formula (2):
−1
 πΔx 
α = 2sin (2)
 
λ
 c 
oSIST prEN ISO 16610-22:2025
ISO/DIS 16610-22:2024(en)
where
Δx
is the sampling interval;
λ
is the cut-off wavelength.
c
4.2.2 Determination of the small-scale lateral component
The small-scale lateral component of an open profile is determined by subtracting the large-scale lateral
component of this open profile, Formula (1), from this open profile according to Formula (3).
nn××11 n×1
rz=−w (3)
where
n×1
is the vector of dimension n×1 of the uniformly sampled open profile;

z
n×1
is the vector of dimension n×1 of the large-scale lateral component of the open profile;

w
n×1
is the vector of dimension n×1 of the small-scale lateral component of the open profile.

r
4.3 Transmission characteristics
4.3.1 Transmission characteristic for the large-scale lateral component
The transmission characteristic for the large-scale lateral component of an open profile (see Figure 1) is
determined from Formula (1) of the spline filter by means of the spatial discrete Fourier transformation and
is given by Formula (4):
−1
a πΔxxπΔ
 22 44 
=+14βα sins+−16 1 βα in (4)
()
 
a λ λ
 
where
a
is the amplitude of a sinusoidal open profile before filtration;
a is the amplitude of this sinusoidal open profile after filtration;
λ is the wavelength of this sinusoidal open profile with λ≥ 2Δx ;

λ is the cut-off wavelength;
c
Δx
is the sampling interval;
α
is the constant to provide 50 % transmission characteristic at the cut-off wavelength λ and is de-
c
fined according to Formula (2);
β is the tension parameter with 01≤≤β .

NOTE The transfer characteristic given by Formula (4) is only exact for a uniformly sampled unbounded profile.
...