oSIST prEN ISO 21920-2:2020

Geometrical product specifications (GPS) - Surface texture: Profile - Part 2: Terms, definitions and surface texture parameters (ISO/DIS 21920-2:2020)

Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Profile - Teil 2: Begriffe und Parameter für die Oberflächenbeschaffenheit (ISO/DIS 21920-2:2020)

Spécification géométrique des produits (GPS) - État de surface: Méthode du profil - Partie 2: Termes, définitions et paramètres d'état de surface (ISO/DIS 21920-2:2020)

Specifikacija geometrijskih veličin izdelka (GPS) - Tekstura površine: profil - 2. del: Izrazi, definicije in parametri teksture površine (ISO/DIS 21920-2:2020)

General Information

• Status: Not Published
• Public Enquiry End Date: 30-Apr-2020
• ICS: 01.040.17 - Metrology and measurement. Physical phenomena (Vocabularies)
• 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-Sep-2021
• Due Date: 28-Oct-2021
• Ref Project: FprEN ISO 21920-2 - Geometrical product specifications (GPS) - Surface texture: Profile - Part 2: Terms, definitions and surface texture parameters (ISO/FDIS 21920-2:2021)

RELATIONS

• Revised: SIST EN ISO 4287:2000/A1:2011 - Geometrical Product Specifications (GPS) - Surface texture: Profile method - Terms, definitions and surface texture parameters - Amendment 1: Peak count number (ISO 4287:1997/Amd 1:2009)
• Effective Date: 30-Nov-2016
• Revised: SIST EN ISO 12085:2000/AC:2008 - Geometrical product specification (GPS) - Surface texture: Profile method - Motif parameters (ISO 12085:1996/Cor 1:1998)
• Effective Date: 30-Nov-2016
• Revised: SIST EN ISO 13565-3:2002 - Geometrical Product Specifications (GPS) - Surface texture: Profile method; surfaces having stratified functional properties - Part 3: Height characterization using the material probability curve (ISO 13565-3:1998)
• Effective Date: 30-Nov-2016
• Revised: SIST EN ISO 13565-2:2000 - Geometrical product specifications (GPS) - Surface texture: Profile method; surfaces having stratified functional properties - Part 2: Height characterization using the linear material ratio curve (ISO 13565-2:1996)
• Effective Date: 30-Nov-2016
• Revised: SIST EN ISO 4287:2000 - Geometrical product specifications (GPS) - Surface texture: Profile method - Terms, definitions and surface texture parameters (ISO 4287:1997)
• Effective Date: 30-Nov-2016
• Revised: SIST EN ISO 4287:2000/AC:2008 - Geometrical product specifications (GPS) - Surface texture: Profile method - Terms, definitions and surface texture parameters (ISO 4287:1997/Cor 1:1998/Cor 2:2005)
• Effective Date: 30-Nov-2016
• Revised: SIST EN ISO 12085:2000 - Geometrical product specification (GPS) - Surface texture: Profile method - Motif parameters (ISO 12085:1996)
• Effective Date: 30-Nov-2016

Standards Content (sample)

SLOVENSKI STANDARD
oSIST prEN ISO 21920-2:2020
01-april-2020

Specifikacija geometrijskih veličin izdelka (GPS) - Tekstura površine: profil - 2. del:

Izrazi, definicije in parametri teksture površine (ISO/DIS 21920-2:2020)

Geometrical product specifications (GPS) - Surface texture: Profile - Part 2: Terms,

definitions and surface texture parameters (ISO/DIS 21920-2:2020)

Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Profile - Teil 2:

Begriffe und Parameter für die Oberflächenbeschaffenheit (ISO/DIS 21920-2:2020)

Spécification géométrique des produits (GPS) - État de surface: Méthode du profil -

Partie 2: Termes, définitions et paramètres d'état de surface (ISO/DIS 21920-2:2020)

Ta slovenski standard je istoveten z: prEN ISO 21920-2
ICS:
01.040.17 Meroslovje in merjenje. Metrology and measurement.
Fizikalni pojavi (Slovarji) Physical phenomena
(Vocabularies)
17.040.20 Lastnosti površin Properties of surfaces
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
oSIST prEN ISO 21920-2:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN ISO 21920-2:2020
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oSIST prEN ISO 21920-2:2020
DRAFT INTERNATIONAL STANDARD
ISO/DIS 21920-2
ISO/TC 213 Secretariat: BSI
Voting begins on: Voting terminates on:
2020-02-19 2020-05-13
Geometrical product specifications (GPS) — Surface
texture: Profile —
Part 2:
Terms, definitions and surface texture parameters

Spécification géométrique des produits (GPS) — État de surface: Méthode du profil —

Partie 2: Termes, définitions et paramètres d’état de surface
ICS: 17.040.40; 01.040.17
THIS DOCUMENT IS A DRAFT CIRCULATED
This document is circulated as received from the committee secretariat.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
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NATIONAL REGULATIONS.
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RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
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PROVIDE SUPPORTING DOCUMENTATION. ISO 2020
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oSIST prEN ISO 21920-2:2020
ISO/DIS 21920-2:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

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oSIST prEN ISO 21920-2:2020
ISO/DIS 21920-2:2020(E)
Contents

FOREWORD ............................................................................................................................................ IV

INTRODUCTION ....................................................................................................................................... V

1 SCOPE ....................................................................................................................................... 1

2 NORMATIVE REFERENCES .......................................................................................................... 1

3 TERMS AND DEFINITIONS ........................................................................................................... 1

3.1 General terms ................................................................................................................................................1

3.2 Geometrical parameter terms ..................................................................................................................... 10

3.3 Geometrical feature terms .......................................................................................................................... 14

4 FIELD PARAMETER DEFINITIONS ............................................................................................... 19

4.1 Height parameters ....................................................................................................................................... 19

4.2 Spatial parameters ...................................................................................................................................... 20

4.3 Hybrid parameters ...................................................................................................................................... 20

4.4 Functions and related parameters ............................................................................................................... 21

4.5 Multi-scale geometric (fractal) methods ...................................................................................................... 29

5 FEATURE PARAMETERS ............................................................................................................ 30

5.1 parameters based on profile elements ........................................................................................................ 32

5.2 parameters based on feature characterization ............................................................................................ 35

ANNEX A (INFORMATIVE) CALCULATION OF THE FIRST AND SECOND DERIVATIVE .................................. 40

ANNEX B (NORMATIVE) CALCULATION OF THE LOCAL CURVATURE ........................................................ 43

ANNEX C (NORMATIVE) CALCULATION OF THE MATERIAL RATIO CURVE ................................................. 44

ANNEX D (NORMATIVE) CALCULATION OF PROFILE PARAMETERS FOR STRATIFIED FUNCTIONAL SURFACES

45

ANNEX E (NORMATIVE) CROSSING THE LINE SEGMENTATION ................................................................ 52

ANNEX F (INFORMATIVE) RELATION TO THE GPS MATRIX MODEL .......................................................... 57

BIBLIOGRAPHY ....................................................................................................................................... 58

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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 documents 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).

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 identified 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 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 the following URL: www.iso.org/iso/foreword.html.

The committee responsible for this document is Technical Committee ISO/TC 213, Dimensional and

geometrical product specifications and verification.
A list of all parts in the ISO 21920 series can be found on the ISO website.

This part of ISO 21920 replaces the following standards: ISO 4287:1997, ISO 4287:1997/Amd 1:2009, ISO

4287:1997/Cor 1:1998, ISO 4287:1997/Cor 2:2005, ISO 13565-2:1996, ISO 13565-2:1996/Cor 1:1998 and ISO

13565-3:1998.
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Introduction

This part of ISO 21920 is a geometrical product specification (GPS) standard and is to be regarded as a

general GPS standard (see ISO 14638). It influences the chain link F of the chains of standards on profile and

areal surface texture.

The ISO/GPS matrix model given in ISO 14638 gives an overview of the ISO/GPS system of which this part of

ISO 21920 is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this part of ISO 21920 and

the default decision rules given in ISO 14253-1 apply to the specifications made in accordance with this part

of ISO 21920, unless otherwise indicated.

For more detailed information of the relation of this part of ISO 21920 to other standards and the GPS matrix

model, see Annex F.

This part of ISO 21920 develops the terminology, concepts and parameters for profile surface texture. It

comprises the former ISO 4287:1997, ISO 13565-2:1996, ISO 13565-3:1998. Compared to ISO 4287:1997

almost all parameters are calculated over the evaluation length.
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oSIST prEN ISO 21920-2:2020
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Geometrical product specification (GPS) — Surface texture: Profile —
Part 2: Terms, definitions and surface texture parameters
1 Scope

This part of ISO 21920 specifies terms, definitions and parameters for the determination of surface texture

by profile methods.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

ISO 21920-1, Geometrical product specification (GPS) — Surface texture: Profile — Part 1: Indication of

surface texture

ISO 21920-3, Geometrical product specification (GPS) — Surface texture: Profile — Part 3: Specification

operators

ISO 16610-1:2015, Geometrical product specification (GPS) — Filtration: Profile — Part 1: Overview and basic

concepts

ISO 17450-1:2011, Geometrical product specification (GPS) — General concepts — Part 1: Model for

geometrical specification and verification
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 17450-1:2011 and ISO 16610-

1:2015 and the following apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at http://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
3.1 General terms
3.1.1.
non-ideal surface model
skin model

model of the physical interface of the workpiece with its environment

[SOURCE: ISO 17450-1:2011, 3.2.2]
3.1.2.
surface texture
geometrical irregularities contained in a scale-limited profile

Note 1 to entry: Surface texture does not include those geometrical irregularities contributing to the form or shape

of the profile.
3.1.3.
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
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[SOURCE: ISO 14406:2010, 3.1.1]

Note 1 to entry: Figure 1 is only an example to show the effect of mechanical filtering and is not related to a real

measured surface.
Key
a skin model
b ideal tactile sphere with radius 𝑟

c envelope curve of the locus of the centre of an ideal tactile sphere rolled over the skin model

d sphere with radius 𝑟

e mechanical surface: boundary of the mathematical erosion, by the sphere d, of the envelope curve c

Figure 1 — Mechanical surface
3.1.4.
mechanical profile

boundary of the mathematical erosion, by a circular disc of radius 𝑟, of the locus of the centre of an ideal

tactile sphere, also with radius 𝑟, rolled along a trace over the skin model of a workpiece

Note 1 to entry: Figure 2 is only an example to show the effect of mechanical filtering and is not related to a real

measured profile.

Note 2 to entry: In most cases the profile trace results from the intersection of the skin model by an intersection

plane perpendicular to the skin model (see Figure 3) and in a specified direction (see ISO 21920-3).

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Note 3 to entry: The treatment of non-measured and/or spurious points is part of the extraction process and is not

considered in this document.
Key
a skin model
b ideal tactile sphere with radius 𝑟

c envelope curve of the locus of the centre of an ideal tactile sphere rolled over the skin model

d circular disc with radius 𝑟

e mechanical profile: boundary of the mathematical erosion, by the circular disc d, of the envelope curve c

Figure 2 — Mechanical profile
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Key
a profile trace b skin model
Figure 3 — Profile trace
3.1.5.
electromagnetic surface

surface obtained by the electromagnetic interaction with the skin model of a workpiece

[SOURCE: ISO 14406:2010, 3.1.2]
Note 1 to entry: See Figure 4.

Note 2 to entry: The electromagnetic surface is an inherent characteristic of a skin model of a workpiece.

Note 3 to entry: Electromagnetic surfaces depend on the optical measurement principal used for extraction.

Figure 4 — Electromagnetic surface
3.1.6.
electromagnetic profile

profile obtained by the electromagnetic interaction with the skin model of a workpiece

Note 1 to entry: See Figure 5.

Note 2 to entry: The electromagnetic profile is an inherent characteristic of a skin model of a workpiece.

Note 3 to entry: Electromagnetic profiles depend on the optical measurement principal used for extraction.

Note 4 to entry: In most cases the profile trace results from the intersection of the skin model by an intersection

plane perpendicular to the skin model (see Figure 3) and in a specified direction (see ISO 21920-3).

Note 5 to entry: The treatment of non-measured and/or spurious points is part of the extraction process and is not

considered in this document.
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Figure 5 — Electromagnetic profile
3.1.7.
auxiliary surface
surface obtained by an arbitrary external source

Note 1 to entry: A software measurement standard is an example for an auxiliary surface. Other physical

measurement principles which differ from a mechanical or electromagnetic surface, such as tunnelling microscopy or

atomic force microscopy, can also serve as an auxiliary surface. See Figure 6.
3.1.8.
auxiliary profile
profile obtained by an arbitrary external source

Note 1 to entry: A software measurement standard is an example for an auxiliary profile. Other physical

measurement principles which differ from a mechanical or electromagnetic profile, such as tunnelling microscopy or

atomic force microscopy, can also serve as an auxiliary profile. See Figure 6.
3.1.9.
nesting index
𝑁𝑖𝑠, 𝑁𝑖𝑐, 𝑁𝑖𝑓

number or set of numbers indicating the relative level of nesting for a particular primary mathematical

model
[SOURCE: ISO 16610-1:2015, 3.2.1]
3.1.10.
specification coordinate system
system of coordinates in which surface texture parameters are specified

Note 1 to entry: If the nominal surface is a plane (or portion of a plane), it is common (practice) to use a rectangular

coordinate system in which the axes form a right-handed Cartesian set, the X-axis and the Y-axis also lying on the

nominal surface, and the Z-axis being in an outward direction (from the material to the surrounding medium). This

convention is adopted throughout the rest of this part of ISO 21920.
3.1.11.
primary surface

surface portion obtained when a surface portion is represented as a specified primary mathematical model

with specified nesting index 𝑁𝑖𝑠
[SOURCE: ISO 16610-1:2015, 3.3]
Note 1 to entry: See Figure 6.
3.1.12.
primary surface profile

surface profile trace obtained when a surface profile trace is represented as a specified primary

mathematical model with specified nesting index 𝑁𝑖𝑠

Note 1 to entry: In this part of ISO 21920-2, a profile S-filter is used to derive the primary surface profile. See

Figure 6.

Note 2 to entry: For some applications, the profile S-filter is not used. In such a case, e.g. for multi-scale analysis, the

nesting index is equal "zero".
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Note 3 to entry: The primary surface profile can also be derived from the mechanical surface (default),

electromagnetic surface or auxiliary surface using an intersection plane perpendicular to the chosen type of surface and

in a specified direction. See Figure 6.
Key
a default case (grey filled)
b [SOURCE: ISO 25178-2:2020, 3.1.4.1]

Figure 6 — Definition of the primary surface and primary surface profile respectively

3.1.13.
profile F-operation
operation which removes form from a profile
3.1.14.
profile filter
filtration operator applied to a profile
3.1.15.
profile S-filter
profile filter which removes small lateral scale components from a profile
Note 1 to entry: See Figure 7.
3.1.16.
profile L-filter
profile filter which removes large lateral scale components from a profile

Note 1 to entry: Some profile L-filters are sensitive to form and require the profile F-operator first as a prefilter

before being applied.
Note 2 to entry: See Figure 7.
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Key
a small lateral scale e structure scales extracted by the profile S-filter
b large lateral scale f structure scales extracted by the profile F-operation
c scale axis g structure scales extracted by the profile L-filter
d amplitude axis
Figure 7 — Relationships between the S-filter, L-filter, F-operation
3.1.17.
scale limited profile
profile structure scales within specified nesting indices

EXAMPLE A profile is scale limited after applying a profile filter with a specified nesting index.

3.1.18.
primary profile
𝑃 profile
( )
𝑝 𝑥

scale limited profile at any position 𝑥 derived from the primary surface profile by removing the form using an

profile F-operation with nesting index 𝑁𝑖𝑓

Note 1 to entry: The primary profile is the basis for evaluation of the primary profile parameters. See Figure 9 and

Figure 10.

Note 2 to entry: The primary profile can also be derived from the S-F surface (Figure 8) using an intersection plane

perpendicular to the S-F surface and in a specified direction.

Note 3 to entry: Usually a straight line total least squares fit is used as profile F-operation.

Note 4 to entry: The profile F-operation can be performed as a multi-stage operation e.g. a combination of a total

least square fit and a profile L-filter.
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Key
a default case (grey filled) c [SOURCE: ISO 25178-2:2020, 3.1.5]
b [SOURCE: ISO 25178-2:2020, 3.1.4.3]

Figure 8 — Primary profile derived from the primary surface profile (default) or S-F surface

3.1.19.
waviness profile
𝑊 profile
( )
𝑤 𝑥

scale limited profile at any position 𝑥 derived from the primary profile by removing small scale lateral

components by a profile S-filter with a specified nesting index 𝑁𝑖𝑐 and with a specified type of filter

Note 1 to entry: The waviness profile is the basis for evaluation of the waviness profile parameters. See Figure 9 and

Figure 10.
3.1.20.
roughness profile
𝑅 profile
𝑟(𝑥)

scale limited profile at any position 𝑥 derived from the primary profile by removing large scale lateral

components by a profile L-filter and with the same nesting index 𝑁𝑖𝑐 and the same type of filter specified for

the profile S-filter to obtain the waviness profile

Note 1 to entry: The roughness profile is the basis for evaluation of the roughness profile parameters. See Figure 9

and Figure 10.
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Key
a small lateral scale e lateral scale content of P profile
b large lateral scale f lateral scale content of W profile
c scale axis g lateral scale content of R profile
d amplitude axis
Figure 9 - Relationships between the P profile, W profile and R profile
Figure 10 — Measuring chain to calculate the P profile, W profile and R profile
3.1.21.
reference line
line corresponding to a specific long lateral scale component

Note 1 to entry: The 𝑥-axis of the coordinate system complies with the reference line of the assessed profile and the

𝑧-axis is oriented in an outward direction (from the material to the surrounding medium). This convention is adopted

throughout the rest of this part of ISO 21920-2.
3.1.22.
reference line for the primary profile

line corresponding to the long lateral scale component suppressed by the profile F-operation

3.1.23.
reference line for the waviness profile

line corresponding to the long lateral scale component suppressed by the profile F-operator

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3.1.24.
reference line for the roughness profile

line corresponding to the large lateral scale component suppressed by the profile F-operator followed by the

profile L-filter
3.1.25.
evaluation length
𝑙𝑚

length in the direction of the 𝑥-axis used for identifying the geometric structures characterising the scale-

limited profile
Note 1 to entry: The traverse length is longer than the evaluation length.

Note 2 to entry: In the former ISO 4287 profile standard the evaluation length was given by 𝑙𝑛.

3.1.26.
section length
𝑙𝑠𝑐

length in the direction of the 𝑥 axis used to obtain height parameters based on profile hills and profile dales

Note 1 to entry: Default values of 𝑙𝑠𝑐 are found in ISO 21920-3.

Note 2 to entry: See Clause 5.1.1 throughout 5.1.6 for parameters based on section length.

3.1.27.
number of sections
𝑛𝑠𝑐

integer number used to obtain height parameters based on profile hills and profile dales

Note 1 to entry: Default values of 𝑛𝑠𝑐 are found in ISO 21920-3.
3.2 Geometrical parameter terms
3.2.1.
field parameter
parameter defined from all the points on a scale limited profile
3.2.1.1
section length based parameter
height parameter defined on a section length
3.2.2.
feature parameter

parameter defined from a subset of predefined topographic features from the scale limited profile

3.2.3.
P-prefix parameter
parameter calculated from the primary profile
3.2.4.
W-prefix parameter
parameter calculated from the waviness profile
3.2.5.
R-prefix parameter
parameter calculated from the roughness profile
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3.2.6.
height
signed normal distance from the reference line to the scale limited profile

Note 1 to entry: Throughout this document, the term “height” is either used for a distance or for an absolute

coordinate. Example: 𝑅𝑝 (see 5.1.2) is an absolute height and 𝑅𝑧 (see 5.1.6) is a distance.

3.2.7.
depth
opposite value of height.
3.2.8.
ordinate value
( )
𝑧 𝑥
( ) ( ) ( )
height of the assessed scale limited profile 𝑝 𝑥 , 𝑤 𝑥 or 𝑟 𝑥 .
Note 1 to entry: See Annex A for the determination of the gradient.
3.2.9.
local gradient
𝑑𝑧(𝑥)
𝑑𝑥
first derivative of the scale limited profile 𝑧 with respect to the position 𝑥
Note 1 to entry: See Annex A for the determination of the gradient.
3.2.10.
local curvature
𝜅(𝑥)
curvature of the scale limited profile 𝑧 with respect to the position 𝑥
d z x dx
( )
 x =
( )
 2
1+ dz x dx
( ( ) )
Note 1 to entry: See Annex B for the determination of the curvature.
Note 2 to entry: For technical surfaces  x d z x dx
( ) ( )
3.2.11.
material ratio
𝑀𝑟(𝑐)

ratio of the cumulated length 𝑀𝑙(𝑐) of the profile portions intersected by a line at height 𝑐, to the evaluation

length 𝑙𝑚
( )
Mc=100%
( )
Note 1 to entry: See Figure 11.

Note 2 to entry: The curve representing material ratio as a function of height is also called Abbott Firestone curve.

Note 3 to entry: See Annex C for the determination of the material ratio curve.
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Key
a height c intersecting height 𝑐
b reference line d evaluation length 𝑙𝑚
Figure 11 — Material ratio
3.2.12.
material ratio curve

function representing the material ratio of the scale limited profile as a function of height

Key
a height d evaluation length 𝑙𝑚
b reference line e material ratio in percent
c intersecting height 𝑐
Figure 12 — Material ratio curve
3.2.13.
inverse material ratio
𝐶(𝑀𝑟)
height at which a given material ratio 𝑀𝑟 in percent is satisfied
3.2.14.
height density curve
𝒉(𝒄)

curve representing the density of the height of the scale limited profile 𝑧 within the evaluation length 𝑙𝑚 in

percent
12 © ISO 2020 – All rights reserved
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oSIST prEN ISO 21920-2:2020
ISO/DIS 21920-2:2020(E)
dM c
( )
hc =
( )
Note 1 to entry: See Figure 13.
Key
a height c evaluation length 𝑙𝑚
b reference line d percent per unit of amplitude
Figure 13 — Height density curve
3.2.15.
normalized autocorrelation function
( )
𝒇 𝒕𝒙
𝑨𝑪𝑭

function which describes the correlation between a scale limited profile 𝑧 and the same profile translated by

𝑡𝑥
min l ,l −t
( )
1 m m x
z x z x+t dx
( ) ( )
max 0,−t
( )
lt−
ft =
( )
ACF x
m 2
z x dx
( )
where
−l t l
m x m
3.2.16.
Fourier transformation
𝑭(𝒑)
operator which transforms the scale limited profile 𝑧 into Fourier space
−ipx
F p = z x e dx ,
( ) ( )
where
𝑝 is the angular spatial frequency.
3.2.17.
power spectral density
𝒇 (𝒑)
𝑷𝑺𝑫

function which describes the power of a scale limited profile 𝑧 in the Fourier space

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oSIST prEN ISO 21920-2:2020
ISO/DIS 21920-2:2020(E)
f p = F p ,
( ) ( )
PSD
where

𝐹(𝑝) is the Fourier transformation of the scale limited profile 𝑧 and 𝑝 the angular spatial frequency.

Note 1 to entry: The power spectral density fulfils the following equation
z x dx= f p dp .
( ) ( )
PSD
l −
3.2.18.
amplitude spectral density
𝒇 (𝒑)
𝑨𝑺𝑫
square root of the power spectral density
f p = F p ,
( ) ( )
ASD
where

𝐹(𝑝) is the Fourier transformation of the scale limited profile 𝑧 and 𝑝 the angular spatial frequency.

3.3 Geometrical feature terms
3.3.1.
watershed segmentation

a filtration operation that spatially decomposes a profile into mutually exclusive portions of that profile

3.3.2.
peak

point on the profile which is higher than all other points within a neighbourhood of that point

Note 1 to entry: There is a theoretical possibility of a plateau. In this case, the peak is the middle single point on the

plateau.
3.3.3.
hill

region around a peak such that all maximal upward paths end at the peak

Note 1 to entry: See Figure 14.
3.3.4.
hill

an outwardly directed (from material to surrounding medium) contiguous portion of the

scale limited profile above the reference line
Note 1 to entry: See Figure 15.
3.3.5.
hill local height
height difference between the
...