ISO 16610-1:2015 幾何学的製品仕様（GPS）—ろ過—パート1：概要と基本概念 | ページ 6

3.1

integral feature

geometrical feature belonging to the real surface of the workpiece or to a surface model

Note 1 to entry: An integral feature is intrinsically defined, e.g. skin of the workpiece.

Note 2 to entry: For a statement of specifications, geometrical features obtained from partition of the surface model or of real surface of workpiece shall be defined. These features, called “integral features”, are models of the different physical parts of the workpiece that have specific functions, especially those in contact with adjacent workpieces.

[SOURCE:ISO 17450‑1:2011, 3.3.5]

3.1.1

surface portion

SP

portion of a partitioned integral feature (3.1)

3.1.2

surface profile

line resulting from the intersection between a surface portion (3.1.1) 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: The concept of profiles is under development and it is possible that the definition of surface profile will be revised.

3.2

primary mathematical model

set of nested hierarchical mathematical models of the surface portion (3.1.1) , wherein each model in the set can be described by a finite number of parameters

Note 1 to entry: Examples include truncated Fourier series, curvature limited (zero to ± value) profiles, and limited Wolf pruning height (100 % to smaller positive percentage) segments.

Note 2 to entry: An example of a primary mathematical model using a truncated Fourier series is given in A.1.

3.2.1

nesting index

NI

value indicating the relative level of nested hierarchy for a particular primary mathematical model (3.2)

Note 1 to entry: 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 to entry: By convention, as the nesting index approaches zero (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.

Note 3 to entry: The cut-off wavelength for the Gaussian filter is an example of a nesting index (see 3.2.1.1). For the morphological filter, the nesting index is the size of the structuring element (e.g. the radius of the disc) which is different from the wavelength concept that underlies the notion of “cut-off” (see 3.2.1.2 and 3.2.1.3).

Note 4 to entry: The term nesting index is derived from a combination of index from index set and nesting from nested hierarchy, both of which are mathematical terms.

3.2.1.1

cut-off wavelength

particular type of nesting index (3.2.1) applicable to linear filters, used to separate surface components into long and short wavelengths

Note 1 to entry: See, for example, ISO 16610-21, ISO 16610-22, and ISO 16610-61.

3.2.1.2

vertical circular disc radius

particular type of nesting index (3.2.1) applicable to profile morphological filters with a structuring element in terms of a circular disc

Note 1 to entry: See, for example, ISO 16610-41 and ISO 16610-49.

3.2.1.3

horizontal line length

particular type of nesting index (3.2.1) applicable to profile morphological filters with a structuring element in terms of a horizontal line

Note 1 to entry: See, for example, ISO 16610-41 and ISO 16610-49.

3.2.1.4

sphere radius

particular type of nesting index (3.2.1) applicable to areal morphological filters with a structuring element in terms of a sphere radius

3.2.1.5

circular disc radius

particular type of nesting index (3.2.1) applicable to areal morphological filters with a structuring element in terms of a circular disc

Note 1 to entry: See, for example, ISO 16610-40 and ISO 16610-41.

3.2.1.6

Wolf pruning height

particular type of nesting index (3.2.1) applicable to areal segmentation filters used to discriminate between significant and non-significant surface features

Note 1 to entry: See, for example, ISO 16610-85.

3.2.2

degree of freedom

primary mathematical model number of independent parameters required to fully describe a particular primary mathematical model (3.2)

3.3

primary surface

ps

surface portion (3.1.1) obtained when the latter is represented as a specified primary mathematical model (3.2) with specified nesting index (3.2.1)

3.3.1

primary profile

line resulting from the intersection between the primary surface (3.3) and an ideal plane

Note 1 to entry: The concept of profiles is under development and it is possible that the definition of primary profile will be revised.

3.4

primary mapping

mapping indexed by the nesting index (3.2.1) used to identify a particular primary surface (3.3) with a specified nesting index (3.2.1) in order to represent a surface portion (3.1.1) that satisfies the sieve and projection criteria

Note 1 to entry: A primary mapping identifies surface portions which have “features” larger than a particular nesting index.

3.4.1

sieve criterion

criterion where two primary mappings (3.4) applied one after another to a surface portion is entirely equivalent to only applying one of these two primary mappings to the surface portion namely that primary mapping with the highest nesting index (3.2.1)

3.4.2

projection criterion

criterion wherein a primary surface (3.3) with a specified nesting index (3.2.1) is mapped onto itself using the primary mapping (3.4) with the same specified nesting index (3.2.1)

Note 1 to entry: This implies that if you apply the primary mapping twice with the same nesting index to a surface, one obtains the same surface as if the primary mapping was applied only once. For example, applying a closing filter with a circular structural element of a given radius twice to a profile results in the same filtered profile as if the closing filter is only applied once.

3.4.3

basic scale

scale established when using a nesting index (3.2.1) assigned to an associated primary mapping (3.4) as a numerical relational system

Note 1 to entry: An example is a basic scale based on sinewaves when using cut-off values associated with a primary mapping derived from a truncated Fourier series.

Note 2 to entry: For a relational system to be stable, the set of entities with their relations have to form a partially ordered set with a greatest element.

3.5

filtration

feature operation used to create a non-ideal feature from a non-ideal feature or to transform one variation curve to another by reducing the level of information

Note 1 to entry: For the purposes of this series of International Standards, a filter is either a primary mapping or can be constructed using a combination of primary mappings, e.g. the weighted mean of primary mappings, the supremum of primary mappings, etc. For example, a Gaussian filter can be constructed from a weighted sum of primary mappings derived from a truncated Fourier series.

[SOURCE:ISO 17450‑1:2011, 3.4.1.3, modified — Note 1 to entry has been added.]

3.5.1

profile filter

operator consisting of a filtration (3.5) operation for use on a surface profile (3.1.2)

Note 1 to entry: Throughout this International Standard, the term “operator” is interpreted in its mathematical context. When it is used in the context of ISO 17450-2:2012, the qualifier “specification” or “verification” is used in front of the term “operator”.

3.5.2

areal filter

operator consisting of a filtration (3.5) operation for use on a surface portion (3.1.1)

3.6

outlier

local portion in a data set that is not representative or not typical for the partitioned integral feature (3.1) and which is characterized by magnitude and scale

Note 1 to entry: Not all outliers can be determined using data alone, but only those that are physically inconsistent with stylus tip geometry. It is sometimes possible to give a warning based on magnitude/scale criteria.

3.7

open profile

finite length surface profile (3.1.2) with two ends

Note 1 to entry: The surface profile does not intersect with itself.

3.8

closed profile

connected finite length surface profile (3.1.2) without ends

Note 1 to entry: The surface profile does not intersect with itself, i.e. it is a simple closed curve or Jordan curve.

3.9

robustness

insensitivity of the output data against specific phenomena in the input data

Note 1 to entry: Outliers, scratches, and steps are examples of specific phenomena. More details can be found in ISO 16610-30.

3.10

filter equation

equation for the mathematical description of the filter

Note 1 to entry: Filter equations do not necessarily specify an algorithm for the numerical realization of the filter.