ISO 18183-1:2024 幾何学的製品仕様（GPS） | ページ 6

3.1

geometrical feature

point, line, surface, volume or a set of these terms

[SOURCE:ISO 17450-1:2011, 3.3, modified — Notes 1 and 2 to entry removed.]

3.2

partition

feature operation used to identify a portion of a geometrical feature (3.1) belonging to the real surface of the workpiece or to a surface model of the workpiece

[SOURCE:ISO 17450-1:2011, 3.4.1.1.]

3.3

nominal model

<of a workpiece> model of the perfect shape defined by the designer

Note 1 to entry: Nominal model represents the design intent.

Note 2 to entry: Partition information is part of the nominal model.

[SOURCE:ISO 17450-1:2011, 3.2.1, modified — Note 2 to entry added.]

3.4

non-ideal surface model

skin model

<of a workpiece> model of the physical interface of the workpiece with its environment

Note 1 to entry: See Reference [7] for different types of physical interfaces of the workpiece with its environment.

[SOURCE:ISO 17450-1:2011, 3.2.2, modified — Note 1 to entry added.]

3.5

fuzzy set

set whose elements have degrees of membership

Note 1 to entry: These degrees of membership range from 1, when the element is in the set, to 0, when it is out of the set, see Reference [8] for more details.

3.5.1

feature uncertainty zone identity set

fuzzy set (3.5) of a cloud of points representing a geometrical feature (3.1) or its boundary in specification or verification

Note 1 to entry: There are three types of feature uncertainty zone identity sets: surface, line and point.

Note 2 to entry: Feature uncertainty zone identity set is the geometrical realization of fuzzy sets.

3.5.2

surface feature uncertainty zone identity set

(F2)

feature uncertainty zone identity set (3.5.1) generated from a geometrical feature (3.1) of type surface

Note 1 to entry: Different partition algorithms (see ISO 18183-3) can generate different surface feature uncertainty zone identity sets.

3.5.3

line feature uncertainty zone identity set

(F1)

feature uncertainty zone identity set (3.5.1) generated from a geometrical feature (3.1) of type line

Note 1 to entry: Different partition algorithms (see ISO 18183-3) can generate different line feature uncertainty zone identity sets.

3.5.4

point feature uncertainty zone identity set

(F0)

feature uncertainty zone identity set (3.5.1) generated from a geometrical feature (3.1) of type point

Note 1 to entry: Different partition algorithms (see ISO 18183-3) can generate different point feature uncertainty zone identity sets.

3.6

invariance class

group of ideal features defined by the same displacement(s) of the ideal feature for which the feature is kept identical in the space

[SOURCE:ISO 17450-1:2011, 3.3.1.2]

3.7

feature discontinuity

<partition> unintentional break in the continuity of a geometrical feature (3.1)

Note 1 to entry: Feature discontinuity can never appear in the nominal model, see 4.3.2 for an example.

Note 2 to entry: The concept of continuity used here is by open sets in a topology, since this also allows for point cloud ‘surfaces’^[9]. The open sets in the topological space (surface, line) are defined from the basis of open disks and open intervals, respectively.

3.8

feature transition

<partition> meeting or merging of features by design

Note 1 to entry: Feature transition shall appear in the nominal model.

3.9

selection

identification of the partitioned feature(s) required to be modified

Note 1 to entry: Examples appear in ISO 18183-2.

Note 2 to entry: This term is an abstraction, abstracted from all the different ways, within the ISO GPS system, to identify partitioned feature(s).

3.10

subdivision

identification of a portion of the selected partitioned feature

Note 1 to entry: This term is an abstraction, abstracted from all the different ways, within the ISO GPS system, to identify a portion of the selected partitioned feature.

3.11

simplification

merging of the selected partitioned features into one partitioned feature

Note 1 to entry: This term is an abstraction, abstracted from all the different ways, within the ISO GPS system, to merge partitioned features.

3.12

face

<nominal> single surface bounded by one or more vertices or edges

3.13

edge

<nominal> line along which two single surfaces meet

Note 1 to entry: the edge is bounded by two vertices or has no vertices

3.13.1

blend edge

<nominal> edge defined by a line along which two single surfaces meet that have a continuous gradient orthogonal to the edge

3.14

vertex

<nominal> meeting point of three or more different single surfaces or the meeting point of two or more edges or the point of intersection of a pencil of lines

Note 1 to entry: An example of a pencil of lines is the vertex of a cone.

3.14.1

blend vertex

<nominal> vertex that has a smooth gradient, in all directions, through the vertex

3.14.2

sharp vertex

<nominal> vertex that is not a blend vertex

3.15

single feature

geometrical feature which is a single point, a single line or a single surface

[SOURCE:ISO 22432:2011, 3.2.9, modified — Note 1 to entry and example removed.]

3.15.1

single surface

continuous surface which is nominally a plane, a cylinder, a sphere, a cone, a torus, another surface of revolute invariance class, a surface of prismatic invariance class, a helix, a surface of complex invariance class or a restricted part of one of them

Note 1 to entry: A revolute surface is a single surface if its generatrix is a single line (see ISO 22432:2011, Figure 11).

Note 2 to entry: ISO 17450-1:2011, Table 1 illustrates the types of single surfaces with their invariance degree.

Note 3 to entry: If a surface contains a surface portion of higher invariance degree than itself, then it is not a single surface. A partial ordering of single-surface types, based on whether they can contain each other, is given in ISO 22432:2011, Figure 12. The ordering is partial because some surface types cannot be contained within each other.

[SOURCE:ISO 22432:2011, 3.2.9.4]

3.15.2

single line

continuous line which is nominally a straight line, a circle or a complex line

Note 1 to entry: An arc is a restricted circle (see ISO 22432:2011, Figure 10).

Note 2 to entry: A single line does not intersect itself.

[SOURCE:ISO 22432:2011, 3.2.9.2]

3.16

compound feature

geometrical feature which is a collection of several single features

[SOURCE:ISO 22432:2011, 3.2.10]

3.17

integral feature

surface or line on a surface

[SOURCE:ISO 22432:2011, 3.3, modified - Notes 1 to 4 to entry removed.]

3.17.1

integral surface portion

integral surface which is a portion of the complete surface

[SOURCE:ISO 22432:2011, 3.3.1]

3.17.2

integral line portion

integral line which is a portion of the complete line

[SOURCE:ISO 22432:2011, 3.3.2]

3.18

complete feature

total feature

geometrical feature containing the totality of the points corresponding to one or more single geometrical features and pertaining to the surface model

[SOURCE:ISO 22432:2011, 3.2.13]

3.19

restricted feature

geometrical feature corresponding to a portion of a complete/total non-ideal feature or having a portion of an (ideal) infinite feature

[SOURCE:ISO 22432:2011, 3.2.14]

3.20

slippable motion

rigid transformation (3.20.1) in which the displacement of every point P belonging to the surface S is tangent to S at the point P

3.20.1

rigid transformation

geometrical transformation that preserves the Euclidean distance between every pair of points

Note 1 to entry: Rotations and translations or any combination of these are rigid transformations.

Note 2 to entry: An example of a non-rigid transformation is a plane translated along its normal.

3.21

curvature

local property of a line or a surface defined at every point quantifying second-order derivative of a line from a straight line or a surface from a plane

Note 1 to entry: Curvature is a fundamental concept in differential geometry. Although the mathematical fundamentals apply to continuous and differentiable lines and surfaces (nominal surface or model of non-ideal surface (skin model)), curvature can be extended to elements of a discrete type (discrete surface, sampled surface or real surface) and referred to discrete curvature (see ISO 18183-3:2024, Clause A.1).

3.21.1

curvature of a planar line

inverse of the radius of the osculating circle

Note 1 to entry: See Figure 1.

Note 2 to entry: The osculating circle is the circle that has the same tangent in given point as the line and has its centre located on the normal to the line at the given point.

Note 3 to entry: The normal vector is anti-clockwise with respect to the tangent vector.

Note 4 to entry: The curvature is positive when the vector from the centre of the osculating circle to the considered point is collinear and the same direction to the normal vector. The curvature is negative when the vector from the centre of the osculating circle to the considered point is collinear and opposite to the normal vector.

Figure 1 — Curvature of a planar line

Key

1	planar line
2	osculating circle
P	point on the line
n	normal vector
t	tangent vector
c	centre of the osculating circle
ρ	radius of the oscillating circle

3.21.2

curvature of a non-planar line

inverse of the radius of the 3D osculating circle

Note 1 to entry: See Figure 2.

Note 2 to entry: The 3D osculating circle is the circle contained on the osculating plane spanned by the tangent vector and the normal vector that has the same tangent in given point as the line and has its centre located on the normal to the line at the given point.

Figure 2 — Curvature of a non-planar line

Key

1	non-planar line
2	osculating plane
3	osculating circle
P	point on the line
n	normal vector
t	tangent vector
c	centre of the osculating circle
ρ	radius of the osculating circle

3.21.3

normal curvature of a surface

curvature of the line lying in the surface and in a normal section of a surface at a given point

Note 1 to entry: See Figure 3.

Note 2 to entry: See ISO 18183-3 for more details.

Figure 3 — Normal curvature of a surface

Key

1	surface
2	normal section
n	normal vector
P	point of surface

3.21.4

principal curvatures of a surface

minimum ( ) values of the normal curvatures at a given point on a surface

Note 1 to entry: See Figure 4.

Figure 4 — Principal curvatures of a surface

Key

1	surface
2	normal direction
3	normal section of minimum curvature
4	normal section of maximum curvature

3.21.5

Gaussian curvature

K

3.21.6

mean curvature

H

3.21.7

shape index

s

3.21.8

curvedness

c

3.22

classification of points

method of classifying points into categories based on curvatures

Note 1 to entry: See ISO 18183-3:2024, Clause A.2.

3.22.1

Gaussian curvature-mean curvature classification

K-H classification

classification of points based on the sign of Gaussian curvature (3.21.5) and mean curvature (3.21.6)

Note 1 to entry: See Table 1.

Note 2 to entry: See ISO 18183-3,2024, Figure A.3 for examples of K-H classification.

Table 1 — K-H classification of points on a surface

	Peak	Ridge	Saddle ridge
	—	Flat	Minimal surface
	Pit	Valley	Saddle valley

3.22.2

shape index-curvedness classification

s-c classification

<partition> classification of points based on the values of shape index (3.21.7) and curvedness (3.21.8)

Note 1 to entry: See Table 2.

Note 2 to entry: See ISO 18183-3:2024, Figure A.4 for examples of s-c classification.

Table 2 — s-c classification of points on a surface

Surface type	Shape index interval	Surface type	Shape index interval
Spherical pit		Spherical peak
Pit		Peak
Valley		Ridge
Saddle valley		Saddle ridge
Saddle		Flat	undefined; c = 0

3.23

discrete surface

reconstructed surface composed of triangular meshes

3.24

discrete normal vectors

discrete analogue of normal vectors for discrete lines and surfaces

3.25

discrete curvature

discrete analogue of curvatures for discrete lines and surfaces