prEN 9300-121

Aerospace series - LOTAR - LOng Term Archiving and Retrieval of digital technical product documentation such as 3D CAD and PDM data - Part 121: Semantic representation of CAD 3D Explicit Geometry with Product and Manufacturing Information

1.1 Introduction
This document defines the requirements for the long term digital preservation of the Semantic Representation of Product and Manufacturing Information (PMI) with their possible links to the 3D explicit shape and geometry of single CAD parts. The goal is to preserve this 3D information, without loss, with respect to the geometry produced by the original CAD system, following the principles laid down in EN 9300 003 “Fundamentals and Concepts”.
The requirements of EN 9300 110 concerning the preservation of the 3D explicit shape shall apply within this Part.
The term “semantic representation” is defined in Clause 3 “Terms, definitions and abbreviations”.
1.2 In scope
The following outlines the total scope of EN 9300 121:
- machine-interpretable PMI “Semantic Representation” (Refer to clause 3 for definition);
- the association of the above with 3D geometric shapes;
- the possible association of the above with Presentation of 3D Product and Manufacturing Information (PMI), and 3D annotations as defined in EN 9300 120.
In EN 9300 121, the technology used to preserve this 3D information is based on semantic representation. The main use cases are Certification, Product Liability and Design re-use.
For the purpose of this document, the semantic definition is at the level that supports associative “Cross-highlighting” for the purpose of human readability.
1.3 Out of scope
The following is outside the scope:
- PMI presentation (defined in EN 9300 120);
- User defined attributes that are assigned to 3D geometric entities or at the part level. The archiving of the UDA is defined in EN 9300 120.
- How to preserve additional information:
- - property rights;
- - form features;
- - CAD Assemblies.
- The semantics of special Notes outside the scope of PMI: ITAR/EAR, proprietary, and title block information, etc.

Luft- und Raumfahrt - LOTAR - Langzeit-Archivierung und -Bereitstellung digitaler technischer Produktdokumentationen, wie zum Beispiel von 3D-, CAD- und PDM-Daten - Teil 121: Semantische Darstellung von eindeutiger 3D-CAD-Geometrie mit Produkt- und Fertigungsinformationen

Série aérospatiale - LOTAR - Archivage long terme et récupération des données techniques produits numériques, telles que CAO 3D et PDM - Partie 121 : Représentation sémantique de la géométrie CAO 3D explicite avec données de produit et de fabrication

Aeronavtika - LOTAR - Dolgotrajno arhiviranje in iskanje digitalne tehnične dokumentacije o izdelkih, kot so podatki o 3D, CAD in PDM - 121. del: Semantična predstavitev CAD 3D eksplicitnih informacij o geometriji z grafičnim izdelkom in izdelavo

General Information

• Status: Not Published
• Publication Date: 23-Feb-2020
• Withdrawal Date: 23-Aug-2020
• ICS: 01.110 - Technical product documentation
• ICS: 35.240.30 - IT applications in information, documentation and publishing
• ICS: 49.020 - Aircraft and space vehicles in general
• Technical Committee: ASD-STAN - Aerospace
• Drafting Committee: ASD-STAN/D 7/WG 1 - LOTAR Long Term Archiving and Retrieval of Digital Technical Product Data
• Current Stage: 4060 - Closure of enquiry - Enquiry
• Start Date: 25-Aug-2022
• Completion Date: 25-Aug-2022
• Ref Project: oSIST prEN 9300-121:2022 - Aerospace series - LOTAR - LOng Term Archiving and Retrieval of digital technical product documentation such as 3D CAD and PDM data - Part 121: Semantic representation of CAD 3D Explicit Geometry with Product and Manufacturing Information

Standards Content (Sample)

SLOVENSKI STANDARD
oSIST prEN 9300-121:2022
01-september-2022
Aeronavtika - LOTAR - Dolgotrajno arhiviranje in iskanje digitalne tehnične
dokumentacije o izdelkih, kot so podatki o 3D, CAD in PDM - 121. del: Semantična
predstavitev CAD 3D eksplicitnih informacij o geometriji z grafičnim izdelkom in
izdelavo

Aerospace series - LOTAR - LOng Term Archiving and Retrieval of digital technical

product documentation such as 3D CAD and PDM data - Part 121: Semantic

representation of CAD 3D Explicit Geometry with Product and Manufacturing Information

Luft- und Raumfahrt - LOTAR - Langzeit-Archivierung und -Bereitstellung digitaler

technischer Produktdokumentationen, wie zum Beispiel von 3D-, CAD- und PDM-Daten -

Teil 121: Semantische Darstellung von eindeutiger 3D-CAD-Geometrie mit Produkt- und

Fertigungsinformationen
Série aérospatiale - LOTAR - Archivage long terme et récupération des données
techniques produits numériques, telles que CAO 3D et PDM - Partie 121 :

Représentation sémantique de la géométrie CAO 3D explicite avec données de produit

et de fabrication
Ta slovenski standard je istoveten z: prEN 9300-121
ICS:
01.110 Tehnična dokumentacija za Technical product
izdelke documentation
35.240.30 Uporabniške rešitve IT v IT applications in information,
informatiki, dokumentiranju in documentation and
založništvu publishing
49.020 Letala in vesoljska vozila na Aircraft and space vehicles in
splošno general
oSIST prEN 9300-121:2022 en,fr,de

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

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oSIST prEN 9300-121:2022
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oSIST prEN 9300-121:2022
DRAFT
EUROPEAN STANDARD
prEN 9300-121
NORME EUROPÉENNE
EUROPÄISCHE NORM
June 2022
ICS 01.110
English Version
Aerospace series - LOTAR - LOng Term Archiving and
Retrieval of digital technical product documentation such
as 3D CAD and PDM data - Part 121: Semantic
representation of CAD 3D Explicit Geometry with Product
and Manufacturing Information

Série aérospatiale - LOTAR - Archivage long terme et Luft- und Raumfahrt - LOTAR - Langzeit-Archivierung

récupération des données techniques produits und -Bereitstellung digitaler technischer

numériques, telles que CAO 3D et PDM - Partie 121 : Produktdokumentationen, wie zum Beispiel von 3D-,

Représentation sémantique de la géométrie CAO 3D CAD- und PDM-Daten - Teil 121: Semantische

explicite avec données de produit et de fabrication Darstellung von eindeutiger 3D-CAD-Geometrie mit

Produkt- und Fertigungsinformationen

This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee ASD-

STAN.

If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations

which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

This draft European Standard was established by CEN in three official versions (English, French, 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, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.

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.

Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without

notice and shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 9300-121:2022 E

worldwide for CEN national Members.
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Contents

European foreword ....................................................................................................................................................... 3

1 Scope .................................................................................................................................................................... 4

1.1 Introduction ...................................................................................................................................................... 4

1.2 In scope ............................................................................................................................................................... 4

1.3 Out of scope ....................................................................................................................................................... 4

2 Normative references .................................................................................................................................... 5

3 Terms, definitions and abbreviations ..................................................................................................... 5

4 Applicability ...................................................................................................................................................... 8

5 Business specifications for the long term archiving and retrieval of CAD PMI ........................ 8

5.1 Introduction ...................................................................................................................................................... 8

5.2 Description of use cases for retrieval of 3D PMI entities .................................................................. 9

6 Essential Information of Product and Manufacturing Information (PMI) .............................. 10

6.1 General ............................................................................................................................................................. 10

6.2 Dimensional tolerancing ........................................................................................................................... 10

6.3 Geometric tolerances .................................................................................................................................. 11

6.4 Associativity between the shape and PMI ........................................................................................... 11

6.5 Other PMI related data ............................................................................................................................... 12

7 Definition of Core Model for Product and Manufacturing Information (PMI) ....................... 12

8 Verification rules for Product and Manufacturing Information ................................................. 12

8.1 Introduction ................................................................................................................................................... 12

8.2 Level of Verification .................................................................................................................................... 13

9 Validation rules of Product and Manufacturing Information ...................................................... 13

9.1 Introduction ................................................................................................................................................... 13

9.2 Levels of Validation ..................................................................................................................................... 14

9.3 Comparison of the PMI Validation Properties (PMIVP) ................................................................. 15

9.4 Results of the Validation ............................................................................................................................ 15

9.4.1 At the ingest process (qualify) ................................................................................................................. 15

9.4.2 At the retrieval process (comparison) ................................................................................................. 15

Bibliography ................................................................................................................................................................. 17

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European foreword

This document (FprEN 9300-121:2022) has been prepared by the Aerospace and Defence Industries

Association of Europe - Standardization (ASD-STAN).
This document is currently submitted to the Enquiry.

After enquiries and votes carried out in accordance with the rules of this Association, this Standard has

received the approval of the National Associations and the Official Services of the member countries of

ASD-STAN, prior to its presentation to CEN.

This European standard was prepared jointly by AIA, ASD-STAN, PDES, Inc., and the prostep ivip

Association. The prostep ivip Association is an international non-profit association in Europe. For

establishing leadership in IT-based engineering it offers a moderated platform to its nearly 200

members from leading industries, system vendors and research institutions. Its product and process

data standardization activities at European and worldwide levels are well known and accepted. The

prostep ivip Association sees this standard and the related parts as a milestone of product data

technology.

PDES Inc. is an international non-profit association in USA. The mission of PDES Inc. is to accelerate the

development and implementation of ISO 10303, enabling enterprise integration and PLM

interoperability for member companies. PDES Inc. gathers members from leading manufacturers,

national government agencies, PLM vendors and research organizations. PDES Inc. supports this

standard as an industry resource to sustain the interoperability of digital product information, ensuring

and maintaining authentic longevity throughout their product lifecycle.

Readers of this standard should note that all standards undergo periodic revisions and that any

reference made herein to any other standard implies its latest edition, unless otherwise stated. The

Standards will be published under two different standards organizations using different prefixes. ASD-

STAN will publish the standard under the number EN 9300–xxx. AIA will publish the standard under

the number NAS 9300–xxx. The content in the EN 9300 and NAS 9300 documents will be the same. The

differences will be noted in the reference documentation (i.e. for EN9300 Geometric Dimensioning and

Tolerancing will be referenced in ISO 1101 and ISO 16792, and for NAS 9300 the same information will

be referenced in ASME Y14.5 and Y 14.41). The document formatting etc., will follow that of the

respective editorial rules of ASD-STAN and AIA.
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1 Scope
1.1 Introduction

This document defines the requirements for the long term digital preservation of the Semantic

Representation of Product and Manufacturing Information (PMI) with their possible links to the 3D

explicit shape and geometry of single CAD parts. The goal is to preserve this 3D information, without

loss, with respect to the geometry produced by the original CAD system, following the principles laid

down in EN 9300-003 “Fundamentals and Concepts”.

The requirements of EN 9300-110 concerning the preservation of the 3D explicit shape shall apply

within this Part.

The term “semantic representation” is defined in Clause 3 “Terms, definitions and abbreviations”.

1.2 In scope
The following outlines the total scope of EN 9300-121:

— machine-interpretable PMI “Semantic Representation” (Refer to Clause 3 for definition);

— the association of the above with 3D geometric shapes;

— the possible association of the above with Presentation of 3D Product and Manufacturing

Information (PMI), and 3D annotations as defined in EN 9300-120.

In EN 9300-121, the technology used to preserve this 3D information is based on semantic

representation. The main use cases are Certification, Product Liability and Design re-use.

For the purpose of this document, the semantic definition is at the level that supports associative

“Cross-highlighting” for the purpose of human readability.
1.3 Out of scope
The following is outside the scope:
— PMI presentation (defined in EN 9300-120);

— User defined attributes that are assigned to 3D geometric entities or at the part level. The archiving

of the UDA is defined in EN 9300-120.
— How to preserve additional information:
— property rights;
— form features;
— CAD Assemblies.

— The semantics of special Notes outside the scope of PMI: ITAR/EAR, proprietary, and title block

information, etc.
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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.

EN 9300 (all parts), Aerospace series — LOTAR — LOng Term Archiving and Retrieval of digital technical

product documentation such as 3D, CAD and PDM data
ASME Y14.5, Dimensioning and Tolerancing
ASME Y14.41:2012, Digital Product Definition Data Practices
3 Terms, definitions and abbreviations

For the purposes of this document, the terms, definitions and abbreviations given in EN 9300-007,

EN 9300-100 and the following apply.

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

— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
The following diagram illustrates the terms introduced in this Part:
Figure 1 — Hierarchy of PMI Terms
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3.1
Product and Manufacturing Information (PMI)

Product and Manufacturing Information (PMI) is used in 3D Computer-aided Design (CAD) systems to

convey information about the definition of a product’s components for manufacturing, inspections and

sustainment, which supplements the geometric shape of the product. This includes – but is not limited

to – data such as dimensions, tolerances, surface finish, weld symbols, material specifications, 3D

annotations and user defined attributes. The term PMI, used by itself, relates to a certain information

content within a product definition; i. e. it indicates what information is being stored, independent from

how it is being stored

Note 1 to entry: Though PMI is generally accepted to be the generic designation, the term Geometric

Dimensions and Tolerances (GD&T; sometimes also listed as Geometric Dimensioning and Tolerancing) is often

used synonymously, as it is the main type of PMI that is currently in focus. Other synonymously used terms are:

General Tolerances and Annotations, Annotation, Smart Dimensions, Functional Tolerancing and Annotation

(FT&A) or Geometric Product Specification (GPS). Some of these are specific to a particular CAD system. Industry

standards for defining PMI include standards such as ASME Y14.5, ASME Y14.41 and ISO 1101, ISO 16792

respectively.
3.2
Geometric Dimensions & Tolerances (GD&T)

Geometric Dimensions & Tolerances (GD&T) are a type of Product and Manufacturing Information

(PMI) that can be either computed automatically by a CAD system, or entered manually by the user

Note 1 to entry: The definitions below are additions to the terms mentioned in 3.6 of EN/NAS 9300-100:

— Explicit Tolerance: Any tolerance with a stated (numeric) value, regardless of how or where it is

applied. Explicit tolerances can be applied through general notes, flag notes, PMI or tolerance dimensions. This

shall be attributable to a specific feature, feature set and/or datum reference (e.g. position, orientation).

Standard ± 03 notes may be explicit, depending on their use.

— Implicit Tolerance: Any tolerance where there is no stated value and acceptability of the feature is

defined by engineering to be through visual comparison to the appearance shown in the CAD model.

Standard ± 03 notes may also be implicit, depending on their use.

— Explicit Dimension: The required nominal value is stated in the CAD model so that it can be obtained

without interrogation.

— Implicit Dimension: The nominal value can only be obtained by interrogation (i.e. feature to feature

measuring) of the CAD model.
3.3
semantic representation

semantic representation designates a certain way how information is being stored; it does not relate to

the information content itself. Semantic Representation captures the meaning (intent) and relationships

(context) of a character, word, phrase, sentence, paragraph, specification, or symbol without using any

of the visual characters or constructs that are needed for a human to understand it – such as the letters,

graphical symbols, lines and arrows used on engineering drawings

Note 1 to entry: The main purpose of Semantic Representation is to facilitate automated consumption of the

data, e.g. for later re-use or for downstream applications. It applies to various types of data, such as PMI,

Composite Material Definition, and others.

EXAMPLE The Semantic Representation of a Linear Dimension includes all of the information needed to

understand the specification (the type of dimension, between which features it is defined…), without any of the

graphic components such as dimension lines and extension lines, their direction, arrowheads and the dimension

value.
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3.4
presentation

presentation designates a certain way how information is being stored; it does not relate to the

information content itself. Presentation defines the visual representation of a character, word, phrase,

sentence, paragraph, specification, or symbol in way that is understandable by humans. Presentation is

a generic term that applies to any form of human-readable information transfer; this can for instance be

a handwritten note, an engineering drawing, or the display of a 3D CAD model on a computer screen

Note 1 to entry: The main purpose of Presentation is to facilitate human comprehension of the data, e.g. to

manufacture, inspect, assemble or maintain the product described by the data. For a correct interpretation of the

presented data, it is required that the reader is familiar with the alphabet used and the general type of information

being presented.

Note 2 to entry: In the context of 3D CAD, the term Presentation relates to elements that are visible in the

display of a 3D model and are either located (positioned) in 3D space, i.e. they rotate and move with the model, or

in a fixed 2D plane. Elements of Presentation can typically by styled (e.g. coloured), organized (e.g. in specific

views), and associated with other elements of the model. Presented types of data typically are geometry (3D

shapes, surfaces, curves, points) and characters (letters, numbers, symbols).
3.4.1
character-based presentation

character-based presentation is a type of Presentation where the conveyed information is stored as

characters (letters, numbers, and symbols). These characters are typically stored in a string variable

that can be retrieved and edited in a consuming application. The appearance of Character-based

Presentation depends on the font being used and may change if the originating system and the

consuming application use different fonts. To ensure no characters are lost from creation to

consumption, the alphabet (character encoding) used must be defined as well. (This supports both

semantic and non-sematic PMI)

EXAMPLE In ASCII, the letter ‘A’ is stored as character code ‘0x41’ (hexadecimal).

Note 1 to entry: Character-based Presentation is often supplemented by geometric elements, such as leader

lines, curves or terminator symbols.
3.4.2
graphic presentation

graphic presentation is a type of Presentation where the conveyed information is converted to

geometric elements (lines, arcs, surfaces) by the source system in a way that preserves the exact

appearance (colour, shape, positioning) of the presented information. The arrangement of these

geometric elements can be interpreted by a competent human by looking at them, while the

information content is no longer directly computer-accessible

EXAMPLE A simple graphic presentation of the letter ‘A’ is given by three straight lines. A more complex

graphic presentation could have ten straight lines and six circular arcs, but would still be recognizable as an ‘A’ to

a human familiar with the Latin alphabet. In both cases, a computer can only access the geometric definition of the

individual elements (start and end coordinates for each line), but not the fact that it is the letter ‘A’ that is being

presented.

Note 1 to entry: Graphic Presentation does not require defining the font or alphabet (character encoding)

originally used in the creation of the presented data. In the way Graphic Presentation data are stored, there is

typically no distinction between geometric elements that are visual representations of characters, and geometric

elements that are visual representations of other constructs, such as leader lines, curves or terminator symbols.

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Note 2 to entry: An indirect way of accessing the information content stored as Graphic Presentation is the

application of character recognition software that will attempt to identify the original characters from the

geometric elements that make up their visual representation. Character recognition, however, has its limitations

depending on the algorithms used, the fonts and alphabet involved, and the granularity of the Graphic

Presentation geometry elements. Its results cannot be used with the same level of reliability as Character-based

Presentation.
3.4.3
polyline presentation

polyline presentation designates a specific implementation form of Graphic Presentation that is

supported by many STEP Application Protocols, including AP203e2 (ISO 10303-203:2011), AP214e3

(ISO 10303-214:2010) and AP242 (ISO 10303-242:2014). It supports all the characteristics of Graphic

Presentation. A Polyline is defined as an ordered list of 3D points, which are consecutively connected by

straight line segments. Circles and circular are the only other allowed geometric elements, and can be

used in combination with Polylines. Filled areas can be defined with the aforementioned elements as

boundaries
3.4.4
tessellated presentation

tessellated presentation designates a specific implementation form of Graphic Presentation that is has

been introduced during the development of STEP AP242 (ISO 10303-242:2014). It supports all the

characteristics of Graphic Presentation. It is based on data model for tessellated geometry and provides

more efficient ways of storing the data, compared to Polyline Presentation. It supports curves

(composed of straight line segments) and surfaces (composed of triangles)

Note 1 to entry: This document defines long term archival and retrieval of 3D PMI using semantic

representation.
4 Applicability
Refer to applicability of prEN 9300-001:2022 ”Structure”, Clause 4.
5 Business specifications for the long term archiving and retrieval of CAD PMI
5.1 Introduction

General specifications for long term archiving of CAD mechanical design information are described in

EN 9300-100:2018 clause “Fundamental and concepts for Long Term Archiving of CAD 3D mechanical

information”. This Part can be applied to PMI entities across other domains (i.e. electrical)

According to EN 9300-100:2018, 5.1 “Different generations of CAD systems and associated methods of

design”, there are several methods of design:

— The first generation of CAD design method allowed the engineer to digitally create a 2D drawing

(without a 3D model). The essential information as well as the Regulatory authority of the design

intent is represented by the 2D drawing.

— The second generation of CAD design method is based on the complementary use of essential

information defined in 3D models and essential information defined in 2D models (drawings).

— The third generation of CAD design method is based on the use of parametric and relational design.

The essential information as well as the Regulatory authority of the design intent is represented by

the 3D model with PMI.
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Figure 2 — Illustration of the major generations of CAD systems

EN 9300-121 aims at describing specifications for long term archiving of CAD 3D explicit geometry with

Semantic PMI.
5.2 Description of use cases for retrieval of 3D PMI entities

The use cases for long term archiving and retrieval of CAD geometry with PMI represents a new

approach for preparing and releasing detail part product definition data. These processes and tools aim

to reduce product definition authoring efforts and provide improved responsiveness to changes as the

product definition matures. The configuration management of these processes requires close adherence

to modelling standards and practices to leverage the data for increased productivity.

Since this methodology provides a single-source of geometric product definition, it reduces conflicts

and mismatch errors between 3D CAD and 2D drawing representations. It eliminates the need to build a

model from 2D drawings in order to use modern machining and Product Acceptance Software (PAS)

tools. These design methodologies also reduce engineering burden by eliminating the need to

supplement incomplete 3D Design with 2D paper drawings, which can be very costly.

This section aims at summing up these general requirements common to the aerospace and defence

industry, focused on the preservation of the 3D explicit geometrical shape, including the PMI. These

requirements have to be reviewed and adapted by each company, according to its products and its

business practices.

As mentioned in EN 9300-002, there are 4 main use cases for long-term archiving and retrieval of

CAD 3D exact geometry:

— documentation of aerospace and defence product design for regulatory and contractual

compliance;
— industry incident investigation (product liability);
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— Design Re-use – product modification;
— product lifecycle support and disposition.

For legal requirements (certification and product liability), the definition of the archived product shall

be preserved without any change. The preservation of the 3D geometrical shape according to the

requirements of EN 9300-110, and of the PMI as semantic representation, is an appropriate answer

because this essential information is converted in a static format, and validation properties ensure the

quality after both conversions (export to the archival format from the original CAD system, and import

into the target CAD system).

For the use case “Design Re-use” – Product modification, producers can update the definition of the

product after being imported back into the CAD system.

NOTE Visualization tools could be used to read the archive CAD representation throughout the product

lifecycle.
6 Essential Information of Product and Manufacturing Information (PMI)
6.1 General

Essential information of Product and Manufacturing Information when preserved semantically, shall be

captured in archive files as:
— dimensional tolerancing;
— geometric tolerances;
— associativity between the shape and PMI.
This essential information is described hereafter.
6.2 Dimensional tolerancing

Dimensional tolerancing is the less complex of the two methods of applying tolerances, and is also

called “direct tolerancing of dimensions” because a tolerance can be specified only where a dimension is

defined. Direct dimensioning and tolerancing address the acceptable range of values of an individual

dimension of a manufactured object. Direct tolerancing means generalizing the single value of a

dimension to be a range.
The dimensions and dimensional tolerances are typically denoted as:
— directional dimensions;
— location dimensions such as angular, curved, or linear distances;
— size dimensions such as angular, thickness, or other;
— the association of dimensions with geometry;
— the representation of dimensional tolerances including:
— plus-or-minus deviations;
— maximum, minimal, and nominal dimensions;
— limits and fits;
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— significant digits;
...