Units/fr

Pour commencer, voici un peu de lecture sur les unités :


 * système SI
 * unités Imperiales
 * SId unités derivées
 * unités d'angles

Exemples
# -- some examples of the FreeCAD unit translation system -- FreeCAD.Units.parseQuantity tu('10 m') tu('3/8 in') tu('100 km/h') tu('100 km/h')/tu('m/s') tu('m^2*kg*s^-3*A^-2') # or tu('(m^2*kg)/(A^2*s^3)') tu('2*pi rad') # full circle tu('2*pi rad') / tu('gon') tu('1ft+(3+7/16)in') tu('1\'(3+7/16)"') # the ' we have to escape because of python tu('sin(pi)') b = Part.makeBox(tu('2in'),tu('2m')/100,10)
 * 1) make a shortcut for the examples
 * 1) 10 meters in internal numbers
 * 1) doing math
 * 1) combined stuff
 * 1) transfer to other units
 * 1) derived units (Ohm)
 * 1) angles
 * 1) as gon
 * 1) more imperial
 * 1) or
 * 1) trigonometry
 * 1) Using translated units as parameters, this command will create a 50.8mm x 20mm x 10mm box

Unités supportées
Voici pour le moment, les unités définies dans FreeCAD. Il est facile pour l'utilisateur, et d'ajouter une nouvelle définition d'unité. La définition des unités supportées sont ici.

Longueurs Métriques "mm"   1.0;        // millimètre       (unité standard interne de longueur) "m"    1000.0;     // mètre "cm"   10.0;       // centimètre "dm"   100.0;      // décimètre "km"   1000000.0;  // kilomètre

Longueurs Imperiales "in" "\"" 25.4;       // inch "ft" "'"   304.8;      // foot "th"       0.0254;     // thou "yr"       914.4;      // yard

Masses Métriques "kg"   1.0;        // kilogramme       (unité standard interne de masse) "g"    0.001;      // gramme "mg"   0.000001;   // milligramme "t"    1000.0;     // tonne

Masse Imperiales "lb"   0.45359237; // pound "oz"   0.45359237; // ounce "st"   6.35029318; // Stone "cwt"  50.80234544;// hundredweights

Angle "deg"  1.0;        // degré         (unité standard interne de d'angle) "rad"  180/M_PI;   // radian "gon"  360.0/400.0;// grade Temps "s"    1.0;        // seconde         (unité standard interne de temps) "min"  60.0;       // minute "h"    3600.0;     // heure

Autres unités SI "A"    1.0;        // Ampère         (unité standard interne de courant électrique) "K"    1.0;        // Kelvin         (unité standard interne de température thermodynamique) "cd"   1.0;        // Candela        (unité standard interne de d'intensité lumineuse) "mol"  1.0;        // Mole           (unité standard interne de quantité de matière) Volumes Métriques "µl"   1.0;        // microlitre mm^3 (dérivé du volume standard) "ml"   1000.0;     // millilitre cm^3 "l"    1000000.0;  // Litre      dm^3

Objectifs et principes : propositions d'extension du système de gestion des unités
Un système de gestion de la vulgarisation des unités, est en développant. Le concept de système d'unités, est proposé dans les sections suivantes, activé lors d'une instance en cours d'exécution de FreeCAD. L'intérêt pour la définition d'un tel concept, est de travailler plus facilement avec le plus grand nombre de type d'unités physique que l'on veut, (même ceux créés par l'utilisateur), sans augmenter la complexité de la gestion de l'unité ni pour l'utilisateur, ni pour les développeurs de  FreeCAD.

En bref, un événement de mise à l'échelle d'unités, est localisé avec précision, et réalisée génériquement.

Atteindre une telle flexibilité, est particulièrement nécessaire lorsque l'on commence à traiter les propriétés des matériaux, qui peuvent avoir des unités très différentes, et difficiles à gérer manuellement.

Le raisonnement proposé, permet la manutention des unités telles que décrites dans le "Guide for the Use of the International System of Units (SI)" et "The International System of Units (SI)", tous les deux du NIST.

Dans cette proposition, une petite section de remise en mémoire, quels sont les contextes possibles, pour lesquelles une gestion des unités est nécessaire ?

In Organizing section, we present the data model retained to achieve unit management, based on 3 objects, the unit, the unit dictionary, and the unit system. Finally, a short API of a 4th object called the unit manager is presented as well.

Résultat
Merci pour cette extension, nous visons à faciliter l'échelle d'unité qui peut se produire, entre différentes tâches professionnelles. Par exemple, les dessins techniques peuvent être fait dans un système d'unité standard, tandis que la modélisation par éléments finis, peut être géré dans un système d'unité plus adapté pour cela.

L'échange de données, entre ces deux types d'activités devient plus facile avec cette extension.

Remise en mémoire
Dans cette section, sont présents les contextes d'utilisation d'un tel système de gestion d'unité. A partir de ces contextes, nous sommes alors en mesure de définir ses spécifications techniques.

2 contextes, sont essentiellement donnés, à titre d'exemple.

Contexte 1 : ouverture de fichiers de données
Ce cas est probablement le cas le plus fréquent. Vous recevez un fichier contenant par exemple un modèle géométrique, ou décrire un matériau avec beaucoup de propriétés. Le modèle géométrique est exprimé en mètres, ou les propriétés des matériaux selon le système d'unités international.

Dommage ...

Vous êtes un expert en FE modélisation, et vous travaillerez généralement avec, des millimètres pour la longueur, MegaPascal pour la pression, tonne pour la masse ...

Dans ce contexte, la gestion de l'unité est nécessaire à l'échelle des données, à partir d'un système unitaire initialement défini dans le fichier d'entrée, dans le système défini par l'utilisateur de l'unité cible.

Contexte 2 : changement entre systèmes d'unités pendant l'exécution
Dans ce cas, vous pouvez être en même temps celui qui réalise le dessin, et celui qui va gérer la modélisation des éléments finis (FE). Comme dans le cas précédent, les systèmes unitaires pour ces 2 tâches, ne sont pas les mêmes, et, vous avez besoin de changer le système d'unité initial, lors de l'exécution de celui que vous préférez.

Logique d'échelle d'une unité
Dans la section 2 de "Remise en mémoire", ont été présentés, les contextes, d'échelles et d'unités en cours d'exécution. Certains éléments, doivent être mis en évidence, à partir de ces deux contextes.

Unit coherence throughout the FreeCAD running instance
The system proposed is based on a primary assumption: the user is working in a coherent unit system. For instance, this means that if the user expresses length in millimeters, necessarily areras will be expressed in terms of squared millimeters, not squared meters. This is hypothesis one.

Unit system
Because of hypothesis one, it is possible and relevant to define an unit system. An unit system applies to: According Guide for the Use of the International System of Units (SI) from NIST, they are 7 physical base units. We chose to express a unit system in terms of these 7 base units.
 * a running FreeCAD instance into which you are working
 * or it may also apply globally to the content of an input file

When working within an instance of FreeCAD, the user has thus to define first the unit system according to which she/he is working before she/he decides to switch to another unit system, or before importing data from an input file.

This unit system will apply till the user decides to change it. If she/he does, all data with dimensions will be scaled.

Considering hypothesis one, all data that the user will input manually in FreeCAD are assumed to be coherent with the chosen unit system.

The benefit to work with a unit system defined at a FreeCAD running instance level, or at data file level (instead of unit which are defined at the data level) is then that unit management is considerably simplified.

Here are some examples of unit systems.
 * meter, kilogram, second, ampere, Kelvin, mole, candela
 * millimeter, tonne, millisecond, ampere, Kelvin, mole, candela
 * millimeter, kilogramme, millisecond, ampere, Kelvin, mole, candela

Base and derived units
Derived units are created by combination of base units. For instance, an acceleration (m/s) combines at the same time length and time. An interesting picture presenting the relationships between base and derived units can be seen here also from NIST.

Thanks to the definition of unit system, it is possible for the user to work with any kind of derived units, without the need for FreeCAD developpers to foresee them in advance.

Base and derived unit symbols
According to The International System of Units (SI), the symbols to specify a units are officially approved. Two consequences can be highlighted from this.
 * it is not easy for a computer program to work with unit symbols because some are greek letters for instance. Hence they can be a bit difficult to process by a program
 * while some units and their symbols can be used widely, they may be not approved officially, like for instance tonne unit (see p32 of The International System of Units (SI))

To overcome these limitations and remain flexible, the proposed system favors the use of unit magnitudes instead of unit symbols, which remain nonetheless available for an ergonomy reason.

Data model
The three core objects of the unit management system are presented, namely the unit, the unit dictionary and the unit system.

Unit
As a foreword, it is important to highlight that a unit object in itself only indicates a dimension like length, mass, time... It doesn't specify a magnitude like meter, millimeter, kilometer... This last information is specified through the unit system.

Dimension
Compulsory string indicating the dimension of the unit. The dimension of the 7 base units are indicated below (from Guide for the Use of the International System of Units (SI)).
 * LENGTH
 * MASS
 * TIME
 * ELECTRIC CURRENT
 * THERMODYNAMIC TEMPERATURE
 * AMOUNT OF SUBSTANCE
 * LUMINOUS INTENSITY

Dimension attribute allows identifying the unit. Two units cannot share the same dimension.

Signature
Compulsory integer array of size 7 (number of base units) that defines what the unit is. The signature of the 7 base units are:
 * LENGTH: [1,0,0,0,0,0,0]
 * MASS: [0,1,0,0,0,0,0]
 * TIME: [0,0,1,0,0,0,0]
 * ELECTRIC CURRENT: [0,0,0,1,0,0,0]
 * THERMODYNAMIC TEMPERATURE: [0,0,0,0,1,0,0]
 * AMOUNT OF SUBSTANCE: [0,0,0,0,0,1,0]
 * LUMINOUS INTENSITY: [0,0,0,0,0,0,1]

From these 7 units, we are then able to express all derived units defined in Guide for the Use of the International System of Units (SI) and create new ones as needed such as for instance:
 * MASS DENSITY: [-3,1,0,0,0,0,0]
 * AREA: [0,2,0,0,0,0,0]

Signature is the attribute thanks to which unit scaling can be achieved in a generic way.

Symbols
Array of [real, string] (meaning [magnitude, symbol]) that lists all symbols known by FreeCAD. Thanks to this array, the unit scaling API becomes more ergonomic because symbols and related magnitudes are linked.

This array can be extended as required.

For instance, the list of symbols of the LENGTH unit, and their related magnitudes is:

[1e+12,"Tm"],[1e+09,"Gm"],[1e+06,"Mm"], [1e+03,"km"],[1e+02,"hm"],[1e+01,"dam"], [1e+00,"m"],[1e-01,"dm"],[1e-02,"cm"], [1e-03,"mm"],[1e-06,"µm"],[1e-09,"nm"], [1e-12,"pm"],[1e-15,"fm"]

Standard symbols can be found on NIST website and p23 to 26 and p32 (metric ton or tonne) of The International System of Units (SI).

Unit dictionary
All the units available in FreeCAD, and new ones created by the user, should be stored in unit dictionary, which is an XML file (FreeCAD configuration file), so as to be retrieved when needed, i.e. when achieving unit scaling.

Units
Array of units, contained in the unit dictionary.

Unit system
A unit system is the object that allows the user defining the current unit magnitude of each base units with which she/he is working. For instance, knowing that the user is working with millimeter, tonne, and second, thanks to the use of a unit system, FreeCAD can know that energy is expressed in terms of milliJoule, force in terms of Newton, and stress in terms of MegaPascal. Hence a unit system is only defined by a name (for instance Standard unit system) and a magnitude table specifying for each of the 7 base units, what is its corresponding magnitude.

Name
String allowing to the user identifying what is the unit system.

Magnitudes
By specifying the magnitude of the 7 base units, a unit system is defined.

For instance [1e-03, 1e+03, 1, 1, 1, 1, 1], meaning millimeter, tonne, second, ampere, Kelvin, mole, candela

Unit management API
Only the logic of some methods is presented, in order to highlight some features. These methods could belong to an object called Unit manager.

isValid
The unit dictionary can be an XML file (FreeCAD configuration file). It contains a list of defined units. Such a dictionary is required for the proposed unit management system to work.

It must fulfills some conditions that should be checked before activating the unit management system. These conditions are:
 * check that all base units are defined
 * check that a dimension is not defined twice through the units
 * check that a symbol is not defined twice in all the existing symbols
 * check that the signatures of all units have all the same size
 * chacke that a standard symbol (for which magnitude is 1) is defined for all units

isCompatibleWithThisSignature
A unit dictionary defines a set of units and their known magnitudes. When managing a unit, it is relevant to check that its signature is compatible with the set of units registered in the unit dictionary, so as to process it. This check includes:
 * check that the input signature length is of the same size than the unit dictionary unit signatures

scaleUnitFromSymbolToSymbol
Knowing a value, an initial unit by its symbol, the target unit by its symbol, scale the value.

scaleUnitFromSymbolToUnitSystem
Knowing a value, an initial unit by its symbol, the target unit system, scale the value.

scaleUnitFromUnitSystemToSymbol
Knowing a value, an initial unit system, the target unit by its symbol, scale the value.

Motivations for such a management: example of application
Let's assume that we are going to setup a finite element model. To build our model, we need the mesh, material properties, and to define numerical parameters. Considering that they can be tens of material properties to manage, expressed with different units, sometimes not always very common, it is interesting for the user to only have to specify a global unit system, without caring much.

FreeCAD would then just do the job.

As FreeCAD developpers and FreeCAD users do not necessarily know all units that can be defined in the material property files, it is interesting to rely on a generic system.

Let's assume that in such a file we have a fair number of exotic material properties expressed with exotic units, and that we want to work in a specific unit system.

It is easy with the proposed extension to scale any of these properties by knowing their signatures, magnitudes, and the target unit system.

For each of the properties, the scaling is obtained by multiplying the initial property value with the factor $$\frac{initialMagnitude}{targetMagnitude}$$.

The targetMagnitude is then simply obtained with the operation $$\prod_{bu} targetMagnitude_{bu}^{signature_{bu}}$$, bu standing for base unit.

It becomes thus very easy to manage any number of properties with any kind of units with very few lines of Python.

Next actions

 * Implementing Quantity and Unit classes (mostly done)
 * Implementing InputField as User front end (in progress)
 * UnitsCalculator as test bed (in progress)
 * Quantity documentation (in progress)
 * UnitsCalculator documentation
 * Update Material framework to work only with Quantities
 * Test Cases