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Alcune letture sulle unità di misura:
Alcune letture sulle unità di misura:
*[http://it.wikipedia.org/wiki/Metrologia Metrologia]
*[http://it.wikipedia.org/wiki/Sistema_internazionale_di_unit%C3%A0_di_misura Sistema Internazionale di Misura SI]
*[http://it.wikipedia.org/wiki/Sistema_internazionale_di_unit%C3%A0_di_misura Sistema Internazionale di Misura SI]
*[http://it.wikipedia.org/wiki/Sistema_imperiale_britannico Sistema imperiale britannico]
*[http://it.wikipedia.org/wiki/Sistema_imperiale_britannico Sistema imperiale britannico]
*[http://en.wikipedia.org/wiki/SI_derived_unit SI derived unit] (in italiano si trovano nella stessa pagina del SI)
*[http://en.wikipedia.org/wiki/SI_derived_unit SI derived unit] (in italiano si trovano nella stessa pagina del SI)
*[http://it.wikipedia.org/wiki/Grado_d%27arco Grado d'arco - Unità angolari]
*[http://it.wikipedia.org/wiki/Grado_d%27arco Grado d'arco - Unità angolari]
*[https://github.com/3drepo/occt/blob/master/src/UnitsAPI/Units.dat Unità implementate in OCC]


== Esempi ==
== Esempi ==


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


# 10 meters in internal numbers
== Unità di misura supportate ==
pq('10 m')


# doing math
Queste sono le unità finora definite in FreeCAD. È facile aggiungere una nuova unità definita dall'utente. La definizione si trova in http://free-cad.svn.sourceforge.net/viewvc/free-cad/trunk/src/Base/UnitsApi.l?view=markup.
pq('3/8 in')


# combined stuff
Lunghezza metrica
pq('100 km/h')
"mm" 1.0; // millimetro (lunghezza standard interna)
"m" 1000.0; // metro
"cm" 10.0; // centimetro
"dm" 100.0; // decimetro
"km" 1000000.0; // kilometro


# transfer to other units
Lunghezza Imperiale
pq('100 km/h')/tu('m/s')
"in" "\"" 25.4; // inch
"ft" "'" 304.8; // foot
"th" 0.0254; // thou
"yr" 914.4; // yard


# derived units (Ohm)
Massa metrica
pq('m^2*kg*s^-3*A^-2')
"kg" 1.0; // kilogrammo (massa standard interna)
"g" 0.001; // grammo
"mg" 0.000001; // milligrammo
"t" 1000.0; // tonnellata


# or
Massa Imperiale
pq('(m^2*kg)/(A^2*s^3)')
"lb" 0.45359237; // pound
"oz" 0.45359237; // ounce
"st" 6.35029318; // Stone
"cwt" 50.80234544;// hundredweights


# angles
Angolo
pq('2*pi rad') # full circle
"deg" 1.0; // gradi (angolo standard interno)
"rad" 180/M_PI; // radianti
"gon" 360.0/400.0;// gon
Tempo
"s" 1.0; // secondo (tempo standard interno)
"min" 60.0; // minuto
"h" 3600.0; // ora


# as gon
Altro del SI
pq('2*pi rad') / tu('gon')
"A" 1.0; // Ampere (internal standard electric current)
"K" 1.0; // Kelvin (internal standard thermodynamic temperature)
"cd" 1.0; // Candela (internal standard luminous intensity)
"mol" 1.0; // Mole (internal standard amount of substance)
Volume metrico
"µl" 1.0; // microliter mm^3(volume standard derivato)
"ml" 1000.0; // milliliter cm^3
"l" 1000000.0; // Liter dm^3


# more imperial
== Finalità e principi: proposta di una estensione del sistema di gestione delle unità ==
tu('1ft (3+7/16)in')


# or
Nelle sezioni successive, sviluppando il concetto di ''sistema di unità'', si propone un sistema di gestione delle unità di misura attivato nel corso dell'esecuzione di una istanza di FreeCAD. Definire tale nuovo concetto offre il vantaggio di lavorare più facilmente con tanti tipi di unità '''fisiche''', quante si vuole, anche con quelle create dall'utente, senza aumentare la complessità di gestione delle unità, né per l'utente, né per gli sviluppatori di FreeCAD.
pq('1\' (3+7/16)"') # the ' we have to escape because of python


# trigonometry
In breve, gli eventi di scalatura delle unità sono localizzati con precisione, e realizzati in modo globale.
pq('sin(pi)')


# Using translated units as parameters, this command will create a 50.8mm x 20mm x 10mm box
Il raggiungimento di tale flessibilità è necessario specialmente quando si passa a lavorare con le proprietà dei materiali che possono avere unità molto diverse e quindi difficili da gestire manualmente una ad una.
b = Part.makeBox(pq('2in'), pq('2m')/100, 10)
}}


==Unità supportate==
Il ragionamento proposto permette di gestire le unità come descritto nella [http://physics.nist.gov/cuu/pdf/sp811.pdf Guida per l'uso del Sistema Internazionale delle unità di misura (SI)] e nel [http://physics.nist.gov/Pubs/SP330/sp330.pdf Sistema internazionale delle unità di misura (SI)], entrambi documenti del NIST.


Un elenco completo di tutte le unità supportate [[Expressions/it#Unità|si trova quì]].
In questa proposta, la prima analisi nella sezione [[Units/it#Riflessioni|Riflessioni]] riguarda i possibili contesti per i quali è utile la gestione delle unità.


== Vedere anche ==
Nella sezione [[Units/it#Organizzazione|Organizzazione]] è presentato il modello di dati prescelto per realizzare la gestione delle unità, sulla base di 3 oggetti, la ''unità'', il ''dizionario delle unità'', e il ''sistema delle unità''. Infine, è anche presentata una breve API di un quarto oggetto chiamato ''gestore delle unità''.


* La pagina [[Expressions#Units|Espressioni]] per una lista dei tutte le unità conosciute.
== Risultati ==
* La documentazione [[Quantity/it|Quantity]].
* Lo strumento [[Std_UnitsCalculator/it|Convertitore di unità]].


Grazie a questa estensione, si mira ad agevolare la scalatura della unità che può verificarsi tra i differenti settori di lavoro di una azienda. Ad esempio, i disegni tecnici possono essere realizzati nel sistema di unità standard, mentre la modellazione per elementi finiti può essere gestita in un sistema di unità più adatto per questo scopo.


{{Powerdocnavi{{#translation:}}}}
Con questa estensione lo scambio di dati tra questi due tipi di attività diventa più facile.

== Riflessioni ==

In questa sezione sono evidenziati i contesti (casi) di uso del sistema di gestione delle unità. Partendo da questi contesti, dopo siamo in grado di definire le loro specifiche tecniche.

Essenzialmente sono considerati 2 contesti, come esempio.

=== Contesto 1: apertura di un file di dati ===

Questo caso probabilmente è quello più frequente.
Si riceve un file contenente ad esempio un modello geometrico, o descrivente un materiale con un bel po' di proprietà. Il modello geometrico è espresso in metri, oppure le proprietà del materiale sono espresse secondo il sistema internazionale di unità di misura.

Peccato ...

You are an expert FE modelling, and you usually work with millimeter for length, MegaPascal for stress, tonne for mass...

In this context, unit management is required to scale data from an initial unit system defined in the input file to a user-defined target unit system.

=== Context 2: switching the unit system at runtime ===
In this case, you can be at the same time the guy that carries out a drawing, and the guy that will manage the FE modelling. Similarly to the previous case, the unit systems for these 2 tasks are not the same, and you need to switch the initial unit system at runtime to your favorite one.

== Organizing ==

=== Logic of unit scaling ===
In the [[Units#Brainstorming|Brainstorming]] section have been presented 2 contexts when using unit scaling.
Some items should be highlighted from these two contexts.

==== 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:
* a running FreeCAD instance into which you are working
* or it may also apply globally to the content of an input file
According [http://physics.nist.gov/cuu/pdf/sp811.pdf 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.

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 [http://physics.nist.gov/cuu/pdf/SIDiagramColorAnnot.pdf 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 [http://physics.nist.gov/Pubs/SP330/sp330.pdf 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 [http://physics.nist.gov/Pubs/SP330/sp330.pdf 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 [http://physics.nist.gov/cuu/pdf/sp811.pdf 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 [http://physics.nist.gov/cuu/pdf/sp811.pdf 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 [http://physics.nist.gov/cuu/Units/units.html NIST website] and p23 to 26 and p32 (''metric ton'' or ''tonne'') of [http://physics.nist.gov/Pubs/SP330/sp330.pdf 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''.

===== Checking the unit dictionary =====

====== 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''

===== Scaling units =====

====== 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 <math>\frac{initialMagnitude}{targetMagnitude}</math>.

The ''targetMagnitude'' is then simply obtained with the operation <math>\prod_{bu} targetMagnitude_{bu}^{signature_{bu}}</math>, ''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


[[Category:Poweruser Documentation]]

{{clear}}
<languages/>

Latest revision as of 20:23, 8 October 2022

Alcune letture sulle unità di misura:

Esempi

# -- some examples of the FreeCAD unit translation system --
# make a shortcut for the examples
pq = FreeCAD.Units.parseQuantity

# 10 meters in internal numbers
pq('10 m')

# doing math
pq('3/8 in')

# combined stuff
pq('100 km/h')

# transfer to other units
pq('100 km/h')/tu('m/s')

# derived units (Ohm)
pq('m^2*kg*s^-3*A^-2')

# or
pq('(m^2*kg)/(A^2*s^3)')

# angles 
pq('2*pi rad') # full circle

# as gon
pq('2*pi rad') / tu('gon')

# more imperial
tu('1ft (3+7/16)in')

# or 
pq('1\' (3+7/16)"') # the ' we have to escape because of python

# trigonometry
pq('sin(pi)')

# Using translated units as parameters, this command will create a 50.8mm x 20mm x 10mm box
b = Part.makeBox(pq('2in'), pq('2m')/100, 10)

Unità supportate

Un elenco completo di tutte le unità supportate si trova quì.

Vedere anche