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Die Größe ist eine Kombination einer Fließkommazahl und einer Einheit. Sie wird überall in FreeCAD benutzt, um Parameter und alle Arten von Ein- und Ausgaben zu behandeln.
Die Größe ist eine Kombination einer Fließkommazahl und einer Einheit. Sie wird überall in FreeCAD benutzt, um Parameter und alle Arten von Ein- und Ausgaben zu behandeln.


== General ==
<span id="General"></span>
== Allgemein ==


In a CAD or CAE system it is very important to keep track of the unit of a value. Lots of trouble can arise when mixing up units or calculating results in different systems of units. One famous disaster is the [http://en.wikipedia.org/wiki/Mars_Climate_Orbiter#Cause_of_failure crash of the Mars Climate Orbiter] due to a unit mix-up. Even in the same system of units the units come in lots of different flavours always tailored to the field of use. Simple examples are e.g. velocity in km/h (cars), m/s (robotics) or mm/minute (milling). A CAD system has to keep track of units reliably. Also it has to do calculations with them and check on the right unit for special parameters.
In einem CAD- oder CAE-System ist es sehr wichtig, die Einheit eines Wertes im Auge zu behalten. Viel Ärger kann entstehen, wenn Einheiten durcheinander geworfen oder Ergebnisse in unterschiedlichen Einheitensystemen berechnet werden. Ein berühmtes Missgeschick ist der [https://de.wikipedia.org/wiki/Mars_Climate_Orbiter Verlust des Mars Climate Orbiter] durch unterschiedliche Einheiten. Selbst innerhalb des gleichen Einheitensystems kommen die Einheiten in unterschiedlichen Varianten abhängig vom Verwendungszweck. Einfache Beispiele sind die Geschwindigkeit in km/h (Autos), m/s (Robotik) oder mm/min (Fräsen). Ein CAD-System muss verlässlich auf die Einheiten achten. Es muss auch mit ihnen rechnen und auf die richtige Einheit bei speziellen Parametern achten.


Aus diesem Grund wurde das FreeCAD-Mengengerüst geschaffen. Es umfasst den gesamten Code und die Objekte zum Umgang mit Einheiten, Berechnungen, Benutzereingaben, Umrechnung in andere Einheitensysteme und die schöne Ausgabe von Werten und Einheiten. Langfristig sollte in FreeCAD kein Parameter nur eine Zahl sein.
For that reason the FreeCAD Quantity framework was created. It includes all the code and objects to deal with units, unit calculations, user input, conversion to other systems of units and the pretty output of units and values. In the long run no parameter in FreeCAD should be just a number.


<span id="Supported_units"></span>
=== Supported units ===
=== Unterstützte Einheiten ===


Der FreeCAD-Eingabe-Parser unterstützt eine Vielzahl von Einheiten und Einheitensystemen. FreeCAD unterstützt den griechischen Buchstaben 'µ' für micro, akzeptiert aber auch 'u' als Ersatz.
The FreeCAD input parser supports a bunch of units and systems of units. We do use the greek letter for micro but also accept 'u' as a replacement.
Eine vollständige Liste aller unterstützter Einheiten befindet sich [[Expressions/de#Einheiten|hier]].


Die detaillierte Beschreibung findest Du im Code:
* Length
* Mengen-Lexer: [http://sourceforge.net/p/free-cad/code/ci/master/tree/src/Base/QuantityParser.l]
** "nm"
* Mengedefinition: [http://sourceforge.net/p/free-cad/code/ci/master/tree/src/Base/Quantity.cpp#l167]
** "µm"
** "mm"
** "cm"
** "dm"
** "m"
** "km"
** "in"
** "ft"
** "thou"
** "mil"
** "yd"
** "mi"


== Interne Darstellung ==
Todo: all the rest...
Alle physikalischen Einheiten können als eine Kombination der sieben [https://de.wikipedia.org/wiki/Internationales_Einheitensystem SI-Einheiten] ausgedrückt werden:


[[File:SI-Derived-Units.jpg|750px]]


The detailed specifications you will find in the code:
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/QuantityLexer.c Quantity lexer]
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/Quantity.cpp#l167 Quantity definitions]


Ein einfacher Weg, eine Einheit auszudrücken, ist ein Feld mit Integerwerten der Größe 7 (Anzahl der Basiseinheiten), das festlegt, was die Einheit darstellt.
== Internal representation ==
All physical units can be expressed as a combination of the seven [http://en.wikipedia.org/wiki/International_System_of_Units SI-Units]:

[[File:SI-Derived-Units.jpg|750px]]


Die Kennzeichnung der sieben Basiseinheiten ist:


* LÄNGE: [1,0,0,0,0,0,0]
An easy way to express a unit is an integer array of size 7 (number of base units) that defines what the unit is.
* MASSE: [0,1,0,0,0,0,0]
The signature of the 7 base units are:
* LENGTH: [1,0,0,0,0,0,0]
* ZEIT: [0,0,1,0,0,0,0]
* MASS: [0,1,0,0,0,0,0]
* STROMSTÄRKE: [0,0,0,1,0,0,0]
* TIME: [0,0,1,0,0,0,0]
* THERMODYNAMISCHE TEMPERATUR: [0,0,0,0,1,0,0]
* ELECTRIC CURRENT: [0,0,0,1,0,0,0]
* STOFFMENGE: [0,0,0,0,0,1,0]
* THERMODYNAMIC TEMPERATURE: [0,0,0,0,1,0,0]
* LICHTSTÄRKE: [0,0,0,0,0,0,1]
* AMOUNT OF SUBSTANCE: [0,0,0,0,0,1,0]
* LUMINOUS INTENSITY: [0,0,0,0,0,0,1]


Using these seven 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:
Mit diesen sieben Einheiten können wir alle abgeleiteten Einheiten (in [http://physics.nist.gov/cuu/pdf/sp811.pdf Guide for the Use of the International System of Units (SI)] nachzulesen) ausdrücken und weitere neue nach Bedarf erstellen, wie etwa:
* MASS DENSITY: [-3,1,0,0,0,0,0]
* MASSENDICHTE: [-3,1,0,0,0,0,0]
* AREA: [0,2,0,0,0,0,0]
* FLÄCHE: [0,2,0,0,0,0,0]


Weil Winkel pysikalisch dimensionslos, aber trotzdem wichtig für ein CAD-System sind, haben wir eine weitere virtuelle Einheit für den Winkel. Das ergibt einen Vektor von 8 in der FreeCAD-Einheitenkennzeichnung.
Since angle is physically dimensionless, but nevertheless important to a CAD system we add one more virtual unit for Angle. This makes a vector of 8 in the FreeCAD unit signature.


== Units calculator ==
== Einheitenrechner ==
Oft muss man Einheiten von einem System in ein anderes umrechnen. Du hast beispielsweise alte Parametertabellen (with wired units). In diesen Fällen bietet FreeCAD ein Umrechnungswerkzeug genannt 'UnitsCalculator', das bei der Übersetzung von Einheiten hilft.
Often you are in need of converting values from one system of units to another. For example you have old parameter tables with wired units. In these cases FreeCAD offers a conversion tool called Units-Calculator which helps in translating units.


Die Beschreibung im Detail befinden sich hier: [[Std_UnitsCalculator/de|Std Einheitenrechner]].
Its description in detail is here:
[[Std_UnitsCalculator]]


== InputField ==
== InputField ==
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The UnitsCalculator uses the InputField already.
The UnitsCalculator uses the InputField already.


Main documentation: [[InputField]]
Hauptdokumentation: [[InputField/de|Eingabefeld]]


Code:
Code:
Line 82: Line 68:


== Python scripting ==
== Python scripting ==
The Unit and Quantity system in FreeCAD is (as nearly everything) fully accessibly via Python.
Das Einheiten- und Mengensystem in FreeCAD ist (wie fast alles) vollständig über Python ansprechbar.


=== Unit ===
=== Unit ===
The Unit class represents the fingerprint of any physical unit. As described in the Basics section a vector of eight numbers is used to represent this fingerprint. The Unit class allows the handling and calculation based on this information.
The Unit class represents the fingerprint of any physical unit. As described in the Basics section a vector of eight numbers is used to represent this fingerprint. The Unit class allows the handling and calculation based on this information.


{{Code|code=
<syntaxhighlight>


from Units import Unit
from FreeCAD import Units


# creating a unit with certain signature
# creating a unit with certain signature
Unit(0,1) # Mass (kg)
Units.Unit(0,1) # Mass (kg)
Unit(1) # Length (mm)
Units.Unit(1) # Length (mm)
Unit(-1,1,-2) # Pressure (kg/mm*s^2)
Units.Unit(-1,1,-2) # Pressure (kg/mm*s^2)


# using predefined constants
# using predefined constants
Unit(FreeCAD.Units.Length)
Units.Unit(Units.Length)
Unit(FreeCAD.Units.Mass)
Units.Unit(Units.Mass)
Unit(FreeCAD.Units.Pressure)
Units.Unit(Units.Pressure)


# parsing unit out of a string
# parsing unit out of a string
Unit('kg/(m*s^2)') # Pressure
Units.Unit('kg/(m*s^2)') # Pressure
Unit('Pa') # the same as combined unit Pascale
Units.Unit('Pa') # the same as combined unit Pascale
Unit('J') # Joul (work,energy) mm^2*kg/(s^2)
Units.Unit('J') # Joule (work,energy) mm^2*kg/(s^2)


# you can use units from all supported systems of units
# you can use units from all supported systems of units
Unit('psi') # Imperial pressure
Units.Unit('psi') # imperial pressure
Unit('lb') # Mass
Units.Unit('lb') # imperial mass
Unit('ft^2') # Area
Units.Unit('ft^2') # imperial area


# comparing units
# comparing units
Unit(0,1) == Unit(FreeCAD.Units.Mass)
Units.Unit(0,1) == Unit(Units.Mass)


# getting type of unit
# getting type of unit
Unit('kg/(m*s^2)').Type == 'Pressure'
Units.Unit('kg/(m*s^2)').Type == 'Pressure'


# calculating
# calculating
Unit('kg') * Unit('m^-1*s^-2') == Unit('kg/(m*s^2)')
Units.Unit('kg') * Units.Unit('m^-1*s^-2') == Units.Unit('kg/(m*s^2)')


}}
</syntaxhighlight>
The unit is mainly used to describe a certain type of unit for a parameter. Therefore a special property type in FreeCAD can pass a unit to check and ensure the right unit.
The unit is mainly used to describe a certain type of unit for a parameter. Therefore a special property type in FreeCAD can pass a unit to check and ensure the right unit.
A unit and a float value is called quantity.
A unit and a float value is called quantity.
Line 126: Line 112:
=== Quantity ===
=== Quantity ===


{{Code|code=
<syntaxhighlight>


from Units import Unit,Quantity
from FreeCAD import Units


# to create a quantity you need a value (float) and a unit
# to create a quantity you need a value (float) and a unit
Quantity(1.0,Unit(0,1)) # Mass 1.0 kg
Units.Quantity(1.0,Units.Unit(0,1)) # Mass 1.0 kg
Quantity(1.0,Unit(1)) # Length 1.0 mm
Units.Quantity(1.0,Units.Unit(1)) # Length 1.0 mm
Quantity(1.0,Unit(-1,1,-2)) # Pressure 1.0 kg/mm*s^2
Units.Quantity(1.0,Units.Unit(-1,1,-2)) # Pressure 1.0 kg/mm*s^2
Quantity(1.0,FreeCAD.Units.Pressure) # Pressure 1.0 kg/mm*s^2
Units.Quantity(1.0,Units.Pressure) # Pressure 1.0 kg/mm*s^2


# you can directly give a signature
# you can directly give a signature
Quantity(1.0,0,1) # Mass 1.0 kg
Units.Quantity(1.0,0,1) # Mass 1.0 kg
Quantity(1.0,1) # Length 1.0 mm
Units.Quantity(1.0,1) # Length 1.0 mm
Quantity(1.0,-1,1,-2) # Pressure 1.0 kg/mm*s^2
Units.Quantity(1.0,-1,1,-2) # Pressure 1.0 kg/mm*s^2


# parsing quantities out of a string
# parsing quantities out of a string
Quantity('1.0 kg/(m*s^2)') # Pressure
Units.Quantity('1.0 kg/(m*s^2)') # Pressure
Quantity('1.0 Pa') # the same as combined Unit Pascale
Units.Quantity('1.0 Pa') # the same as combined Unit Pascale
Quantity('1.0 J') # Joul (Work,Energy) mm^2*kg/(s^2)
Units.Quantity('1.0 J') # Joule (Work,Energy) mm^2*kg/(s^2)


# You can use a point or comma as float delimiter
# You can use a point or comma as float delimiter
Quantity('1,0 m')
Units.Quantity('1,0 m')
Quantity('1.0 m')
Units.Quantity('1.0 m')


# you can use units from all supported systems of units
# you can use units from all supported systems of units
Quantity('1.0 psi') # Imperial pressure
Units.Quantity('1.0 psi') # imperial pressure
Quantity('1.0 lb') # Mass
Units.Quantity('1.0 lb') # imperial mass
Quantity('1.0 ft^2')
Units.Quantity('1.0 ft^2') # imperial area


# the quantity parser can do calculations too
# the quantity parser can do calculations too
Quantity('360/5 deg') # splitting circle
Units.Quantity('360/5 deg') # splitting circle
Quantity('1/16 in') # fractions
Units.Quantity('1/16 in') # fractions
Quantity('5.3*6.3 m^2') # calculating an area
Units.Quantity('5.3*6.3 m^2') # calculating an area
Quantity('1/(log(2.3)/sin(pi)*3.4)+1.8e-3 m')
Units.Quantity('1/(log(2.3)/sin(pi)*3.4)+1.8e-3 m')
Quantity('1ft 3in') # imperial style
Units.Quantity('1ft 3in') # imperial style


# and for sure calculation and comparison
# and for sure calculation and comparison
Quantity('1 Pa')* Quantity(2.0) == Quantity('2 Pa')
Units.Quantity('1 Pa') * Units.Quantity(2.0) == Units.Quantity('2 Pa')
Quantity('1 m')* Quantity('2 m') == Quantity('2 m^2')
Units.Quantity('1 m') * Units.Quantity('2 m') == Units.Quantity('2 m^2')
Quantity('1 m')* Quantity('2 ft') + Quantity('2 mm^2')
Units.Quantity('1 m') * Units.Quantity('2 ft') + Units.Quantity('2 mm^2')
Quantity('1 m') > Quantity('2 ft')
Units.Quantity('1 m') > Units.Quantity('2 ft')


# accessing the components
# accessing the components
Quantity('1 m').Value # get the number (allways internal system (mm/kg/s))
Units.Quantity('1 m').Value # get the number (always internal system (mm/kg/s))
Quantity('1 m').Unit # get the unit
Units.Quantity('1 m').Unit # get the unit
Quantity('1 m') == Quantity( Quantity('1 m').Value , Quantity('1 m').Unit )
Units.Quantity('1 m') == Units.Quantity( Units.Quantity('1 m').Value , Units.Quantity('1 m').Unit)


# translating the value into other units than the internal system (mm/kg/s)
# translating the value into other units than the internal system (mm/kg/s)
Quantity('1 km/h').getValueAs('m/s') # translate value
Units.Quantity('1 km/h').getValueAs('m/s') # translate value
Quantity('1 m').getValueAs(2.45,1) # translation value and unit signature
Units.Quantity('1 m').getValueAs(2.45,1) # translation value and unit signature
Quantity('1 kPa').getValueAs(FreeCAD.Units.Pascal) # predefined standard units
Units.Quantity('1 kPa').getValueAs(Units.Pascal) # predefined standard units
Quantity('1 MPa').getValueAs(Quantity('N/m^2')) # a quantity
Units.Quantity('1 MPa').getValueAs(Units.Quantity('N/m^2')) # a quantity
}}
</syntaxhighlight>


=== User facing values ===
=== User facing values ===
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The Quantity class has two options to use the actual schema translation:
The Quantity class has two options to use the actual schema translation:


{{Code|code=
<syntaxhighlight>
from FreeCAD import Units

from Units import Unit,Quantity


# Use the translated string:
# Use the translated string:
Quantity('1m').UserString # '1000 mm' in 1; '1 m' in 2; and '1.09361 yr' in 3
Units.Quantity('1m').UserString # '1000 mm' in 1; '1 m' in 2; and '1.09361 yr' in 3
}}


</syntaxhighlight>
This does the job if you only need a string. But sometimes you need more control, e.g. if you want to have a dialog button which dials up and down. Then you need more information about the translation output. Therefore the getUserPreferred() method of quantity is used:
This does the job if you only need a string. But sometimes you need more control, e.g. if you want to have a dialog button which dials up and down. Then you need more information about the translation output. Therefore the getUserPreferred() method of quantity is used:


{{Code|code=
<syntaxhighlight>
Units.Quantity('22 m').getUserPreferred() # gets a tuple:('22 m', 1000.0, 'm')

Quantity('22 m').getUserPreferred() # gets a tuple:('22 m', 1000.0, 'm')
Units.Quantity('2 m').getUserPreferred() # Tuple: ('2000 mm', 1.0, 'mm')
}}
Quantity('2 m').getUserPreferred() # Tuple: ('2000 mm', 1.0, 'mm')

</syntaxhighlight>
Here you get more information using a tuple (three items). You get the string as before, plus the factor of the value and the raw string with only the unit chosen by the translation schema. With this information you can implement a much richer user interaction.
Here you get more information using a tuple (three items). You get the string as before, plus the factor of the value and the raw string with only the unit chosen by the translation schema. With this information you can implement a much richer user interaction.


Line 212: Line 193:
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/UnitsSchemaInternal.cpp Internal]
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/UnitsSchemaInternal.cpp Internal]
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/UnitsSchemaMKS.cpp MKS]
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/UnitsSchemaMKS.cpp MKS]
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/UnitsSchemaImperial.cpp Imperial]
* [https://github.com/FreeCAD/FreeCAD/blob/master/src/Base/UnitsSchemaImperial1.cpp Imperial]


== Appendix ==
=== Precision ===


The precision of quantities is within FreeCAD dialogs the number of decimals specified [[Preferences_Editor#Units|in the preferences]]. To use this settings for your script (for example in dialogs), you can get it with this code:
=== Parser supported units ===
{{Code|code=
Although all physical units can be described with the seven SI units, most of the units used in technical areas are common combined units (like Pa = N/m^2 Pascal ). Therefore the units parser in FreeCAD supports lot of SI and Imperial combined units. These units are defined in src/Base/QuantityParser.l file and can be further expanded in the future.
import FreeCAD


params = App.ParamGet("User parameter:BaseApp/Preferences/Units")
params.GetInt('Decimals') # returns an int
}}


<span id="Appendix"></span>
"nm" = Quantity(1.0e-6 ,Unit(1)); // nano meter
== Anhang ==
"µm" = Quantity(1.0e-3 ,Unit(1)); // micro meter

"mm" = Quantity(1.0 ,Unit(1)); // milli meter
=== Parser-unterstützte Einheiten ===
"cm" = Quantity(10.0 ,Unit(1)); // centi meter
Obwohl alle physikalischen Einheiten mit den sieben SI-Einheiten beschrieben werden können, bestehen die meisten in technischen Bereichen benutzten Einheiten aus üblichen zusammengesetzten Einheiten (wie Pa = N/m^2 Pascal). Deshalb unterstützt der Einheiten-Parser in FreeCAD viele SI- und Imperial-kombinierte Einheiten. Diese Einheiten sind in der Datei src/Base/QuantityParser.l definiert und können in der Zukunft noch erweitert werden.
"dm" = Quantity(100.0 ,Unit(1)); // deci meter

"m" = Quantity(1.0e3 ,Unit(1)); // meter
{{Code|code=
"km" = Quantity(1.0e6 ,Unit(1)); // kilo meter

"l" = Quantity(1000000.0 ,Unit(3)); // Liter dm^3
from FreeCAD import Units

"nm" = Units.Quantity(1.0e-6 ,Units.Unit(1)); // nano meter
"µm" = Units.Quantity(1.0e-3 ,Units.Unit(1)); // micro meter
"mm" = Units.Quantity(1.0 ,Units.Unit(1)); // milli meter
"cm" = Units.Quantity(10.0 ,Units.Unit(1)); // centi meter
"dm" = Units.Quantity(100.0 ,Units.Unit(1)); // deci meter
"m" = Units.Quantity(1.0e3 ,Units.Unit(1)); // meter
"km" = Units.Quantity(1.0e6 ,Units.Unit(1)); // kilo meter
"l" = Units.Quantity(1000000.0 ,Units.Unit(3)); // liter dm^3
"µg" = Quantity(1.0e-9 ,Unit(0,1)); // micro gram
"µg" = Units.Quantity(1.0e-9 ,Units.Unit(0,1)); // micro gram
"mg" = Quantity(1.0e-6 ,Unit(0,1)); // milli gram
"mg" = Units.Quantity(1.0e-6 ,Units.Unit(0,1)); // milli gram
"g" = Quantity(1.0e-3 ,Unit(0,1)); // gram
"g" = Units.Quantity(1.0e-3 ,Units.Unit(0,1)); // gram
"kg" = Quantity(1.0 ,Unit(0,1)); // kilo gram
"kg" = Units.Quantity(1.0 ,Units.Unit(0,1)); // kilo gram
"t" = Quantity(1000.0 ,Unit(0,1)); // ton
"t" = Units.Quantity(1000.0 ,Units.Unit(0,1)); // ton
"s" = Quantity(1.0 ,Unit(0,0,1)); // second (internal standard time)
"s" = Units.Quantity(1.0 ,Units.Unit(0,0,1)); // second (internal standard time)
"min" = Quantity(60.0 ,Unit(0,0,1)); // minute
"min" = Units.Quantity(60.0 ,Units.Unit(0,0,1)); // minute
"h" = Quantity(3600.0 ,Unit(0,0,1)); // hour
"h" = Units.Quantity(3600.0 ,Units.Unit(0,0,1)); // hour
"A" = Quantity(1.0 ,Unit(0,0,0,1)); // Ampere (internal standard electric current)
"A" = Units.Quantity(1.0 ,Units.Unit(0,0,0,1)); // Ampere (internal standard electric current)
"mA" = Quantity(0.001 ,Unit(0,0,0,1)); // milli Ampere
"mA" = Units.Quantity(0.001 ,Units.Unit(0,0,0,1)); // milli Ampere
"kA" = Quantity(1000.0 ,Unit(0,0,0,1)); // kilo Ampere
"kA" = Units.Quantity(1000.0 ,Units.Unit(0,0,0,1)); // kilo Ampere
"MA" = Quantity(1.0e6 ,Unit(0,0,0,1)); // Mega Ampere
"MA" = Units.Quantity(1.0e6 ,Units.Unit(0,0,0,1)); // Mega Ampere
"K" = Quantity(1.0 ,Unit(0,0,0,0,1)); // Kelvin (internal standard thermodynamic temperature)
"K" = Units.Quantity(1.0 ,Units.Unit(0,0,0,0,1)); // Kelvin (internal standard thermodynamic temperature)
"mK" = Quantity(0.001 ,Unit(0,0,0,0,1)); // Kelvin
"mK" = Units.Quantity(0.001 ,Units.Unit(0,0,0,0,1)); // Kelvin
"µK" = Quantity(0.000001 ,Unit(0,0,0,0,1)); // Kelvin
"µK" = Units.Quantity(0.000001 ,Units.Unit(0,0,0,0,1)); // Kelvin

"mol" = Quantity(1.0 ,Unit(0,0,0,0,0,1)); // Mole (internal standard amount of substance)


"cd" = Quantity(1.0 ,Unit(0,0,0,0,0,0,1)); // Candela (internal standard luminous intensity)
"mol" = Units.Quantity(1.0 ,Units.Unit(0,0,0,0,0,1)); // Mole (internal standard amount of substance)


"deg" = Quantity(1.0 ,Unit(0,0,0,0,0,0,0,1)); // degree (internal standard angle)
"cd" = Units.Quantity(1.0 ,Units.Unit(0,0,0,0,0,0,1)); // Candela (internal standard luminous intensity)
"rad" = Quantity(180/M_PI ,Unit(0,0,0,0,0,0,0,1)); // radian
"gon" = Quantity(360.0/400.0 ,Unit(0,0,0,0,0,0,0,1)); // gon


"in" = Quantity(25.4 ,Unit(1)); // inch
"deg" = Units.Quantity(1.0 ,Units.Unit(0,0,0,0,0,0,0,1)); // degree (internal standard angle)
"\"" = Quantity(25.4 ,Unit(1)); // inch
"rad" = Units.Quantity(180/M_PI ,Units.Unit(0,0,0,0,0,0,0,1)); // radian
"fo" = Quantity(304.8 ,Unit(1)); // foot
"gon" = Units.Quantity(360.0/400.0 ,Units.Unit(0,0,0,0,0,0,0,1)); // gon
"'" = Quantity(304.8 ,Unit(1)); // foot
"th" = Quantity(0.0254 ,Unit(1)); // thou
"yd" = Quantity(914.4 ,Unit(1)); // yard


"in" = Units.Quantity(25.4 ,Units.Unit(1)); // inch
"\"" = Units.Quantity(25.4 ,Units.Unit(1)); // inch
"fo" = Units.Quantity(304.8 ,Units.Unit(1)); // foot
"'" = Units.Quantity(304.8 ,Units.Unit(1)); // foot
"th" = Units.Quantity(0.0254 ,Units.Unit(1)); // thou
"yd" = Units.Quantity(914.4 ,Units.Unit(1)); // yard


"lb" = Quantity(0.45359237 ,Unit(0,1)); // pound
"lb" = Units.Quantity(0.45359237 ,Units.Unit(0,1)); // pound
"oz" = Quantity(0.0283495231 ,Unit(0,1)); // ounce
"oz" = Units.Quantity(0.0283495231 ,Units.Unit(0,1)); // ounce
"st" = Quantity(6.35029318 ,Unit(0,1)); // Stone
"st" = Units.Quantity(6.35029318 ,Units.Unit(0,1)); // Stone
"cwt" = Quantity(50.80234544 ,Unit(0,1)); // hundredweights
"cwt" = Units.Quantity(50.80234544 ,Units.Unit(0,1)); // hundredweights
}}


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Latest revision as of 10:43, 1 April 2023

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Die Größe ist eine Kombination einer Fließkommazahl und einer Einheit. Sie wird überall in FreeCAD benutzt, um Parameter und alle Arten von Ein- und Ausgaben zu behandeln.

Allgemein

In einem CAD- oder CAE-System ist es sehr wichtig, die Einheit eines Wertes im Auge zu behalten. Viel Ärger kann entstehen, wenn Einheiten durcheinander geworfen oder Ergebnisse in unterschiedlichen Einheitensystemen berechnet werden. Ein berühmtes Missgeschick ist der Verlust des Mars Climate Orbiter durch unterschiedliche Einheiten. Selbst innerhalb des gleichen Einheitensystems kommen die Einheiten in unterschiedlichen Varianten abhängig vom Verwendungszweck. Einfache Beispiele sind die Geschwindigkeit in km/h (Autos), m/s (Robotik) oder mm/min (Fräsen). Ein CAD-System muss verlässlich auf die Einheiten achten. Es muss auch mit ihnen rechnen und auf die richtige Einheit bei speziellen Parametern achten.

Aus diesem Grund wurde das FreeCAD-Mengengerüst geschaffen. Es umfasst den gesamten Code und die Objekte zum Umgang mit Einheiten, Berechnungen, Benutzereingaben, Umrechnung in andere Einheitensysteme und die schöne Ausgabe von Werten und Einheiten. Langfristig sollte in FreeCAD kein Parameter nur eine Zahl sein.

Unterstützte Einheiten

Der FreeCAD-Eingabe-Parser unterstützt eine Vielzahl von Einheiten und Einheitensystemen. FreeCAD unterstützt den griechischen Buchstaben 'µ' für micro, akzeptiert aber auch 'u' als Ersatz. Eine vollständige Liste aller unterstützter Einheiten befindet sich hier.

Die detaillierte Beschreibung findest Du im Code:

  • Mengen-Lexer: [1]
  • Mengedefinition: [2]

Interne Darstellung

Alle physikalischen Einheiten können als eine Kombination der sieben SI-Einheiten ausgedrückt werden:


Ein einfacher Weg, eine Einheit auszudrücken, ist ein Feld mit Integerwerten der Größe 7 (Anzahl der Basiseinheiten), das festlegt, was die Einheit darstellt.

Die Kennzeichnung der sieben Basiseinheiten ist:

  • LÄNGE: [1,0,0,0,0,0,0]
  • MASSE: [0,1,0,0,0,0,0]
  • ZEIT: [0,0,1,0,0,0,0]
  • STROMSTÄRKE: [0,0,0,1,0,0,0]
  • THERMODYNAMISCHE TEMPERATUR: [0,0,0,0,1,0,0]
  • STOFFMENGE: [0,0,0,0,0,1,0]
  • LICHTSTÄRKE: [0,0,0,0,0,0,1]

Mit diesen sieben Einheiten können wir alle abgeleiteten Einheiten (in Guide for the Use of the International System of Units (SI) nachzulesen) ausdrücken und weitere neue nach Bedarf erstellen, wie etwa:

  • MASSENDICHTE: [-3,1,0,0,0,0,0]
  • FLÄCHE: [0,2,0,0,0,0,0]

Weil Winkel pysikalisch dimensionslos, aber trotzdem wichtig für ein CAD-System sind, haben wir eine weitere virtuelle Einheit für den Winkel. Das ergibt einen Vektor von 8 in der FreeCAD-Einheitenkennzeichnung.

Einheitenrechner

Oft muss man Einheiten von einem System in ein anderes umrechnen. Du hast beispielsweise alte Parametertabellen (with wired units). In diesen Fällen bietet FreeCAD ein Umrechnungswerkzeug genannt 'UnitsCalculator', das bei der Übersetzung von Einheiten hilft.

Die Beschreibung im Detail befinden sich hier: Std Einheitenrechner.

InputField

The InputField is a QLineEdit derived Qt widget to handle all kinds of user interaction with quantities and parameters. It features the following properties:

  • parsing arbitrary value/unit input
  • checking on the right unit (if given) and give the user feedback
  • special context menu for operations on quantities/values
  • history management (save the last used values)
  • save often needed values as shortcut in context menu
  • selecting values with mouse wheel and arrow keys (tbd)
  • selecting with middle mouse button and mouse move (tbd)
  • Python integration for usage in Python only dialogs (tbd)

The UnitsCalculator uses the InputField already.

Hauptdokumentation: Eingabefeld

Code:

Python scripting

Das Einheiten- und Mengensystem in FreeCAD ist (wie fast alles) vollständig über Python ansprechbar.

Unit

The Unit class represents the fingerprint of any physical unit. As described in the Basics section a vector of eight numbers is used to represent this fingerprint. The Unit class allows the handling and calculation based on this information.

from FreeCAD import Units

# creating a unit with certain signature
Units.Unit(0,1)      # Mass     (kg)
Units.Unit(1)        # Length   (mm)
Units.Unit(-1,1,-2)  # Pressure (kg/mm*s^2)

# using predefined constants
Units.Unit(Units.Length)
Units.Unit(Units.Mass)
Units.Unit(Units.Pressure)

# parsing unit out of a string
Units.Unit('kg/(m*s^2)')    # Pressure
Units.Unit('Pa')            # the same as combined unit Pascale
Units.Unit('J')             # Joule (work,energy) mm^2*kg/(s^2)

# you can use units from all supported systems of units
Units.Unit('psi')           # imperial pressure
Units.Unit('lb')            # imperial  mass
Units.Unit('ft^2')          # imperial area

# comparing units
Units.Unit(0,1) == Unit(Units.Mass)

# getting type of unit
Units.Unit('kg/(m*s^2)').Type == 'Pressure'

# calculating
Units.Unit('kg') * Units.Unit('m^-1*s^-2') == Units.Unit('kg/(m*s^2)')

The unit is mainly used to describe a certain type of unit for a parameter. Therefore a special property type in FreeCAD can pass a unit to check and ensure the right unit. A unit and a float value is called quantity.

Quantity

from FreeCAD import Units

# to create a quantity you need a value (float) and a unit
Units.Quantity(1.0,Units.Unit(0,1))     # Mass       1.0 kg
Units.Quantity(1.0,Units.Unit(1))       # Length    1.0 mm
Units.Quantity(1.0,Units.Unit(-1,1,-2)) # Pressure  1.0 kg/mm*s^2
Units.Quantity(1.0,Units.Pressure)      # Pressure  1.0 kg/mm*s^2

# you can directly give a signature
Units.Quantity(1.0,0,1)     # Mass       1.0 kg
Units.Quantity(1.0,1)       # Length    1.0 mm
Units.Quantity(1.0,-1,1,-2) # Pressure  1.0 kg/mm*s^2

# parsing quantities out of a string
Units.Quantity('1.0 kg/(m*s^2)') # Pressure
Units.Quantity('1.0 Pa')         # the same as combined Unit Pascale
Units.Quantity('1.0 J')          # Joule (Work,Energy) mm^2*kg/(s^2)

# You can use a point or comma as float delimiter
Units.Quantity('1,0 m')
Units.Quantity('1.0 m')

# you can use units from all supported systems of units
Units.Quantity('1.0 psi')  # imperial pressure
Units.Quantity('1.0 lb')   # imperial mass
Units.Quantity('1.0 ft^2') # imperial area

# the quantity parser can do calculations too
Units.Quantity('360/5 deg')        # splitting circle 
Units.Quantity('1/16 in')          # fractions
Units.Quantity('5.3*6.3 m^2')      # calculating an area
Units.Quantity('1/(log(2.3)/sin(pi)*3.4)+1.8e-3 m')
Units.Quantity('1ft 3in')          # imperial style

# and for sure calculation and comparison
Units.Quantity('1 Pa') * Units.Quantity(2.0) == Units.Quantity('2 Pa')
Units.Quantity('1 m') * Units.Quantity('2 m') == Units.Quantity('2 m^2')
Units.Quantity('1 m') * Units.Quantity('2 ft') + Units.Quantity('2 mm^2')
Units.Quantity('1 m') > Units.Quantity('2 ft')

# accessing the components
Units.Quantity('1 m').Value # get the number (always internal system (mm/kg/s))
Units.Quantity('1 m').Unit  # get the unit
Units.Quantity('1 m') == Units.Quantity( Units.Quantity('1 m').Value , Units.Quantity('1 m').Unit)

# translating the value into other units than the internal system (mm/kg/s)
Units.Quantity('1 km/h').getValueAs('m/s')                  # translate value
Units.Quantity('1 m').getValueAs(2.45,1)                    # translation value and unit signature
Units.Quantity('1 kPa').getValueAs(Units.Pascal)            # predefined standard units 
Units.Quantity('1 MPa').getValueAs(Units.Quantity('N/m^2')) # a quantity

User facing values

Normally in scripts you can use Quantity for all kinds of calculations and checking, but there comes the time you have to output information to the user. You could use getValueAs() to force a certain unit, but normally the user sets his preferred unit-schema in the preferences. This unit-schema does all the translations to the representation the user likes to see. At the moment there are three schemes implemented:

  • 1: Internal (mm/kg/s)
  • 2: MKS (m/kg/s)
  • 3: US customary (in/lb)

There can be easily additional schemas implemented in the future...

The Quantity class has two options to use the actual schema translation:

from FreeCAD import Units

# Use the translated string:
Units.Quantity('1m').UserString           # '1000 mm' in 1; '1 m' in 2; and '1.09361 yr' in 3

This does the job if you only need a string. But sometimes you need more control, e.g. if you want to have a dialog button which dials up and down. Then you need more information about the translation output. Therefore the getUserPreferred() method of quantity is used:

Units.Quantity('22 m').getUserPreferred() # gets a tuple:('22 m', 1000.0, 'm')
Units.Quantity('2  m').getUserPreferred() # Tuple: ('2000 mm', 1.0, 'mm')

Here you get more information using a tuple (three items). You get the string as before, plus the factor of the value and the raw string with only the unit chosen by the translation schema. With this information you can implement a much richer user interaction.

The code of the schema translation can be found here:

Precision

The precision of quantities is within FreeCAD dialogs the number of decimals specified in the preferences. To use this settings for your script (for example in dialogs), you can get it with this code:

import FreeCAD

params = App.ParamGet("User parameter:BaseApp/Preferences/Units")
params.GetInt('Decimals') # returns an int

Anhang

Parser-unterstützte Einheiten

Obwohl alle physikalischen Einheiten mit den sieben SI-Einheiten beschrieben werden können, bestehen die meisten in technischen Bereichen benutzten Einheiten aus üblichen zusammengesetzten Einheiten (wie Pa = N/m^2 Pascal). Deshalb unterstützt der Einheiten-Parser in FreeCAD viele SI- und Imperial-kombinierte Einheiten. Diese Einheiten sind in der Datei src/Base/QuantityParser.l definiert und können in der Zukunft noch erweitert werden.

from FreeCAD import Units

 "nm"  = Units.Quantity(1.0e-6    ,Units.Unit(1));         // nano meter
 "µm"  = Units.Quantity(1.0e-3    ,Units.Unit(1));         // micro meter
 "mm"  = Units.Quantity(1.0       ,Units.Unit(1));         // milli meter
 "cm"  = Units.Quantity(10.0      ,Units.Unit(1));         // centi meter
 "dm"  = Units.Quantity(100.0     ,Units.Unit(1));         // deci meter
 "m"   = Units.Quantity(1.0e3     ,Units.Unit(1));         // meter
 "km"  = Units.Quantity(1.0e6     ,Units.Unit(1));         // kilo meter
 "l"   = Units.Quantity(1000000.0 ,Units.Unit(3));         // liter dm^3
                                                  
 "µg"  = Units.Quantity(1.0e-9    ,Units.Unit(0,1));       // micro gram
 "mg"  = Units.Quantity(1.0e-6    ,Units.Unit(0,1));       // milli gram
 "g"   = Units.Quantity(1.0e-3    ,Units.Unit(0,1));       // gram
 "kg"  = Units.Quantity(1.0       ,Units.Unit(0,1));       // kilo gram
 "t"   = Units.Quantity(1000.0    ,Units.Unit(0,1));       // ton
                                                  
 "s"   = Units.Quantity(1.0       ,Units.Unit(0,0,1));     // second (internal standard time)
 "min" = Units.Quantity(60.0      ,Units.Unit(0,0,1));     // minute
 "h"   = Units.Quantity(3600.0    ,Units.Unit(0,0,1));     // hour  
                                                  
 "A"   = Units.Quantity(1.0       ,Units.Unit(0,0,0,1));   // Ampere (internal standard electric current)
 "mA"  = Units.Quantity(0.001     ,Units.Unit(0,0,0,1));   // milli Ampere         
 "kA"  = Units.Quantity(1000.0    ,Units.Unit(0,0,0,1));   // kilo Ampere         
 "MA"  = Units.Quantity(1.0e6     ,Units.Unit(0,0,0,1));   // Mega Ampere         
                                                  
 "K"   = Units.Quantity(1.0       ,Units.Unit(0,0,0,0,1)); // Kelvin (internal standard thermodynamic temperature)
 "mK"  = Units.Quantity(0.001     ,Units.Unit(0,0,0,0,1)); // Kelvin         
 "µK"  = Units.Quantity(0.000001  ,Units.Unit(0,0,0,0,1)); // Kelvin         

 "mol" = Units.Quantity(1.0       ,Units.Unit(0,0,0,0,0,1)); // Mole (internal standard amount of substance)        

 "cd"  = Units.Quantity(1.0       ,Units.Unit(0,0,0,0,0,0,1)); // Candela (internal standard luminous intensity)        

 "deg" = Units.Quantity(1.0         ,Units.Unit(0,0,0,0,0,0,0,1)); // degree (internal standard angle)
 "rad" = Units.Quantity(180/M_PI    ,Units.Unit(0,0,0,0,0,0,0,1)); // radian         
 "gon" = Units.Quantity(360.0/400.0 ,Units.Unit(0,0,0,0,0,0,0,1)); // gon         

 "in"  = Units.Quantity(25.4        ,Units.Unit(1));       // inch
 "\""  = Units.Quantity(25.4        ,Units.Unit(1));       // inch
 "fo"  = Units.Quantity(304.8       ,Units.Unit(1));       // foot
 "'"   = Units.Quantity(304.8       ,Units.Unit(1));       // foot
 "th"  = Units.Quantity(0.0254      ,Units.Unit(1));       // thou
 "yd"  = Units.Quantity(914.4       ,Units.Unit(1));       // yard

 "lb"  = Units.Quantity(0.45359237   ,Units.Unit(0,1));    // pound
 "oz"  = Units.Quantity(0.0283495231 ,Units.Unit(0,1));    // ounce
 "st"  = Units.Quantity(6.35029318   ,Units.Unit(0,1));    // Stone
 "cwt" = Units.Quantity(50.80234544  ,Units.Unit(0,1));    // hundredweights