Expressions/es: Difference between revisions

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<languages/>
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<span id="Overview"></span>
<div style="float:right; clean:both; margin-left:0.5em;">__TOC__</div>
==Resumen==


Es posible definir propiedades utilizando expresiones matemáticas. En la interfaz gráfica de usuario, los cuadros de giro o campos de entrada que están vinculados a las propiedades contienen un icono azul [[Image:Bound-expression.svg|24px]]. Haciendo clic en el icono o escribiendo el signo igual {{KEY|&#61;}} aparece el editor de expresiones para esa propiedad en particular.
{{Version|0.16}}


Es una expresión matemática que usa la notación de los [[#Supported_operators|operadores]], [[#Supported_functions|funciones]] y [[#Supported_constants|constantes predefinidas]] matemáticas estándar como se describe a continuación. Además, la expresión puede hacer referencia a otras propiedades de objetos, y también utilizar [[#Conditional_expressions|condicionales]]. Los números en una expresión pueden tener una [[#Units|unidad]] opcional adjunta.
It is now possible to define properties using mathematical expressions. From the GUI, spin boxes or input fields that are bound to properties contain a blue icon [[Image:Sketcher_Expressions.png|24px]]. Clicking on the icon or typing the equal sign (=) brings up the expression editor for that particular property.


Los números pueden usar ya sea una coma {{incode|,}} o un punto decimal {{incode|.}} para separar los dígitos enteros de los decimales. Cuando se usa el marcador decimal, ''debe'' ser seguido por al menos un dígito. Por lo tanto, las expresiones {{incode | 1.+2.}} y {{incode | 1,+2,}} son inválidas, pero {{incode | 1.0+2.0}} y {{incode | 1,0+2,0}} son válidas.
A FreeCAD expression is a mathematical expression following notation for the standard mathematical operators and functions as described below. In addition, the expression may reference other properties, and also use conditionals. Numbers in an expression may have an optional unit attached to them.


Los operadores y las funciones son conscientes de la unidad y requieren combinaciones válidas de unidades, si se suministran. Por ejemplo, {{incode | 2mm+4mm}} es una expresión válida, mientras que {{incode | 2mm+4}} no lo es. Esto también se aplica a las referencias a propiedades de objetos que tienen unidades, como las propiedades de longitud. Por lo tanto, {{incode|Pad001.Length + 1}} es inválido ya que agrega un número puro a una propiedad con unidades de longitud, se requiere {{incode|Pad001.Length + 1mm}}.
Numbers may use either a comma ',' or a decimal point '.' separating whole digits from decimals.
When the decimal marker is used, it ''must'' be followed by at least one digit.
Thus, the expressions '''1.+2.''' and '''1,+2,''' are invalid, but '''1.0+2.0''' and '''1,0+2,0''' are valid.


Algunos errores relacionados con las unidades pueden parecer poco intuitivos, ya que las expresiones se rechazan o producen resultados que no coinciden con las unidades de la propiedad que se establece. Aquí hay unos ejemplos:
The constants ''pi'' and ''e'' are predefined, and must be written in lowercase.


{{incode|1/2mm}} no se interpreta como medio milímetro sino como {{incode|1/(2mm)}}, lo que da como resultado: {{incode|0.5 mm^-1}}.
Operators and functions are unit-aware, and require valid combinations of units, if supplied. For example, 2mm+4mm is a valid expression, while 2mm+4 is not (the reason for this is that an expression like 1in + 4 will most likely be interpreted as 1in + 4in by humans, but all units are converted to the SI system internally, and the system is not able to guess this).


{{incode|sqrt(2)mm}} no es válido porque la llamada a la función no es un número. Esto debe ingresarse como {{incode|sqrt(2) * 1mm}}.
You can refer to an object by its {{incode|Name}} or by its {{incode|Label}}. In the case of a {{incode|Label}}, it must be enclosed in double {{incode|<<}} and {{incode|>>}} symbols, such as {{incode|<<Label>>}}.


<span id="Function_arguments"></span>
Then you can reference any numerical property of this object. For example, to refer to a Cylinder's height, you may use {{incode|Cylinder.Height}} or {{incode|<<Long_name_of_cylinder>>.Height}}.
===Argumentos de la función===


Múltiples argumentos a una función pueden estar separados por un punto y coma {{incode |;}} o una coma <em> seguida por un espacio </em> {{incode |, }}. En el último caso, la coma se convierte a un punto y coma después de la entrada. Cuando se usa un punto y coma, no es necesario un espacio final.
== Supported Operators ==


Los argumentos pueden incluir referencias a las celdas en una hoja de cálculo. Una referencia de celda consiste en la letra mayúscula de fila de la celda seguida de su número de columna, por ejemplo {{incode | A1}}. También se puede hacer referencia a una celda utilizando el alias de la celda, por ejemplo, {{incode|Spreadsheet.MyPartWidth}}.
The following operators are supported:

{| class="wikitable float-right mw-collapsible mw-uncollapsed"
<span id="Referencing_objects"></span>
!style="width: 33%;"|Operator
===Referencia de objetos===

Como ya se mostró arribam puede hacer referencia a un objeto por su {{PropertyData | Name}}. Pero también puedes usar su {{PropertyData | Label}}. En el caso de un {{PropertyData | Label}}, debe estar encerrado en doble símbolos {{incode | <<}} y {{incode | >>}}, como {{incode | <<Label>>}}.

Puede referenciar cualquier propiedad de un objeto. Por ejemplo, para referenciar la altura de un Cilindro puede usar {{incode|Cylinder.Height}} o {{incode|<<Label_of_cylinder>>.Height}}.

Para más información de como referenciar objetos, vea [[#Referencia_a_los_datos_CAD|Referencia a los datos CAD]].
{{Top}}
<span id="Supported_constants"></span>
== Constantes soportadas ==

Las siguientes constantes están soportadas.

{| class="wikitable"
!style="width: 33%;"|Constant
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| style="text-align:center;" | '''e'''
| +
| [https://en.wikipedia.org/wiki/Addition Addition]
| [https://es.wikipedia.org/wiki/N%C3%BAmero_e Número de Euler]
|-
| -
| [https://en.wikipedia.org/wiki/Subtraction Subtraction]
|-
| *
| [https://en.wikipedia.org/wiki/Multiplication Multiplication]
|-
| /
| [https://en.wikipedia.org/wiki/Division_(mathematics) Division]
|-
|-
| style="text-align:center;" | '''pi'''
| ^
| [https://en.wikipedia.org/wiki/Exponentiation Exponentiation]
| [https://es.wikipedia.org/wiki/N%C3%BAmero_%CF%80 Pi]
|}
|}
{{Top}}
<span id="Supported_operators"></span>
== Operadores soportados ==


Los siguientes operadores son soportados.
== Supported Constants==


{| class="wikitable"
The following constants are supported:
!style="width: 33%;"|Operator
{| class="wikitable float-right mw-collapsible mw-uncollapsed"
!style="width: 33%;"|Constant
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| style="text-align:center;" |'''+'''
| e
| [https://en.wikipedia.org/wiki/E_(mathematical_constant) Euler's number]
| [https://es.wikipedia.org/wiki/Adici%C3%B3n_(matem%C3%A1tica) Suma]
|-
|-
| style="text-align:center;" |'''-'''
| pi
| [https://en.wikipedia.org/wiki/Pi Pi]
| [https://es.wikipedia.org/wiki/Resta Resta]
|-
| style="text-align:center;" | '''*'''
| [https://es.wikipedia.org/wiki/Multiplicaci%C3%B3n Multiplicación]
|-
| style="text-align:center;" | '''/'''
| [https://es.wikipedia.org/wiki/Divisi%C3%B3n_(matem%C3%A1tica) Division] de punto flotante
|-
| style="text-align:center;" | '''%'''
| [https://es.wikipedia.org/wiki/Resto Residuo]
|-
| style="text-align:center;" | '''^'''
| [https://es.wikipedia.org/wiki/Potenciaci%C3%B3n Potenciación]
|}
|}
{{Top}}
<span id="Supported_functions"></span>
== Funciones soportadas ==


<span id="General_mathematical_functions"></span>
== Supported Functions ==
=== Funciones matemáticas generales ===


Las siguientes funciones matemáticas son soportadas:
=== General Mathematical Functions ===


<span id="Trigonometric_functions"></span>
The mathematical functions listed below are available.
==== Funciones trigonométricas ====


Las [https://es.wikipedia.org/wiki/Funci%C3%B3n_trigonom%C3%A9trica Funciones trigonométricas] utilizan el grado sexagesimal como unidad predeterminada. Para radianes, agregue {{incode|rad}} después del <em>primer</em> valor de una expresión. Entonces, por ejemplo, {{incode|cos(45)}} es lo mismo que {{incode|cos(pi rad / 4)}}. Las expresiones en grados pueden usar {{incode|deg}} o {{incode|°}}, por ejemplo, {{incode|360deg - atan2(3; 4)}} o {{incode|360&deg; - atan2(3; 4)}}. Si una expresión no tiene unidades y debe convertirse a grados o radianes para garantizar la compatibilidad, multiplíquela por {{incode|1deg}}, {{incode|1°}} o {{incode|1rad}} como apropiado, por ejemplo, {{incode|(360 - X) * 1deg}}; {{incode|(360 - X) * 1°}}; {{incode|(0,5 + pi / 2) * 1rad}}.
Multiple arguments to a function may be separated by either a semicolon ';' or a comma <em>followed by a space</em> ', '. In the latter case, the comma is converted to a semicolon after entry. When a semicolon is used, no trailing space is necessary.


{| class="wikitable"
[https://en.wikipedia.org/wiki/Trigonometric_functions Trigonometric functions] use degree as their default unit. For radian measure, add '''rad''' following the <em>first</em> value in an expression. So e.g. '''cos(45)''' is the same as '''cos(pi rad / 4)'''.<br/>
!style="width: 15%;"|Function
These trigonometric functions are supported:
!style="width: 55%;"|Description
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Function
!style="width: 30%;"|Input range
!style="width: 33%;"|Description
!style="width: 33%;"|Value range
|-
|-
| acos(x)
| {{incode|acos(x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc cosine]
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc cosine]
| -1 <= x <= 1
| -1 <= x <= 1
|-
|-
| asin(x)
| {{incode|asin(x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc sine]
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc sine]
| -1 <= x <= 1
| -1 <= x <= 1
|-
|-
| atan(x)
| {{incode|atan(x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent]
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent], return value in the range -90° < value < 90°
| all
| all
|-
|-
| atan2(x, y)
| {{incode|atan2(y; x)}}
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent] of ''x/y''
| [https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Basic_properties Arc tangent] of ''y/x'' accounting for quadrant, return value in the range -180° < value <= 180°
| all, except y = 0
| all, the invalid input x = y = 0 returns 0
|-
|-
| cos(x)
| {{incode|cos(x)}}
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Cosine]
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Cosine]
| all
| all
|-
|-
| cosh(x)
| {{incode|cosh(x)}}
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic cosine]
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic cosine]
| all
| all
|-
|-
| sin(x)
| {{incode|sin(x)}}
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Sine]
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Sine]
| all
| all
|-
|-
| sinh(x)
| {{incode|sinh(x)}}
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic sine]
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic sine]
| all
| all
|-
|-
| tan(x)
| {{incode|tan(x)}}
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Tangent]
| [https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions Tangent]
| all, except of x = n·90 with n = integer
| all, except x = n*90 with n = odd integer
|-
|-
| tanh(x)
| {{incode|tanh(x)}}
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic tangent]
| [https://en.wikipedia.org/wiki/Hyperbolic_function#Trigonometric_definitions Hyperbolic tangent]
| all
| all
|-
| {{incode|hypot(x; y)}}
| [https://en.wikipedia.org/wiki/Pythagorean_addition Pythagorean addition] ('''hypot'''enuse), e.g. hypot(4; 3) = 5
| x and y >= 0
|-
| {{incode|cath(x; y)}}
| Given hypotenuse, and one side, returns other side of triangle, e.g. cath(5; 3) = 4
| x >= y >= 0
|}
|}


<span id="Exponential_and_logarithmic_functions"></span>
These functions for exponentiation and logarithmization are supported:
==== Funciones exponenciales y logarítmicas ====
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable"
!style="width: 33%;"|Function
!style="width: 33%;"|Function
!style="width: 33%;"|Description
!style="width: 33%;"|Description
!style="width: 33%;"|Value range
!style="width: 33%;"|Input range
|-
|-
| exp(x)
| {{incode|exp(x)}}
| [https://en.wikipedia.org/wiki/Exponential_function#Formal_definition Exponential function]
| [https://en.wikipedia.org/wiki/Exponential_function#Formal_definition Exponential function]
| all
| all
|-
|-
| log(x)
| {{incode|log(x)}}
| [https://en.wikipedia.org/wiki/Natural_logarithm Natural logarithm]
| [https://en.wikipedia.org/wiki/Natural_logarithm Natural logarithm]
| x > 0
| x > 0
|-
|-
| log10(x)
| {{incode|log10(x)}}
| [https://en.wikipedia.org/wiki/Common_logarithm Common logarithm]
| [https://en.wikipedia.org/wiki/Common_logarithm Common logarithm]
| x > 0
| x > 0
|-
|-
| pow(x, y)
| {{incode|pow(x; y)}}
| [https://en.wikipedia.org/wiki/Exponentiation Exponentiation]
| [https://en.wikipedia.org/wiki/Exponentiation Exponentiation]
| all
| all
|-
|-
| sqrt(x)
| {{incode|sqrt(x)}}
| [https://en.wikipedia.org/wiki/Square_root Square root]
| [https://en.wikipedia.org/wiki/Square_root Square root]
| x >= 0
| x >= 0
|-
| {{incode|cbrt(x)}} {{Version|0.21}}
| [https://en.wikipedia.org/wiki/Cube_root Cubic root]
| all
|}
|}


<span id="Rounding,_truncation_and_remainder_functions"></span>
These functions for rounding, truncation and remainder are supported:
==== Funciones de redondeo, truncamiento y resto. ====
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable"
!style="width: 20%;"|Function
!style="width: 20%;"|Function
!style="width: 55%;"|Description
!style="width: 55%;"|Description
!style="width: 25%;"|Value range
!style="width: 25%;"|Input range
|-
|-
| abs(x)
| {{incode|abs(x)}}
| [https://en.wikipedia.org/wiki/Absolute_value Absolute value]
| [https://en.wikipedia.org/wiki/Absolute_value Absolute value]
| all
| all
|-
|-
| ceil(x)
| {{incode|ceil(x)}}
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Ceiling function] smallest integer value greater than or equal to x
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Ceiling function], smallest integer value greater than or equal to x
| all
| all
|-
|-
| floor(x)
| {{incode|floor(x)}}
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Floor function], largest integer value less than or equal to x
| [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions Floor function], largest integer value less than or equal to x
| all
| all
|-
|-
| mod(x, y)
| {{incode|mod(x; y)}}
| [https://en.wikipedia.org/wiki/Remainder Remainder] after dividing ''x'' by ''y''
| [https://en.wikipedia.org/wiki/Remainder Remainder] after dividing ''x'' by ''y'', sign of result is that of the dividend.
| all, except y = 0
| all, except y = 0
|-
|-
| round(x)
| {{incode|round(x)}}
| [https://en.wikipedia.org/wiki/Rounding Rounding] to the nearest integer
| [https://en.wikipedia.org/wiki/Rounding Rounding] to the nearest integer
| all
| all
|-
|-
| trunc(x)
| {{incode|trunc(x)}}
| [https://en.wikipedia.org/wiki/Truncation Truncation] to the nearest integer
| [https://en.wikipedia.org/wiki/Truncation Truncation] to the nearest integer in the direction of zero
| all
| all
|}
|}
{{Top}}
<span id="Statistical_/_aggregate_functions"></span>
=== Funciones estadísticas/agregadas ===


[https://en.wikipedia.org/wiki/Aggregate_function Aggregate functions] take one or more arguments.<br>
=== Statistical / Aggregate Functions ===
[https://en.wikipedia.org/wiki/Aggregate_function Aggregate functions] take one or more arguments, separated by a semicolon ';' or a comma ''and'' a space ', '.<br/>
Arguments may include references to cells in a spreadsheet. Cell references consist of the (CAPITAL) row letter followed by the column number.<br/>
Arguments may include ranges of cells (two cell references separated by a colon), for example '''average(B1:B8)'''.


Individual arguments to aggregate functions may consist of ranges of cells. A range of cells is expressed as two cell references separated by a colon {{Incode|:}}, for example {{Incode|average(B1:B8)}} or {{Incode|sum(A1:A4; B1:B4)}}.
These aggregate functions are supported:
The cell references may also use cell aliases, for example {{Incode|average(StartTemp:EndTemp)}}.
{| class="wikitable float-right mw-collapsible mw-collapsed"

Las siguientes funciones agregadas son soportadas:

{| class="wikitable"
!style="width: 20%;"|Function
!style="width: 20%;"|Function
!style="width: 55%;"|Description
!style="width: 55%;"|Description
!style="width: 25%;"|Value range
!style="width: 25%;"|Input range
|-
|-
| average(x:y)
| {{incode|average(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Arithmetic_mean Arithmetic mean] of values in cells x through y; sum(x:y) / count(x:y)
| [https://en.wikipedia.org/wiki/Arithmetic_mean Average] value of the arguments, same as sum(a; b; c; ...) / count(a; b; c; ...)
| all
| all
|-
|-
| count(x:y)
| {{incode|count(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Counting Counting] of cells from x through y
| [https://en.wikipedia.org/wiki/Counting Count] of the arguments, typically used for cell ranges
| all
| all
|-
|-
| max(x:y)
| {{incode|max(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Maxima_and_minima Maximum] value in cells x through y
| [https://en.wikipedia.org/wiki/Maxima_and_minima Maximum] value of the arguments
| all
| all
|-
|-
| min(x:y)
| {{incode|min(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Maxima_and_minima Minimum] value in cells x through y
| [https://en.wikipedia.org/wiki/Maxima_and_minima Minimum] value of the arguments
| all
| all
|-
|-
| stddev(x:y)
| {{incode|stddev(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Standard_deviation Standard deviation] of values in cells x through y
| [https://en.wikipedia.org/wiki/standard_deviation Standard deviation] of the values of the arguments
| all
| all
|-
|-
| sum(x: y)
| {{incode|sum(a; b; c; ...)}}
| [https://en.wikipedia.org/wiki/Summation Sum] of values in cells x through y
| [https://en.wikipedia.org/wiki/Summation Sum] of the values of the arguments, typically used for cell ranges
| all
| all
|}
|}
{{Top}}
<span id="String_manipulation"></span>
=== Manipulación de cadenas ===


<span id="String_identification"></span>
== Conditional Expressions ==
==== Identificación de cadena ====

Las cadenas se identifican en las expresiones rodeándolas con comillas angulares dobles de apertura/cierre (al igual que las etiquetas).

En el siguiente ejemplo, "TEXTO" se reconoce como una cadena: {{incode|<<TEXTO>>}}

<span id="String_concatenation"></span>
==== Concatenación de cadenas ====

Las cadenas se pueden concatenar usando el signo '+'.

El siguiente ejemplo {{incode|<<MI>> + <<TEXTO>>}} se concatenará con "MITEXTO".

<span id="String_conversion"></span>
==== Conversión de cadenas ====

Los valores numéricos se pueden convertir en cadenas con la función {{incode|str}}:

{{incode|str(Box.Length.Value)}}

<span id="String_formatting"></span>
==== Formato de cadena ====

El formato de cadena se admite utilizando el estilo (antiguo) % de Python.

Todos los especificadores % tal como se definen en la [https://docs.python.org/3/library/stdtypes.html#printf-style-string-formatting documentación de Python].

Como ejemplo, supongamos que tiene un cubo predeterminado de 10 mm de lado llamado 'Box' (nombramiento predeterminado de FreeCAD), la siguiente expresión {{incode|<<Longitud del cubo: %s>> % Box.Length}} se expandirá a "Longitud del cubo: 10.0 mm"

Para más de un especificador % utilice la siguiente sintaxis: {{incode|<<La longitud del cubo es %s y el ancho es %s>> % tuple(Box.Length; Box.Width)}}. O use concatenación: {{incode|<<La longitud del cubo es %s>> % Box.Length + << y el ancho es %s>> % Box.Width}}. Ambos se expandirán a "La longitud del cubo es de 10.0 mm y el ancho es de 10.0 mm".

Está disponible un archivo de muestra de FreeCAD que utiliza formato de cadena [https://forum.freecadweb.org/viewtopic.php?f=8&t=58657 en el foro]
{{Top}}
<span id="Object_creation_functions"></span>
=== Funciones de creación de objetos ===

Los siguientes objetos se pueden crear en expresiones utilizando las siguientes funciones:

{| class="wikitable"
! Type
! Function
! Description
|-
| {{incode|Tuple}}
| {{incode|tuple(a; b; ...)}}
| Example: {{incode|tuple(2; 1; 2)}}
|-
| {{incode|List}}
| {{incode|list(a; b; ...)}}
| Example: {{incode|list(2; 1; 2)}}
|-
| rowspan="2" | [[Vector API|{{incode|Vector}}]]
| {{incode|vector(x; y; z)}}
| rowspan="2" | Create a vector using three unit-less or {{incode|Length}} unit values.
Example: {{incode|vector(2; 1; 3)}}
|-
| {{incode|create(<<vector>>; x; y; z)}}
|-
| rowspan="2" | [[Matrix API|{{incode|Matrix}}]]
|
matrix(
a<sub>11</sub>; a<sub>12</sub>; a<sub>13</sub>; a<sub>14</sub>;
a<sub>21</sub>; a<sub>22</sub>; a<sub>23</sub>; a<sub>24</sub>;
a<sub>31</sub>; a<sub>32</sub>; a<sub>33</sub>; a<sub>34</sub>;
a<sub>41</sub>; a<sub>42</sub>; a<sub>43</sub>; a<sub>44</sub>
)
| rowspan="2" | Create a 4x4 matrix in [https://en.wikipedia.org/wiki/Row-_and_column-major_order row-major order]:
<math>
\begin{bmatrix}
a_{11} & a_{12} & a_{13} & a_{14} \\
a_{21} & a_{22} & a_{23} & a_{24} \\
a_{31} & a_{32} & a_{33} & a_{34} \\
a_{41} & a_{42} & a_{43} & a_{44} \\
\end{bmatrix}
</math>

Se puede proporcionar un mínimo de 1 argumento, como {{incode|matrix(1)}}, que crea una matriz de identidad.

Example: {{incode|matrix(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16)}}
|-
| {{incode|create(<<matrix>>; a<sub>11</sub>; a<sub>12</sub>; ...; a<sub>44</sub>)}}
|-
| rowspan="4" | {{incode|Rotation}}
| {{incode|rotation(axis; angle)}}
| rowspan="4" | Create a {{incode|Rotation}} by specifying its {{incode|axis}} ({{incode|Vector}}) and {{incode|angle}} ({{incode|Angle}} unit or unit-less), or three Euler angles {{incode|α}}, {{incode|β}}, {{incode|γ}}.
Examples:
* {{incode|rotation(vector(0; 1; 0); 45)}}
* {{incode|create(<<rotation>>; 30; 30; 30)}}
|-
| {{incode|rotation(α; β; γ)}}
|-
| {{incode|create(<<rotation>>; axis; angle)}}
|-
| {{incode|create(<<rotation>>; α; β; γ)}}
|-
| rowspan="5" | [[Placement_API|{{incode|Placement}}]]
| {{incode|placement(base; rotation)}}
| rowspan="5" | Create a {{incode|Placement}} with various parameters, including:
* {{incode|base}}: base location ({{incode|Vector}})
* {{incode|center}}: center location ({{incode|Vector}})
* {{incode|rotation}}: {{incode|Rotation}}
* {{incode|axis}}: Rotation axis ({{incode|Vector}})
* {{incode|angle}}: Rotation angle (unit-less or {{incode|Angle}} unit value)
* {{incode|matrix}}: {{incode|Matrix}}

Examples:
* {{incode|placement(vector(2; 1; 3); rotation(vector(0; 0; 1); 45))}}
* {{incode|create(<<placement>>; create(<<vector>>; 2; 1; 2); create(<<rotation>>; create(<<vector>>; 0; 1; 0); 45))}}
|-
| {{incode|placement(base; rotation; center)}}
|-
| {{incode|placement(base; axis; angle)}}
|-
| {{incode|placement(matrix)}}
|-
| {{incode|create(<<placement>>; ...)}}
|}
{{Top}}
<span id="Vector_functions"></span>
=== Funciones vectoriales ===

<div class="mw-translate-fuzzy">
Funciones: {{Version|0.22}}.
</div>

{| class="wikitable"
! Function / Operator
! Description
|-
| {{incode|v1 + v2}}
| Add two vectors.
|-
| {{incode|v1 - v2}}
| Subtract two vectors.
|-
| {{incode|v * s}}
| Uniformly scale a vector by {{incode|s}}.
|-
| {{incode|vangle(v1; v2)}}
| Angle between two vectors in degrees.
|-
| {{incode|vcross(v1; v2)}}
| Cross product of two vectors <math>v_1 \times v_2</math>.
|-
| {{incode|v1 * v2}}
| rowspan="2" | Dot product of two vectors <math>v_1 \cdot v_2</math>.
|-
| {{incode|vdot(v1; v2)}}
|-
| {{incode|vlinedist(v1; v2; v3)}}
| Distance between vector {{incode|v1}} and a line through {{incode|v2}} in direction {{incode|v3}}.
|-
| {{incode|vlinesegdist(v1; v2; v3)}}
| Distance between vector {{incode|v1}} and the closest point on a line segment from {{incode|v2}} to {{incode|v3}}.
|-
| {{incode|vlineproj(v1; v2; v3)}}
| Project vector {{incode|v1}} on a line through {{incode|v2}} in direction {{incode|v3}}.
|-
| {{incode|vnormalize(v)}}
| Normalize a vector to a unit vector.
|-
| {{incode|vplanedist(v1)}}
| Distance between vector {{incode|v1}} and a plane defined by a point {{incode|v2}} and a normal {{incode|v3}}.
|-
| {{incode|vplaneproj(v1)}}
| Project vector {{incode|v1}} on a plane defined by a point {{incode|v2}} and a normal {{incode|v3}}.
|-
| {{incode|vscale(v; sx; sy; sz)}}
| rowspan="4" | Non-uniformly scale a vector by {{incode|sx}} in the X direction, {{incode|sy}} in the Y direction, and {{incode|sz}} in the Z direction.
|-
| {{incode|vscalex(v; sx)}}
|-
| {{incode|vscaley(v; sy)}}
|-
| {{incode|vscalez(v; sz)}}
|}
{{Top}}
<span id="Matrix_functions"></span>
=== Funciones matriciales ===

{{incode|Rotation}} and {{incode|Placement}} can each be represented by a {{incode|Matrix}}. The following functions all take in a {{incode|Matrix}}, {{incode|Rotation}}, or {{incode|Placement}} as their first parameter denoted in the table below by {{incode|m}}. The type of the returned object is the same as the object supplied in the first argument except when using {{incode|mtranslate}} on a {{incode|Rotation}}, in which case a {{incode|Placement}} will be returned.

{| class="wikitable"
! Function
! Description
|-
| {{incode|minvert(m)}}
| Calculate the [https://en.wikipedia.org/wiki/Invertible_matrix Inverse matrix].
|-
| {{incode|mrotate(m; rotation)}}
| rowspan="3" | [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] by either:
* a {{incode|Rotation}}
* an axis ({{incode|Vector}}) and an angle ({{incode|Angle}} unit or unit-less)
* three Euler angles {{incode|α}}, {{incode|β}}, {{incode|γ}}
|-
| {{incode|mrotate(m; axis; angle)}}
|-
| {{incode|mrotate(m; α; β; γ)}}
|-
| {{incode|mrotatex(m; angle)}}
| [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] around the X axis.
|-
| {{incode|mrotatey(m; angle)}}
| [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] around the Y axis.
|-
| {{incode|mrotatez(m; angle)}}
| [https://en.wikipedia.org/wiki/Transformation_matrix#Rotation_2 Rotate] around the Z axis.
|-
| {{incode|mtranslate(m; vector)}}
| rowspan="2" | [https://en.wikipedia.org/wiki/Translation_(geometry)#Matrix_representation Translate] by a {{incode|vector}} ({{incode|Vector}}) or X, Y, Z values. If a {{incode|Rotation}} is translated, the returned object is a {{incode|Placement}}.
|-
| {{incode|mtranslate(m; x; y; z)}}
|-
| {{incode|mscale(m; vector)}}
| rowspan="2" | [https://en.wikipedia.org/wiki/Scaling_(geometry)#Matrix_representation Scale] by a {{incode|vector}} ({{incode|Vector}}) or X, Y, Z values.
|-
| {{incode|mscale(m; x; y; z)}}
|}
{{Top}}
<span id="Conditional_expressions"></span>
== Expresiones condicionales ==


Conditional expressions are of the form '''condition ? resultTrue : resultFalse'''. The condition is defined as an expression that evaluates to either '0' (false) or non-zero (true).
Conditional expressions are of the form {{incode|condition ? resultTrue : resultFalse}}. The condition is defined as an expression that evaluates to either {{incode|0}} (false) or non-zero (true).


The following [https://en.wikipedia.org/wiki/Relational_operator#Standard_relational_operators relational operators] are defined:
The following [https://en.wikipedia.org/wiki/Relational_operator#Standard_relational_operators relational operators] are defined:
{| class="wikitable float-right mw-collapsible mw-uncollapsed"
{| class="wikitable"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| style="text-align:center;" | '''=='''
| ==
| equal to
| equal to
|-
|-
| style="text-align:center;" | '''!='''
| !=
| not equal to
| not equal to
|-
|-
| style="text-align:center;" | '''>'''
| >
| greater than
| greater than
|-
|-
| style="text-align:center;" | '''<'''
| <
| less than
| less than
|-
|-
| style="text-align:center;" | '''>='''
| >=
| greater than or equal to
| greater than or equal to
|-
|-
| style="text-align:center;" | '''<='''
| <=
| less than or equal to
| less than or equal to
|}
|}
{{Top}}
<span id="Units"></span>
== Unidades ==


Las unidades se pueden utilizar directamente en expresiones. El analizador los conecta con el valor anterior. Entonces {{incode|2mm}} o {{incode|2 mm}} es válido mientras que {{incode|mm}} no es válido porque no hay un valor anterior.
== Units ==

Units can directly be used in expressions. The parser connects them to the previous value. So ''''2mm'''' or ''''2 mm'''' is valid while '''' mm'''' is invalid because there is no preceding value.


All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.<br/>
All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.<br/>
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number ''1.5'' and refer to it for a pad height. This only works because the pad height predefines the unit ''mm'' that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. '''Sketch1.Constraints.Width - Spreadsheet.B1''' because ''Sketch1.Constraints.Width'' has a unit and ''Spreadsheet.B1'' has not.
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number {{incode|1.5}} and refer to it for a pad height. This only works because the pad height predefines the unit {{incode|mm}} that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. {{incode|Sketch1.Constraints.Width - Spreadsheet.B1}} because {{incode|Sketch1.Constraints.Width}} has a unit and {{incode|Spreadsheet.B1}} has not.


Se pueden ingresar directamente unidades con exponentes. Entonces, por ejemplo, {{incode|mm^3}} se reconocerá como mm³ y {{incode|m^3}} se reconocerá como m³.
Units with exponents can directly be entered. So e.g. '''mm^3''' will be recognized as mm³ and '''m^3''' will be recognized as m³.


If you have a variable with a name of a unit you must put the variable into '''<< >>''' to prevent that it will be recognized as unit. For example if you have the dimension ''''Sketch.Constraints.A'''' it would be recognized as unit ampere. Therefore you must write it in the expression as ''''Sketch.Constraints.<<A>>''''.
Si tienes una variable cuyo nombre es el de una unidad debes poner la variable entre {{incode|<< >>}} para evitar que sea reconocida como una unidad. Por ejemplo, si tiene la dimensión {{incode|Sketch.Constraints.A}}, se reconocerá como la unidad amperio. Por lo tanto debes escribirlo en la expresión como {{incode|Sketch.Constraints.<<A>>}}.


El analizador de expresiones reconoce las siguientes unidades:
The following units are recognized by the expression parser:


<span id="Amount_of_substance"></span>
Amount of substance:
=== Cantidad de sustancia ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
| mmol
| Milli[https://en.wikipedia.org/wiki/Mole_(unit) mole]
|-
|-
| mol
| mol
Line 258: Line 532:
|}
|}


Angle:
<span id="Angle"></span>
=== Ángulo ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| °
| °
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit ''deg''
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit deg
|-
|-
| deg
| deg
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit ''°''
| [https://en.wikipedia.org/wiki/Degree_(angle) Degree]; alternative to the unit °
|-
|-
| rad
| rad
Line 276: Line 552:
|-
|-
| S
| S
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]; alternative to the unit ″
|-
|-
| ″
| ″
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]; alternative to the unit ''S''
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Second of arc]; alternative to the unit S
|-
|-
| M
| M
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]; alternative to the unit ′
|-
|-
| ′
| ′
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]; alternative to the unit ''M''
| [https://en.wikipedia.org/wiki/Minute_and_second_of_arc Minute of arc]; alternative to the unit M
|}
|}


Current:
<span id="Current"></span>
=== Corriente ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 306: Line 584:
|}
|}


<span id="Electric_capacitance"></span>
Energy / Work:
=== Capacitancia electrica ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| pF
| Pico[https://en.wikipedia.org/wiki/Farad farad]
|-
| nF
| Nano[https://en.wikipedia.org/wiki/Farad farad]
|-
| uF
| Micro[https://en.wikipedia.org/wiki/Farad farad]; alternative to the unit µF
|-
| µF
| Micro[https://en.wikipedia.org/wiki/Farad farad]; alternative to the unit uF
|-
| mF
| Milli[https://en.wikipedia.org/wiki/Farad farad]
|-
| F
| [https://en.wikipedia.org/wiki/Farad Farad]; 1 F = 1 s^4·A^2/m^2/kg
|}

<span id="Electric_charge"></span>
=== Carga eléctrica ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| C
| [https://en.wikipedia.org/wiki/Coulomb Coulomb]; 1 C = 1 A*s
|}

<span id="Electric_conductivity"></span>
=== Conductividad eléctrica ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| uS
| Micro[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]; alternative to the unit µS
|-
| µS
| Micro[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]; alternative to the unit uS
|-
| mS
| Milli[https://en.wikipedia.org/wiki/Siemens_(unit) siemens]
|-
| S
| [https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]; 1 S = 1 s^3·A^2/kg/m^2
|-
| kS
| Kilo[https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]
|-
| MS
| Mega[https://en.wikipedia.org/wiki/Siemens_(unit) Siemens]
|}

<span id="Electric_inductance"></span>
=== Inductancia eléctrica ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| nH
| Nano[https://en.wikipedia.org/wiki/Henry_(unit) henry]
|-
| uH
| Micro[https://en.wikipedia.org/wiki/Henry_(unit) henry]; alternative to the unit µH
|-
| µH
| Micro[https://en.wikipedia.org/wiki/Henry_(unit) henry]; alternative to the unit uH
|-
| mH
| Milli[https://en.wikipedia.org/wiki/Henry_(unit) henry]
|-
| H
| [https://en.wikipedia.org/wiki/Henry_(unit) Henry]; 1 H = 1 kg·m^2/s^2/A^2
|}

<span id="Electric_potential"></span>
=== Potencial eléctrico ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| mV
| Milli[https://en.wikipedia.org/wiki/Volt volt]
|-
| V
| [https://en.wikipedia.org/wiki/Volt Volt]
|-
| kV
| Kilo[https://en.wikipedia.org/wiki/Volt volt]
|}

<span id="Electric_resistance"></span>
=== Resistencia electrica ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| Ohm
| [https://en.wikipedia.org/wiki/Ohm Ohm]; 1 Ohm = 1 kg·m^2/s^3/A^2
|-
| kOhm
| Kilo[https://en.wikipedia.org/wiki/Ohm ohm]
|-
| MOhm
| Mega[https://en.wikipedia.org/wiki/Ohm ohm]
|}

<span id="Energy/work"></span>
=== Energía/trabajo ===

{| class="wikitable float-right mw-collapsible mw-collapsed"
{| class="wikitable float-right mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
| mJ
| Milli[https://en.wikipedia.org/wiki/Joule joule]
|-
|-
| J
| J
| [https://en.wikipedia.org/wiki/Joule Joule]
| [https://en.wikipedia.org/wiki/Joule Joule]
|-
| kJ
| Kilo[https://en.wikipedia.org/wiki/Joule joule]
|-
| eV
| [https://en.wikipedia.org/wiki/Electronvolt Electronvolt]; 1 eV = 1.602176634e-19 J
|-
| keV
| Kilo[https://en.wikipedia.org/wiki/Electronvolt electronvolt]
|-
| MeV
| Mega[https://en.wikipedia.org/wiki/Electronvolt electronvolt]
|-
| kWh
| [https://en.wikipedia.org/wiki/Kilowatt_hour Kilowatt hour]; 1 kWh = 3.6e6 J
|-
|-
| Ws
| Ws
| [https://en.wikipedia.org/wiki/Joule#Watt_second Watt second]; alternative to the unit ''Joule''
| [https://en.wikipedia.org/wiki/Joule#Watt_second Watt second]; alternative to the unit Joule
|-
|-
| VAs
| VAs
| [https://en.wikipedia.org/wiki/Joule Volt-ampere-second]; alternative to the unit ''Joule''
| [https://en.wikipedia.org/wiki/Joule Volt-ampere-second]; alternative to the unit Joule
|-
|-
| CV
| CV
| [https://en.wikipedia.org/wiki/Joule Coulomb·Volt]; alternative to the unit ''Joule''
| [https://en.wikipedia.org/wiki/Joule Coulomb-volt]; alternative to the unit Joule
|-
| cal
| [https://en.wikipedia.org/wiki/Calorie Calorie]; 1 cal = 4.184 J
|-
| kcal
| Kilo[https://en.wikipedia.org/wiki/Calorie calorie]
|}
|}


Force:
<span id="Force"></span>
=== Fuerza ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 345: Line 771:
|}
|}


Length:
<span id="Length"></span>
=== Longitud ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 354: Line 782:
|-
|-
| um
| um
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit ''µm''
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit µm
|-
|-
| µm
| µm
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit ''mu''
| Micro[https://en.wikipedia.org/wiki/Metre meter]; alternative to the unit um
|-
|-
| mm
| mm
Line 364: Line 792:
| cm
| cm
| Centi[https://en.wikipedia.org/wiki/Metre meter]
| Centi[https://en.wikipedia.org/wiki/Metre meter]
|-
| mm
| Milli[https://en.wikipedia.org/wiki/Metre meter]
|-
|-
| dm
| dm
Line 378: Line 803:
|-
|-
| mil
| mil
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit ''thou''
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit thou
|-
|-
| thou
| thou
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit ''mil''
| [https://en.wikipedia.org/wiki/Thousandth_of_an_inch Thousandth of an inch]; alternative to the unit mil
|-
|-
| in
| in
| [https://en.wikipedia.org/wiki/Inch Inch]
| [https://en.wikipedia.org/wiki/Inch Inch]; alternative to the unit "
|-
| "
| [https://en.wikipedia.org/wiki/Inch Inch]; alternative to the unit in
|-
|-
| ft
| ft
Line 390: Line 818:
|-
|-
| '
| '
| [https://en.wikipedia.org/wiki/Foot_(unit) Foot]; alternative to the unit ''ft''
| [https://en.wikipedia.org/wiki/Foot_(unit) Foot]; alternative to the unit ft
|-
|-
| yd
| yd
Line 399: Line 827:
|}
|}


<span id="Luminous_intensity"></span>
Luminous intensity:
=== Intensidad luminosa ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 408: Line 838:
|}
|}


<span id="Magnetic_flux"></span>
Mass:
=== Flujo magnético ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| Wb
| [https://en.wikipedia.org/wiki/Weber_(unit) Weber]; 1 Wb = 1 kg*m^2/s^2/A
|}

<span id="Magnetic_flux_density"></span>
=== Densidad de flujo magnético ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
|-
| G
| [https://en.wikipedia.org/wiki/Gauss_(unit) Gauss]; 1 G = 1 e-4 T
|-
| T
| [https://en.wikipedia.org/wiki/Tesla_(unit) Tesla]; 1 T = 1 kg/s^2/A
|}

<span id="Mass"></span>
=== Masa ===

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| ug
| ug
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit ''µg''
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit µg
|-
|-
| µg
| µg
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit ''ug''
| Micro[https://en.wikipedia.org/wiki/Gram gram]; alternative to the unit ug
|-
|-
| mg
| mg
Line 435: Line 892:
|-
|-
| lb
| lb
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit ''lbm''
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit lbm
|-
|-
| lbm
| lbm
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit ''lb''
| [https://en.wikipedia.org/wiki/Pound_(mass) Pound]; alternative to the unit lb
|-
|-
| st
| st
Line 447: Line 904:
|}
|}


Power:
<span id="Power"></span>
=== Potencia ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 455: Line 914:
| [https://en.wikipedia.org/wiki/Watt Watt]
| [https://en.wikipedia.org/wiki/Watt Watt]
|-
|-
| VA
| kW
| [https://en.wikipedia.org/wiki/Volt-ampere Volt-ampere]
| Kilo[https://en.wikipedia.org/wiki/Watt watt]
|}
|}


Pressure:
<span id="Pressure"></span>
=== Presión ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 477: Line 938:
|-
|-
| uTorr
| uTorr
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit ''µTorr''
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit µTorr
|-
|-
| µTorr
| µTorr
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit ''uTorr''
| Micro[https://en.wikipedia.org/wiki/Torr torr]; alternative to the unit uTorr
|-
|-
| mTorr
| mTorr
Line 486: Line 947:
|-
|-
| Torr
| Torr
| [https://en.wikipedia.org/wiki/Torr Torr]
| [https://en.wikipedia.org/wiki/Torr Torr]; 1 Torr = 133.32 Pa
|-
|-
| psi
| psi
| [https://en.wikipedia.org/wiki/Pounds_per_square_inch Pound-force per square inch]
| [https://en.wikipedia.org/wiki/Pounds_per_square_inch Pound-force per square inch]; 1 psi = 6.895 kPa
|-
|-
| ksi
| ksi
Line 495: Line 956:
|}
|}


Temperature:
<span id="Temperature"></span>
=== Temperatura ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| uK
| uK
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit ''µK''
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit µK
|-
|-
| µK
| µK
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit ''uK''
| Micro[https://en.wikipedia.org/wiki/Kelvin kelvin]; alternative to the unit uK
|-
|-
| mK
| mK
Line 513: Line 976:
|}
|}


<span id="Time"></span>
Time:
=== Tiempo ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
Line 526: Line 991:
| h
| h
| [https://en.wikipedia.org/wiki/Hour Hour]
| [https://en.wikipedia.org/wiki/Hour Hour]
|-
| Hz (1/s)
| [https://en.wikipedia.org/wiki/Hertz Hertz]
|-
| kHz
| Kilo[https://en.wikipedia.org/wiki/Hertz hertz],
|-
| MHz
| Mega[https://en.wikipedia.org/wiki/Hertz hertz]
|-
| GHz
| Giga[https://en.wikipedia.org/wiki/Hertz hertz]
|-
| THz
| Tera[https://en.wikipedia.org/wiki/Hertz hertz]
|}
|}


<span id="Volume"></span>
Torque:
=== Volumen ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| Nm
| ml
| [https://en.wikipedia.org/wiki/Newton_metre Newton metre]
| Milli[https://en.wikipedia.org/wiki/Litre liter]
|-
| l
| [https://en.wikipedia.org/wiki/Litre Liter]
|-
| cft
| Cubic[https://en.wikipedia.org/wiki/Foot_(unit) foot]
|}
|}


<span id="Special_imperial_units"></span>
Volume:
=== Unidades imperiales especiales ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 33%;"|Unit
!style="width: 33%;"|Unit
!style="width: 66%;"|Description
!style="width: 66%;"|Description
|-
|-
| l
| mph
| [https://en.wikipedia.org/wiki/Litre Liter]
| [https://en.wikipedia.org/wiki/Miles_per_hour Miles per hour]
|-
| sqft
| [https://en.wikipedia.org/wiki/Square_foot Square foot]
|}
|}


<span id="Unsupported_units"></span>
The following commonly used units are not yet supported:
=== Unidades no compatibles ===
{| class="wikitable float-right mw-collapsible mw-collapsed"

The following commonly used units are not yet supported, for some an alternative is provided:

{| class="wikitable mw-collapsible mw-collapsed"
!style="width: 25%;"|Unit
!style="width: 25%;"|Unit
!style="width: 50%;"|Description
!style="width: 50%;"|Description
!style="width: 25%;"|Alternative
!style="width: 25%;"|Alternative
|-
|-
| C
| °C
| [https://en.wikipedia.org/wiki/Coulomb Coulomb]
| [https://en.wikipedia.org/wiki/Celsius Celsius ]
| [°C] + 273.15 K
| 1 A*s
|-
|-
| Hz
| °F
| [https://en.wikipedia.org/wiki/Hertz Hertz]
| [https://en.wikipedia.org/wiki/Fahrenheit Fahrenheit];
| ([°F] + 459.67) × ​5/9
| 1 /s
|-
| V
| [https://en.wikipedia.org/wiki/Volt Volt]
| 1 W/A
|-
| eV
| [https://en.wikipedia.org/wiki/Electronvolt Electronvolt]
| 1.602176634e-19 J
|-
| kWh
| [https://en.wikipedia.org/wiki/Kilowatt_hour Kilowatt hour]
| 3.6e6 J
|-
| bar
| [https://en.wikipedia.org/wiki/Bar_(unit) Bar]
| 100 kPa
|-
| T
| [https://en.wikipedia.org/wiki/Tesla_(unit) Tesla]
| 1 kg/s^2/A
|-
| F
| [https://en.wikipedia.org/wiki/Farad Farad]
| 1 s^4*A^2/m^2/kg
|-
| H
| [https://en.wikipedia.org/wiki/Henry_(unit) Henry]
| 1 kg*m^2/s^2/A^2
|-
|-
| u
| u
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Atomic mass unit]; alternative to the unit 'Da'
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Atomic mass unit]; alternative to the unit Da
| 1.66053906660e-27 kg
| 1.66053906660e-27 kg
|-
|-
| Da
| Da
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Dalton]; alternative to the unit 'u'
| [https://en.wikipedia.org/wiki/Unified_atomic_mass_unit Dalton]; alternative to the unit u
| 1.66053906660e-27 kg
| 1.66053906660e-27 kg
|-
| cal
| [https://en.wikipedia.org/wiki/Calorie Calorie]
| 4.184 J
|-
|-
| sr
| sr
Line 612: Line 1,077:
| not directly
| not directly
|-
|-
| Mpsi
| px
| Mega[https://en.wikipedia.org/wiki/Pounds_per_square_inch pound-force per square inch]
| [https://en.wikipedia.org/wiki/Pixel Pixel]
| not directly
| 1000 ksi
|}
|}
{{Top}}
<span id="Invalid_characters_and_names"></span>
==Caracteres y nombres no válidos==

The expression feature is very powerful but to achieve this power it has some limitations concerning some characters. To overcome this, FreeCAD offers to use labels and reference them instead of the object names. In labels you can use almost all special characters.

In cases where you cannot use a label, such as the name of a sketch's constraints, you must be aware what characters are not allowed.

<span id="Labels"></span>
===Etiquetas===

For [[Object_name#Label|labels]] there are no invalid characters, however some characters need to be escaped:
{| class="wikitable"
!style="width: 33%;"|Characters
!style="width: 66%;"|Description
|-
| {{incode|'}}, {{incode|\}}, {{incode|"}}
| Need to be escaped by adding {{incode|\}} in front of them.
|}

For example, the label {{incode|Sketch\002}} must be referenced as {{incode|<<Sketch\\002>>}}.

<span id="Names"></span>
===Nombres===

[[Object_name#Name|Names]] of objects like dimensions, sketches, etc. may not have the characters or character sequences listed below, otherwise the name is invalid:

{| class="wikitable"
!style="width: 33%;"|Characters / Character sequences
!style="width: 66%;"|Description
|-
| '''+''', '''-''', '''*''', '''/''', '''^''', '''_''', '''<''', '''>''', '''(''', ''')''', '''{''', '''}''', '''[''', ''']''', '''.''', ''',''', '''='''
| Characters that are math operators or part of mathematical constructs
|-
| '''A''', '''kA''', '''mA''', '''MA''', '''J''', '''K''', ''' ' ''', ''' ft ''', '''°''', and many more!
| Characters and character sequences that are units (see the [[#Units|Units]] paragraph)
|-
| '''#''', '''!''', '''?''', '''§''', '''$''', '''%''', '''&''', ''':''', ''';''', '''\''', '''<nowiki>|</nowiki>''', '''~''', '''∆''', '''¿''', and many more!
| Characters used as placeholder or to trigger special operations
|-
| '''pi''', '''e'''
| Mathematical constants
|-
| '''´''', '''`''', ''' ' ''', '''"'''
| Characters used for accents
|-
| space
| A space defines the end of a name and can therefore not be used
|}

For example, the following name is valid: {{incode|<<Sketch>>.Constraints.T2üßµ@}}. While these are invalid names: {{incode|<<Sketch>>.Constraints.test\result_2}} (\r means "carriage return") or {{incode|<<Sketch>>.Constraints.mol}} (mol is a unit).

Since shorter names (especially if they have only one or two characters) can easily result in invalid names, consider using longer names and/or establishing a suitable naming convention.

===Cell aliases===

See [[Spreadsheet_SetAlias#Usage|Spreadsheet SetAlias]].
{{Top}}
<span id="Reference_to_CAD_data"></span>
== Referencia a los datos CAD ==

It is possible to use data from the model itself in an expression. To reference a property use {{incode|object_name.property}} or {{incode|<<object_label>>.property}}, labels must be enclosed in {{incode|<<}} and {{incode|>>}}. If you want to use labels they must be unique.

All next examples reference the object by its name, but in all cases the object label can also be used.

If the property is a compound of fields, the individual fields can be accessed as {{incode|object_name.property.field}}.


Para referenciar una lista de objetos use {{incode|object_label.list[list_index]}}. Si quiere por ejemplo referenciar una restricción de un croquis use {{incode|Sketch.Constraints[16]}}. Si está en el mismo croquis puede omitir su nombre y solo usar {{incode|Constraints[16]}}.Note que el índice inicia en 0, por lo que la restricción 17 tiene que ser referenciada como {{incode|Constraints[16]}}
== Reference To CAD-Data ==


To reference the object itself use the {{incode|_self}} pseudo property: {{incode|object_name._self}}.
It is possible to use data from the model itself in an expression. To reference a property use "object.property". If the property is a compound of fields, the individual fields can be accessed as "object.property.field".


The following table shows some examples:
The following table shows some more examples:
{| class="wikitable"
{|{{Prettytable}}
!CAD-Data
!CAD data
!Call in expression
!Call in expression
!Result
!Result
|-
|-
|Parametric Length of a Part-Workbench Cube
|Length of a [[Part_Box|Part Box]]
|Cube.Length
|{{incode|Box.Length}}
|Length with units mm
|Length with units (mm)
|-
|-
|Volume of the Cube
|Volume of the Box
|Cube.Shape.Volume
|{{incode|Box.Shape.Volume}}
|Volume in mm&sup3; without units
|Volume in mm&sup3; without units
|-
|-
|Type of the Cube-shape
|Shape type of the Box
|Cube.Shape.ShapeType
|{{incode|Box.Shape.ShapeType}}
|String: Solid
|String: Solid
|-
|-
|Label of the Cube
|Label of the Box
|Cube.Label
|{{incode|Box.Label}}
|String: Label
|String: Label
|-
|-
|x-coordinate of center of mass of the Cube
|X-coordinate of center of mass of the Box
|Cube.Shape.CenterOfMass.x
|{{incode|Box.Shape.CenterOfMass.x}}
|x-coordinate in mm without units
|X-coordinate in mm without units
|-
|X-coordinate of the Box placement
|{{incode|Box.Placement.Base.x}}
|X-coordinate with units (mm)
|-
|X-component of the rotation axis of the Box placement
|{{incode|Box.Placement.Rotation.Axis.x}}
|X-component of the unit vector in mm without units
|-
|Rotation angle of the Box placement
|{{incode|Box.Placement.Rotation.Angle}}
|Rotation angle with units (deg)
|-
|Full Box object
|{{incode|Box._self}}
|Object of type <Part::PartFeature>
|-
|-
|Value of constraint in a sketch
|Value of constraint in a sketch
|Constraints.Width
|{{incode|Constraints.Width}}
|Numeric value of the named constraint 'Width' in the sketch, if the expression is used in the sketch itself.
|Numeric value of the named constraint {{incode|Width}} in the sketch, if the expression is used in the sketch itself.
|-
|-
|Value of constraint in a sketch
|Value of constraint in a sketch
|MySketch.Constraints.Width
|{{incode|MySketch.Constraints.Width}}
|Numeric value of the named constraint 'Width' in the sketch, if the expression is used outside of the sketch.
|Numeric value of the named constraint {{incode|Width}} in the sketch, if the expression is used outside of the sketch.
|-
|-
|Value of a spreadsheet alias
|Value of a spreadsheet alias
|Spreadsheet.Depth
|{{incode|Spreadsheet.Depth}}
|Value of the alias "Depth" in the spreadsheet "Spreadsheet"
|Value of the alias {{incode|Depth}} in the spreadsheet {{incode|Spreadsheet}}
|-
|-
|Value of a local property
|Value of a local property
|Length
|{{incode|Length}}
|Value of the Length property in e.g a Pad object, if the expression is used in e.g Length2 in the same object.
|Value of the {{PropertyData|Length}} property in e.g a Pad object, if the expression is used in e.g {{PropertyData|Length2}} in the same object.
|}
|}


=== Cyclic dependencies ===
== Document-wide global variables ==


FreeCAD checks dependencies based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. You have to use two spreadsheets, one to drive your model and the other for reporting.
There is no concept of global variables in FreeCAD at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the [[Spreadsheet Workbench|Spreadsheet workbench]], and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.


As a workaround it is possible to display a cell range from the second spreadsheet in the first (or vice versa) by creating a [[Spreadsheet_Workbench#Cell_binding|cell binding]] with the {{MenuCommand|Hide dependency of binding}} option.
== Cross-document linking ==


Another way to workaround cyclic dependencies is to hide the reference by using the {{incode|href}} or {{incode|hiddenref}} function for individual expressions, for example: {{incode|href(Box.Length)}}.
It is possible (with limitations) to define a Property of an object in your current document (".FCstd" file) by using an Expression to reference a Property of an object contained in a different document (".FCstd" file). For example, a cell in a spreadsheet or the Length of a Part Cube, etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.


Please note that both mentioned workarounds should be used with caution, and that they do not work if the properties that are reported depend on dimensions that are driven from the same spreadsheet.
A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.
{{Top}}
<span id="Document-wide_global_variables"></span>
== Variables globales de todo el documento ==


There is no concept of global variables in FreeCAD at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the [[Spreadsheet Workbench|Spreadsheet workbench]], and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.
Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document "master", the spreadsheet "modelConstants", and give a cell an alias-name "Length", you can then access the value as:
{{Top}}
<span id="Cross-document_linking"></span>
== Enlace entre documentos ==


It is possible (with limitations) to define a Property of an object in your current document (".FCstd" file) by using an Expression to reference a Property of an object contained in a different document (".FCstd" file). For example, a cell in a spreadsheet or the {{PropertyData|Length}} of a Part Cube, etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.
master#modelConstants.Length


A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.
Note that the master document must be loaded for the values in the master to be available to the dependent document.


Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document {{incode|master}}, the spreadsheet {{incode|modelConstants}}, and give a cell an alias-name {{incode|Length}}, you can then access the value as:
Unfortunately, the integrated checker sometimes claims that a valid name doesn't exist. Continue typing anyway. When you have completed the full reference, the {{Button|OK}} button will become active.


{{incode|master#modelConstants.Length}}
Of course, it's up to you to load the corresponding documents later when you want to change anything.


Note that the master document must be loaded for the values in the master to be available to the dependent document.
== Known issues / remaining tasks ==


Of course, it's up to you to load the corresponding documents later when you want to change anything.
* The dependency graph is based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. As a work-around, use multiple spreadsheets -- one to drive your model, and one for reporting.
{{Top}}
* The expression parser does not handle parentheses well, and is unable to properly parse some expressions. For example: "'''= (A1 > A2) ? 1 : 0'''" results in an error, while "'''= A1 > A2 ? 1 : 0'''" is accepted. The expression "'''= 5 + ((A1>A2) ? 1 : 0)'''" cannot be entered in any form.
<span id="Known_issues_/_remaining_tasks"></span>
* There is no expression manager implemented where all expressions in a document are listed, and can be created, deleted, queried, etc.
== Problemas conocidos / tareas pendientes ==
* The names of Sketcher constraints must not contain any blanks when the value is calculated by an expression, see [https://forum.freecadweb.org/viewtopic.php?p=302500#p302381; forum discussion].
* Open bugs/tickets for Expressions can be found in the [https://freecadweb.org/tracker/set_project.php?project_id=4;20 FreeCAD Bugtracker Expressions category]


* FreeCAD does not yet have a built-in expression manager where all expressions in a document are listed, and can be created, deleted, queried, etc. But an addon is available: [https://github.com/gbroques/fcxref fcxref expression manager].
<div class="mw-translate-fuzzy">
* Open bugs/tickets for Expressions can be found on [https://github.com/FreeCAD/FreeCAD/issues?q=is%3Aissue+is%3Aopen+label%3AExpressions GitHub].
[[Category:User Documentation/es]]
{{Top}}
</div>


{{Powerdocnavi{{#translation:}}}}
{{clear}}
[[Category:Spreadsheet{{#translation:}}]]

Latest revision as of 10:03, 21 April 2024

Resumen

Es posible definir propiedades utilizando expresiones matemáticas. En la interfaz gráfica de usuario, los cuadros de giro o campos de entrada que están vinculados a las propiedades contienen un icono azul . Haciendo clic en el icono o escribiendo el signo igual = aparece el editor de expresiones para esa propiedad en particular.

Es una expresión matemática que usa la notación de los operadores, funciones y constantes predefinidas matemáticas estándar como se describe a continuación. Además, la expresión puede hacer referencia a otras propiedades de objetos, y también utilizar condicionales. Los números en una expresión pueden tener una unidad opcional adjunta.

Los números pueden usar ya sea una coma , o un punto decimal . para separar los dígitos enteros de los decimales. Cuando se usa el marcador decimal, debe ser seguido por al menos un dígito. Por lo tanto, las expresiones 1.+2. y 1,+2, son inválidas, pero 1.0+2.0 y 1,0+2,0 son válidas.

Los operadores y las funciones son conscientes de la unidad y requieren combinaciones válidas de unidades, si se suministran. Por ejemplo, 2mm+4mm es una expresión válida, mientras que 2mm+4 no lo es. Esto también se aplica a las referencias a propiedades de objetos que tienen unidades, como las propiedades de longitud. Por lo tanto, Pad001.Length + 1 es inválido ya que agrega un número puro a una propiedad con unidades de longitud, se requiere Pad001.Length + 1mm.

Algunos errores relacionados con las unidades pueden parecer poco intuitivos, ya que las expresiones se rechazan o producen resultados que no coinciden con las unidades de la propiedad que se establece. Aquí hay unos ejemplos:

1/2mm no se interpreta como medio milímetro sino como 1/(2mm), lo que da como resultado: 0.5 mm^-1.

sqrt(2)mm no es válido porque la llamada a la función no es un número. Esto debe ingresarse como sqrt(2) * 1mm.

Argumentos de la función

Múltiples argumentos a una función pueden estar separados por un punto y coma ; o una coma seguida por un espacio , . En el último caso, la coma se convierte a un punto y coma después de la entrada. Cuando se usa un punto y coma, no es necesario un espacio final.

Los argumentos pueden incluir referencias a las celdas en una hoja de cálculo. Una referencia de celda consiste en la letra mayúscula de fila de la celda seguida de su número de columna, por ejemplo A1. También se puede hacer referencia a una celda utilizando el alias de la celda, por ejemplo, Spreadsheet.MyPartWidth.

Referencia de objetos

Como ya se mostró arribam puede hacer referencia a un objeto por su Datos Name. Pero también puedes usar su Datos Label. En el caso de un Datos Label, debe estar encerrado en doble símbolos << y >>, como <<Label>>.

Puede referenciar cualquier propiedad de un objeto. Por ejemplo, para referenciar la altura de un Cilindro puede usar Cylinder.Height o <<Label_of_cylinder>>.Height.

Para más información de como referenciar objetos, vea Referencia a los datos CAD.

Inicio

Constantes soportadas

Las siguientes constantes están soportadas.

Constant Description
e Número de Euler
pi Pi

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Operadores soportados

Los siguientes operadores son soportados.

Operator Description
+ Suma
- Resta
* Multiplicación
/ Division de punto flotante
% Residuo
^ Potenciación

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Funciones soportadas

Funciones matemáticas generales

Las siguientes funciones matemáticas son soportadas:

Funciones trigonométricas

Las Funciones trigonométricas utilizan el grado sexagesimal como unidad predeterminada. Para radianes, agregue rad después del primer valor de una expresión. Entonces, por ejemplo, cos(45) es lo mismo que cos(pi rad / 4). Las expresiones en grados pueden usar deg o °, por ejemplo, 360deg - atan2(3; 4) o 360° - atan2(3; 4). Si una expresión no tiene unidades y debe convertirse a grados o radianes para garantizar la compatibilidad, multiplíquela por 1deg, o 1rad como apropiado, por ejemplo, (360 - X) * 1deg; (360 - X) * 1°; (0,5 + pi / 2) * 1rad.

Function Description Input range
acos(x) Arc cosine -1 <= x <= 1
asin(x) Arc sine -1 <= x <= 1
atan(x) Arc tangent, return value in the range -90° < value < 90° all
atan2(y; x) Arc tangent of y/x accounting for quadrant, return value in the range -180° < value <= 180° all, the invalid input x = y = 0 returns 0
cos(x) Cosine all
cosh(x) Hyperbolic cosine all
sin(x) Sine all
sinh(x) Hyperbolic sine all
tan(x) Tangent all, except x = n*90 with n = odd integer
tanh(x) Hyperbolic tangent all
hypot(x; y) Pythagorean addition (hypotenuse), e.g. hypot(4; 3) = 5 x and y >= 0
cath(x; y) Given hypotenuse, and one side, returns other side of triangle, e.g. cath(5; 3) = 4 x >= y >= 0

Funciones exponenciales y logarítmicas

Function Description Input range
exp(x) Exponential function all
log(x) Natural logarithm x > 0
log10(x) Common logarithm x > 0
pow(x; y) Exponentiation all
sqrt(x) Square root x >= 0
cbrt(x) introduced in version 0.21 Cubic root all

Funciones de redondeo, truncamiento y resto.

Function Description Input range
abs(x) Absolute value all
ceil(x) Ceiling function, smallest integer value greater than or equal to x all
floor(x) Floor function, largest integer value less than or equal to x all
mod(x; y) Remainder after dividing x by y, sign of result is that of the dividend. all, except y = 0
round(x) Rounding to the nearest integer all
trunc(x) Truncation to the nearest integer in the direction of zero all

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Funciones estadísticas/agregadas

Aggregate functions take one or more arguments.

Individual arguments to aggregate functions may consist of ranges of cells. A range of cells is expressed as two cell references separated by a colon :, for example average(B1:B8) or sum(A1:A4; B1:B4). The cell references may also use cell aliases, for example average(StartTemp:EndTemp).

Las siguientes funciones agregadas son soportadas:

Function Description Input range
average(a; b; c; ...) Average value of the arguments, same as sum(a; b; c; ...) / count(a; b; c; ...) all
count(a; b; c; ...) Count of the arguments, typically used for cell ranges all
max(a; b; c; ...) Maximum value of the arguments all
min(a; b; c; ...) Minimum value of the arguments all
stddev(a; b; c; ...) Standard deviation of the values of the arguments all
sum(a; b; c; ...) Sum of the values of the arguments, typically used for cell ranges all

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Manipulación de cadenas

Identificación de cadena

Las cadenas se identifican en las expresiones rodeándolas con comillas angulares dobles de apertura/cierre (al igual que las etiquetas).

En el siguiente ejemplo, "TEXTO" se reconoce como una cadena: <<TEXTO>>

Concatenación de cadenas

Las cadenas se pueden concatenar usando el signo '+'.

El siguiente ejemplo <<MI>> + <<TEXTO>> se concatenará con "MITEXTO".

Conversión de cadenas

Los valores numéricos se pueden convertir en cadenas con la función str:

str(Box.Length.Value)

Formato de cadena

El formato de cadena se admite utilizando el estilo (antiguo) % de Python.

Todos los especificadores % tal como se definen en la documentación de Python.

Como ejemplo, supongamos que tiene un cubo predeterminado de 10 mm de lado llamado 'Box' (nombramiento predeterminado de FreeCAD), la siguiente expresión <<Longitud del cubo: %s>> % Box.Length se expandirá a "Longitud del cubo: 10.0 mm"

Para más de un especificador % utilice la siguiente sintaxis: <<La longitud del cubo es %s y el ancho es %s>> % tuple(Box.Length; Box.Width). O use concatenación: <<La longitud del cubo es %s>> % Box.Length + << y el ancho es %s>> % Box.Width. Ambos se expandirán a "La longitud del cubo es de 10.0 mm y el ancho es de 10.0 mm".

Está disponible un archivo de muestra de FreeCAD que utiliza formato de cadena en el foro

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Funciones de creación de objetos

Los siguientes objetos se pueden crear en expresiones utilizando las siguientes funciones:

Type Function Description
Tuple tuple(a; b; ...) Example: tuple(2; 1; 2)
List list(a; b; ...) Example: list(2; 1; 2)
Vector vector(x; y; z) Create a vector using three unit-less or Length unit values.

Example: vector(2; 1; 3)

create(<<vector>>; x; y; z)
Matrix
matrix(
  a11; a12; a13; a14;
  a21; a22; a23; a24;
  a31; a32; a33; a34;
  a41; a42; a43; a44
)
Create a 4x4 matrix in row-major order:

Se puede proporcionar un mínimo de 1 argumento, como matrix(1), que crea una matriz de identidad.

Example: matrix(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16)

create(<<matrix>>; a11; a12; ...; a44)
Rotation rotation(axis; angle) Create a Rotation by specifying its axis (Vector) and angle (Angle unit or unit-less), or three Euler angles α, β, γ.

Examples:

  • rotation(vector(0; 1; 0); 45)
  • create(<<rotation>>; 30; 30; 30)
rotation(α; β; γ)
create(<<rotation>>; axis; angle)
create(<<rotation>>; α; β; γ)
Placement placement(base; rotation) Create a Placement with various parameters, including:
  • base: base location (Vector)
  • center: center location (Vector)
  • rotation: Rotation
  • axis: Rotation axis (Vector)
  • angle: Rotation angle (unit-less or Angle unit value)
  • matrix: Matrix

Examples:

  • placement(vector(2; 1; 3); rotation(vector(0; 0; 1); 45))
  • create(<<placement>>; create(<<vector>>; 2; 1; 2); create(<<rotation>>; create(<<vector>>; 0; 1; 0); 45))
placement(base; rotation; center)
placement(base; axis; angle)
placement(matrix)
create(<<placement>>; ...)

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Funciones vectoriales

Function / Operator Description
v1 + v2 Add two vectors.
v1 - v2 Subtract two vectors.
v * s Uniformly scale a vector by s.
vangle(v1; v2) Angle between two vectors in degrees.
vcross(v1; v2) Cross product of two vectors .
v1 * v2 Dot product of two vectors .
vdot(v1; v2)
vlinedist(v1; v2; v3) Distance between vector v1 and a line through v2 in direction v3.
vlinesegdist(v1; v2; v3) Distance between vector v1 and the closest point on a line segment from v2 to v3.
vlineproj(v1; v2; v3) Project vector v1 on a line through v2 in direction v3.
vnormalize(v) Normalize a vector to a unit vector.
vplanedist(v1) Distance between vector v1 and a plane defined by a point v2 and a normal v3.
vplaneproj(v1) Project vector v1 on a plane defined by a point v2 and a normal v3.
vscale(v; sx; sy; sz) Non-uniformly scale a vector by sx in the X direction, sy in the Y direction, and sz in the Z direction.
vscalex(v; sx)
vscaley(v; sy)
vscalez(v; sz)

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Funciones matriciales

Rotation and Placement can each be represented by a Matrix. The following functions all take in a Matrix, Rotation, or Placement as their first parameter denoted in the table below by m. The type of the returned object is the same as the object supplied in the first argument except when using mtranslate on a Rotation, in which case a Placement will be returned.

Function Description
minvert(m) Calculate the Inverse matrix.
mrotate(m; rotation) Rotate by either:
  • a Rotation
  • an axis (Vector) and an angle (Angle unit or unit-less)
  • three Euler angles α, β, γ
mrotate(m; axis; angle)
mrotate(m; α; β; γ)
mrotatex(m; angle) Rotate around the X axis.
mrotatey(m; angle) Rotate around the Y axis.
mrotatez(m; angle) Rotate around the Z axis.
mtranslate(m; vector) Translate by a vector (Vector) or X, Y, Z values. If a Rotation is translated, the returned object is a Placement.
mtranslate(m; x; y; z)
mscale(m; vector) Scale by a vector (Vector) or X, Y, Z values.
mscale(m; x; y; z)

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Expresiones condicionales

Conditional expressions are of the form condition ? resultTrue : resultFalse. The condition is defined as an expression that evaluates to either 0 (false) or non-zero (true).

The following relational operators are defined:

Unit Description
== equal to
!= not equal to
> greater than
< less than
>= greater than or equal to
<= less than or equal to

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Unidades

Las unidades se pueden utilizar directamente en expresiones. El analizador los conecta con el valor anterior. Entonces 2mm o 2 mm es válido mientras que mm no es válido porque no hay un valor anterior.

All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number 1.5 and refer to it for a pad height. This only works because the pad height predefines the unit mm that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. Sketch1.Constraints.Width - Spreadsheet.B1 because Sketch1.Constraints.Width has a unit and Spreadsheet.B1 has not.

Se pueden ingresar directamente unidades con exponentes. Entonces, por ejemplo, mm^3 se reconocerá como mm³ y m^3 se reconocerá como m³.

Si tienes una variable cuyo nombre es el de una unidad debes poner la variable entre << >> para evitar que sea reconocida como una unidad. Por ejemplo, si tiene la dimensión Sketch.Constraints.A, se reconocerá como la unidad amperio. Por lo tanto debes escribirlo en la expresión como Sketch.Constraints.<<A>>.

El analizador de expresiones reconoce las siguientes unidades:

Cantidad de sustancia

Unit Description
mmol Millimole
mol Mole

Ángulo

Unit Description
° Degree; alternative to the unit deg
deg Degree; alternative to the unit °
rad Radian
gon Gradian
S Second of arc; alternative to the unit ″
Second of arc; alternative to the unit S
M Minute of arc; alternative to the unit ′
Minute of arc; alternative to the unit M

Corriente

Unit Description
mA Milliampere
A Ampere
kA Kiloampere
MA Megaampere

Capacitancia electrica

Unit Description
pF Picofarad
nF Nanofarad
uF Microfarad; alternative to the unit µF
µF Microfarad; alternative to the unit uF
mF Millifarad
F Farad; 1 F = 1 s^4·A^2/m^2/kg

Carga eléctrica

Unit Description
C Coulomb; 1 C = 1 A*s

Conductividad eléctrica

Unit Description
uS Microsiemens; alternative to the unit µS
µS Microsiemens; alternative to the unit uS
mS Millisiemens
S Siemens; 1 S = 1 s^3·A^2/kg/m^2
kS KiloSiemens
MS MegaSiemens

Inductancia eléctrica

Unit Description
nH Nanohenry
uH Microhenry; alternative to the unit µH
µH Microhenry; alternative to the unit uH
mH Millihenry
H Henry; 1 H = 1 kg·m^2/s^2/A^2

Potencial eléctrico

Unit Description
mV Millivolt
V Volt
kV Kilovolt

Resistencia electrica

Unit Description
Ohm Ohm; 1 Ohm = 1 kg·m^2/s^3/A^2
kOhm Kiloohm
MOhm Megaohm

Energía/trabajo

Unit Description
mJ Millijoule
J Joule
kJ Kilojoule
eV Electronvolt; 1 eV = 1.602176634e-19 J
keV Kiloelectronvolt
MeV Megaelectronvolt
kWh Kilowatt hour; 1 kWh = 3.6e6 J
Ws Watt second; alternative to the unit Joule
VAs Volt-ampere-second; alternative to the unit Joule
CV Coulomb-volt; alternative to the unit Joule
cal Calorie; 1 cal = 4.184 J
kcal Kilocalorie

Fuerza

Unit Description
mN Millinewton
N Newton
kN Kilonewton
MN Meganewton
lbf Pound of force

Longitud

Unit Description
nm Nanometer
um Micrometer; alternative to the unit µm
µm Micrometer; alternative to the unit um
mm Millimeter
cm Centimeter
dm Decimeter
m Meter
km Kilometer
mil Thousandth of an inch; alternative to the unit thou
thou Thousandth of an inch; alternative to the unit mil
in Inch; alternative to the unit "
" Inch; alternative to the unit in
ft Foot; alternative to the unit '
' Foot; alternative to the unit ft
yd Yard
mi Mile

Intensidad luminosa

Unit Description
cd Candela

Flujo magnético

Unit Description
Wb Weber; 1 Wb = 1 kg*m^2/s^2/A

Densidad de flujo magnético

Unit Description
G Gauss; 1 G = 1 e-4 T
T Tesla; 1 T = 1 kg/s^2/A

Masa

Unit Description
ug Microgram; alternative to the unit µg
µg Microgram; alternative to the unit ug
mg Milligram
g Gram
kg Kilogram
t Tonne
oz Ounce
lb Pound; alternative to the unit lbm
lbm Pound; alternative to the unit lb
st Stone
cwt Hundredweight

Potencia

Unit Description
W Watt
kW Kilowatt

Presión

Unit Description
Pa Pascal
kPa Kilopascal
MPa Megapascal
GPa Gigapascal
uTorr Microtorr; alternative to the unit µTorr
µTorr Microtorr; alternative to the unit uTorr
mTorr Millitorr
Torr Torr; 1 Torr = 133.32 Pa
psi Pound-force per square inch; 1 psi = 6.895 kPa
ksi Kilopound-force per square inch

Temperatura

Unit Description
uK Microkelvin; alternative to the unit µK
µK Microkelvin; alternative to the unit uK
mK Millikelvin
K Kelvin

Tiempo

Unit Description
s Second
min Minute
h Hour
Hz (1/s) Hertz
kHz Kilohertz,
MHz Megahertz
GHz Gigahertz
THz Terahertz

Volumen

Unit Description
ml Milliliter
l Liter
cft Cubicfoot

Unidades imperiales especiales

Unit Description
mph Miles per hour
sqft Square foot

Unidades no compatibles

The following commonly used units are not yet supported, for some an alternative is provided:

Unit Description Alternative
°C Celsius [°C] + 273.15 K
°F Fahrenheit; ([°F] + 459.67) × ​5/9
u Atomic mass unit; alternative to the unit Da 1.66053906660e-27 kg
Da Dalton; alternative to the unit u 1.66053906660e-27 kg
sr Steradian not directly
lm Lumen not directly
lx Lux not directly
px Pixel not directly

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Caracteres y nombres no válidos

The expression feature is very powerful but to achieve this power it has some limitations concerning some characters. To overcome this, FreeCAD offers to use labels and reference them instead of the object names. In labels you can use almost all special characters.

In cases where you cannot use a label, such as the name of a sketch's constraints, you must be aware what characters are not allowed.

Etiquetas

For labels there are no invalid characters, however some characters need to be escaped:

Characters Description
', \, " Need to be escaped by adding \ in front of them.

For example, the label Sketch\002 must be referenced as <<Sketch\\002>>.

Nombres

Names of objects like dimensions, sketches, etc. may not have the characters or character sequences listed below, otherwise the name is invalid:

Characters / Character sequences Description
+, -, *, /, ^, _, <, >, (, ), {, }, [, ], ., ,, = Characters that are math operators or part of mathematical constructs
A, kA, mA, MA, J, K, ' , ft , °, and many more! Characters and character sequences that are units (see the Units paragraph)
#, !, ?, §, $, %, &, :, ;, \, |, ~, , ¿, and many more! Characters used as placeholder or to trigger special operations
pi, e Mathematical constants
´, `, ' , " Characters used for accents
space A space defines the end of a name and can therefore not be used

For example, the following name is valid: <<Sketch>>.Constraints.T2üßµ@. While these are invalid names: <<Sketch>>.Constraints.test\result_2 (\r means "carriage return") or <<Sketch>>.Constraints.mol (mol is a unit).

Since shorter names (especially if they have only one or two characters) can easily result in invalid names, consider using longer names and/or establishing a suitable naming convention.

Cell aliases

See Spreadsheet SetAlias.

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Referencia a los datos CAD

It is possible to use data from the model itself in an expression. To reference a property use object_name.property or <<object_label>>.property, labels must be enclosed in << and >>. If you want to use labels they must be unique.

All next examples reference the object by its name, but in all cases the object label can also be used.

If the property is a compound of fields, the individual fields can be accessed as object_name.property.field.

Para referenciar una lista de objetos use object_label.list[list_index]. Si quiere por ejemplo referenciar una restricción de un croquis use Sketch.Constraints[16]. Si está en el mismo croquis puede omitir su nombre y solo usar Constraints[16].Note que el índice inicia en 0, por lo que la restricción 17 tiene que ser referenciada como Constraints[16]

To reference the object itself use the _self pseudo property: object_name._self.

The following table shows some more examples:

CAD data Call in expression Result
Length of a Part Box Box.Length Length with units (mm)
Volume of the Box Box.Shape.Volume Volume in mm³ without units
Shape type of the Box Box.Shape.ShapeType String: Solid
Label of the Box Box.Label String: Label
X-coordinate of center of mass of the Box Box.Shape.CenterOfMass.x X-coordinate in mm without units
X-coordinate of the Box placement Box.Placement.Base.x X-coordinate with units (mm)
X-component of the rotation axis of the Box placement Box.Placement.Rotation.Axis.x X-component of the unit vector in mm without units
Rotation angle of the Box placement Box.Placement.Rotation.Angle Rotation angle with units (deg)
Full Box object Box._self Object of type <Part::PartFeature>
Value of constraint in a sketch Constraints.Width Numeric value of the named constraint Width in the sketch, if the expression is used in the sketch itself.
Value of constraint in a sketch MySketch.Constraints.Width Numeric value of the named constraint Width in the sketch, if the expression is used outside of the sketch.
Value of a spreadsheet alias Spreadsheet.Depth Value of the alias Depth in the spreadsheet Spreadsheet
Value of a local property Length Value of the DatosLength property in e.g a Pad object, if the expression is used in e.g DatosLength2 in the same object.

Cyclic dependencies

FreeCAD checks dependencies based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. You have to use two spreadsheets, one to drive your model and the other for reporting.

As a workaround it is possible to display a cell range from the second spreadsheet in the first (or vice versa) by creating a cell binding with the Hide dependency of binding option.

Another way to workaround cyclic dependencies is to hide the reference by using the href or hiddenref function for individual expressions, for example: href(Box.Length).

Please note that both mentioned workarounds should be used with caution, and that they do not work if the properties that are reported depend on dimensions that are driven from the same spreadsheet.

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Variables globales de todo el documento

There is no concept of global variables in FreeCAD at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the Spreadsheet workbench, and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.

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Enlace entre documentos

It is possible (with limitations) to define a Property of an object in your current document (".FCstd" file) by using an Expression to reference a Property of an object contained in a different document (".FCstd" file). For example, a cell in a spreadsheet or the DatosLength of a Part Cube, etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.

A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.

Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document master, the spreadsheet modelConstants, and give a cell an alias-name Length, you can then access the value as:

master#modelConstants.Length

Note that the master document must be loaded for the values in the master to be available to the dependent document.

Of course, it's up to you to load the corresponding documents later when you want to change anything.

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Problemas conocidos / tareas pendientes

  • FreeCAD does not yet have a built-in expression manager where all expressions in a document are listed, and can be created, deleted, queried, etc. But an addon is available: fcxref expression manager.
  • Open bugs/tickets for Expressions can be found on GitHub.

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