Equations,
Expressions and Variables 
Variable, equations and expressions can be used to parametrically drive parts, sketches and drawing sheets. Variables can be created and assigned absolute values or values implicitly derived from dimensions. Expressions can be created and used as input during command prompts. Expressions can contain variables as well as conditional (if/then/else) operators.
Equations can be created that contain variables as well as one or more expressions (i.e., equation sets). You can set equations to be solved sequentially (linear) or simultaneously (nonlinear). You can also test the results of an equation set on the active part.
Insert
Equation Set (Part Level)
Use this command at the Part Level to create a part equation (or equation set) using the Equation Set Editor. A part equation set is one that resides in the active part. The active part can have any number of equation sets. Each equation set can consist of one or more equations. You can also create a new equation set in a new VX file at the same time using the New File/Object Form. See also Using Command Line Expressions.
Tools
History Manager
(on Equation Set) Edit
New equation sets are assigned system generated names (i.e., EquationSet1, EquationSet2, EquationSet3, etc...). You can rename or edit the equation set by right-clicking on its name in the History Manager and selecting Edit or Rename. You can use the History Manager filter to list only the equation sets.
Edit Equations... (Sketch Level)Use this command at the Sketch Level
to create or load a sketch equation (or equation set) into the Equation
Set Editor. A sketch equation is one that resides in and is always
associated with the sketch that is active at the time it is created. Thus,
there is only one equation set per sketch and it is created and editing
in the same way.
Insert
Equation Set (Part Level)
Use this editor to build an equation or equation set (non-linear and simultaneous). As you build each equation, it is appended to the scrolling list of equations. An equation set is constructed of any number of individual expressions. You can test the results of the equation set on the active part by picking Apply.
Enter a variable name in the input field provided.
Build an expression in the input field provided. You can use the Get Dimension or Get Variable buttons as described below to add dimensions or variables to the expression.
After the expression is defined, press the Submit button. The values currently expressed in the Name, Expression, Min, and Max input fields are appended to the end of the scrolling list of equations or replaces any existing equation with the same variable name.
The format used to display the definition of an equation in the list is:
name = value {expression} [min, max]
If an expression hasn't been evaluated yet, its result is shown as an underscored blank space. The Apply button logs changes to the Equation Set to the database and updates the values.
Repeat steps 1, 2, and 3 as desired to build an equation set.
Pick OK to save the equation
set or pick Apply, Reset, or Cancel as desired (see
Other Options below).
Name
Enter the variable name for the equation or pick Get Dimension
and select a dimension or pick Get Variable and select a variable
from the Variable Browser.
The name of the dimension or variable will appear in the input field and will be used as the variable name.
Min/Max
Enter the Minimum/Maximum value for the variable. An error message is displayed if a variable exceeds its limits. No change to its value is made.
Distance
Check this box if the variable as a distance. When a variable is flagged as a distance, the variable's value is converted to the active units when it is displayed. The expressions that define a variable are still interpreted as millimeters and degrees unless alternate units are explicitly declared (e.g., 5.in).
Expression
Build the expression for the equation in the text input field provided (e.g., eq1-10 or (v1+2)/v2). You can use existing dimensions and variables within the expression. Pick Get Dimension and select a dimension or pick Get Variable and select a variable from the Variable Browser. See also Using If, Then, Else Operators in Expressions
Get Dimension
Select a dimension from the active part or press and hold the F7 key to select a dimension external to the active part.
The dimension name will be appended to either the Variable Name or Expression input field depending on which one is currently active. The name of the root object that the dimension belongs to is automatically appended to the dimension name. Refer to Variable Naming Conventions for more information.
Get Variable
Select a variable from the Variable Browser. The variable name will be appended to either the Name or Expression input field depending on which one is currently active. If the variable belongs to a root object other than the active root object, the name of the root object that the variable belongs to is automatically appended to the variable name. Refer to Variable Naming Conventions for more information.
Display Dimension Value
Temporarily change the display format of all dimensions. The display format returns to Value when the Equation Set Editor is dismissed. Select from the following
display dimensions as values - Display all dimensions as values.
display dimension name - Display all dimensions as their variable names.
display dimension name and value - Display all dimensions as both values and variable names.
Edit
The values for the selected equation will be displayed in the input fields. Edit the equation values and pick Submit update the equation in the set.
Delete
Deletes the selected equations in the list.
Move Up, Move Down
These move the actively selected equations up or down in the equation list. This is useful for re-ordering equations that are solved sequentially.
Unpick All
Unselect all equations that are currently selected.
Import
Use this option to import variables or equations
from a file. This supports the "family-of-parts" concept by
allowing equation sets to be externally driven by a tabulated list of
variables and their values or by equations. See Importing
and Exporting Equations below for a more complete discussion of this
topic.
Export
Enter a path and file name to export the equation
set to or pick the folder icon to use the File Browser.
Picking the Export button will then export the equation set to
the file in ASCII format. See Importing
and Exporting Equations below for a more complete discussion of this
topic.
Solve Method
Sets the method for solving the equation set. Select from the following:
Sequential - Equations are solved sequentially (linear).
Simultaneous - Equations are solved simultaneously (non-linear). This is the default method.
Submit
Submits modifications in the equation edit area to the main equation list at the top of the Equation Set Editor. If the equation doesn't already exist in the list, it is added Before or After the actively-highlighted equation based on the setting of the Before/After toggle (see below).
Before, After
Insert an equation before or after the selected equation. Build the new equation in the input fields. Pick Submit to insert the equation.
OK - Saves the equation set and closes the Editor.
Apply - Logs changes to the Equation Set to the database and updates the values in the list.
Reset - Restores the equation set as it was previously saved.
Cancel - Closes the Editor without saving the equation set.
Importing and
Exporting Equations
The Import and Export buttons on the Equation Set Editorallow you to import or export variable values or equations to or from an ASCII file. If the variable already exists, you can choose to have its value updated from the file. If it does not exist, it is added to the Equation Set. The file formats for variable values and equations are different. Each is illustrated below followed by the operational sequence.
ASCII File Format
for Variable Values
Comments may be included in the file. They are lines preceded by a pound (#) sign. The first non-commented (#) row should be a list of comma-delimited or (tab-delimited) variable names preceded by a configuration label.
Subsequent rows should consist of a configuration name followed by a comma-delimited list of variable values that correspond to the variable names in the first row. If the character @ is appended to the end of a variable name (e.g., Config0001@), It will be flagged as a distance variable.
ASCII File Format
for Equations
If the first non-blank, non-comment (#) line in the file contains the keyword "equations" (upper, lower or mixed case), it is assumed that subsequent lines contain equations formatted just as they appear in the in the
Equation Set Editor, as shown below :
Variable_Name=result {expression} [min,max]
"result" should be followed by a units abbreviation (e.g. mm) if the variable is a distance. If the value of "result" is not known, enter it as zero. Once the equations are loaded, the Solve button can be used to calculate the variable values (i.e. results).
The equation format should be followed exactly, including the inclusion or exclusion of blank spaces. The only exception is the format of "expression", which is not sensitive to the inclusion of extraneous blank spaces.
Enter min,max as [0,0] if there are no known or intended minimum and maximum bounds for "result".
Operational Sequence
(Importing Equations)
Pick the Import button
from the Equation Set Editor.
Enter the path
and file name of the file to import or export in the text field provided
or pick the folder icon to select a file using the File
Browser.
Pick the Import button
and select a file using the File Browser. If the
file contain variable values (see example above), it is opened and loaded
into the Import Variable Data Form shown below (go to step 3).
If the file contains equations (see example above), it is imported directly
into the equation list and you are given the opportunity to overwrite
any values if the equations currently exist in the list.
Select a row of data from the
form and pick OK. The highlighted row of data is parsed and used
to update the active Equation Set.
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Import Variable Data Form
Variables Imported into the
Equation Set Editor (only partially shown)
Operational Sequence
(Exporting Equations)
Pick the Export button and enter a file name to export to using File Browser. The file extension is optional (e.g., equation.txt). The file will be exported to the file in ASCII format (refer to the example above).
Variable names should start with an alphabetic character and all other characters must be alphanumeric or "_". Variable names can begin with numeric characters if the entire variable name is enclosed in brackets. If you submit an invalid name, like "Var One", you will get the following error message: "Character 4 of name [Var One] is invalid."
Existing equation sets (prior to VX 6.5) which currently contain invalid variable names will regenerate. However if you edit an equation set with an invalid variable name, VX will now require you to fix any invalid variable names before the edited equation set can be saved.
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Variable Naming Conventions | |
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variable name Example: height |
All sub-objects of the active root object are searched for the variable named "height". |
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root name:variable name Example: bracket:height or equation_set_name:height |
All sub-objects of the root object named "bracket" are searched for the variable named "height". The root object must reside in a active session or a file located in one of the directories listed in the VX Search Path Form. If you want to reference a variable from a root equation set, you would do it using "equation set name:variable name". |
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~function name:string Example: ~ObjectVolume:Part2 |
If a variable name begins with a tilde, it is assumed to
be the name of a C language function of type "double function(char
*)". For example, the variable named "~VxPathParam"
retrieves the "path parameter" associated with the active target
object. The string following the colon (i.e., Part2) is passed to the function. The return value of ObjectVolume() is output by this function as "value".If there is not a string following the function name, a NULL pointer is passed to the function. |
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variable name [22base_3] |
Variable names can begin with numeric characters if the entire variable name is enclosed in brackets. |
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@file_name,variable_name |
When a variable with this syntax is included in an expression, it is evaluated by searching "vxpaths" for the file named "file_name." This file is then searched for a string with the syntax {variable_name=value}. If it is found, "value" is parsed from the string and is used as the value of the variable. |
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file_name:part_name:variable_name |
A variable in another part can be referenced as "part_name:variable_name." VX searches "vxpaths" for the first file that contains "part_name." To speed up the search, and to account for multiple files with the same part name, you can optionally specify a file name along with the part name and variable name. See also Referencing Variables from Parts Associated with Drawing Sheets below (this page) for exceptions. |
Variable Names
and Sketch Dimensions
Variable names can have the same name as an existing dimension in a sketch. This is one way to drive dimensions in sketches. At the path level, checking is still done to prevent a variable introduced by an equation set from having the same name as another variable or dimension in the part. In a part, to drive a dimension by a variable, you have to use the variable as input for the feature parameter associated with the dimension.
Using Command
Line Expressions
When prompted for a value during many VX commands, you can right-click to display an input options menu that contains the option called Expression. Selecting this option will display the Input Expression Form shown below. An input field is provided for entering an expression that contains valid expression functions. You can also get dimensions and variables to use in your expressions. Each option is described below. When you pick OK, the expression is evaluated and entered as input for the active command prompt.
Expression input field
Enter the desired expression here. Refer to Valid Expression Functions and Using If, Then, Else Operators in Expressions for guidance.
Get Dimension
Select a dimension from the active part or press and hold the F7 key to select a dimension external to the active part.
The dimension name will be appended to the expression input field. The name of the root object that the dimension belongs to is automatically appended to the dimension name. Refer to Variable Naming Conventions for more information.
Get Variable
Select a variable from the Variable Browser. The variable name will be appended to the expression input field. If the variable belongs to a root object other than the active root object, the name of the root object that the variable belongs to is automatically appended to the variable name. Refer to Variable Naming Conventions for more information.
The following are considered valid functions for use in expressions (where X and Y are valid VX expressions).
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Valid Expression Functions | |
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sin(X), cos(X), tan(X) |
Standard trig functions |
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sec(X), csc(X) and cot(X) |
Standard trig functions where:
sec(X) = 1.0 / cos(X) csc(X) = 1.0 / sin(X) cot(X) = 1.0 / tan(X) |
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sinh(X), cosh(X), and tanh(X) |
Hyperbolic trig functions where:
sinh(X) == ( exp(X) - exp(-X) ) / 2.0 cosh(X) == ( exp(X) + exp(-X) ) / 2.0 tanh(X) == sinh(X)/cosh(X) |
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asin(X), acos(X), atan(X) |
Inverse of standard trig functions |
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atan2(Y, X) |
Angle whose tangent is Y/X |
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abs(X) |
Absolute value |
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log(X), ln(X) |
logarithms (base 10, base e) |
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sqrt(X) |
Square root |
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exp(X) |
e to the power X |
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floor(X) |
Greatest integer not greater than X |
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mod(X) |
A function that returns the decimal portion of X, hence it is a double in the interval [0, 1). For positive values of X you may think of mod(X) = X - floor(X) |
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atan2(Y,X) |
Returns the angle (in radians) whose tangent is y/x. |
Using If, Then,
Else Operators in Expressions
If_then_else type operators can be used in the expression evaluator. The syntax is similar to the conditional operator in the C programming language (E1 ? E2 : E3), you will enter "E1 then E2 else E3", which evaluates to E2 if E1 is "True" and E3 if E1 is "False". Expressions of the form "E1 then E2" are also supported. This expression is equivalent to the expression "E1 then E2 else 0", that is, if E1 is true it returns the value E2, if E1 is false it returns a value of zero.
The logical and relational operators shown below are also
available to help form "True" and "False" expressions
for E1 above.
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Logical and Relational Operators used in Expressions | |
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Operator |
Description |
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< |
less than |
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> |
greater than |
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= |
equal to |
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& |
and |
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| |
or |
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! |
not |
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All the other typical relations can be formed from these (i.e., A != B is same as !( A = B ), A <= B is same as !(A > B ), ... ). | |
The hierarchy of operations assumed is also similar to standard
C:
parenthesis
logical "not" (!)
unary + and -
exponents
unit conversion factors
MULTAX or divide
add or subtract
ordering relations (<, >, =)
logical "and", "or"
conditional expressions ( E1 then E2 else E3 )
variables and function evaluation
As usual, parenthesis should be used to avoid confusion.
Note:
"V = (5>11) then 55 else 111" would assign a value of 111 to V,
"V = 5>11 then 55 else 111" would assign a value of 0 to V,
because in this case the expression is treated like:
"5 > (11 then 55 else 111)" == "5 >
55" == "0".
Using Units within
Expressions
The specification of unit or unit expressions must begin
with a '.' (4.2 .in). These may be concatenated (44.ft.lb) or inverted
(100.kg/1.sec). VX interprets the notation "expression.units"
as the value of "expression" currently expressed in "units"
and converts to its equivalent value in system database units.
In the hierarchy of operations conversion is higher than
multiplication, but lower than exponentiation. Thus 55.5.in*0.34.km is
processed as (55.5.in) * (0.34.km) and 25^2.m is processed as (25^2).m.
Parentheses have the highest priority and may always be used to avoid
confusion.
If the expression only contains a numeric constant and it is known that the expression defines a distance, it is assumed that the constant defines a distance in the active units. Otherwise, no assumptions are made about the units of a number unless the units are explicitly declared as described above.
You can embed variables inside text strings in parts, sketches and drawing sheets. The format is as follows:
Inside a text string: "You can embed this [$varname] inside of this text string."
Where varname is the name of the variable.
VX predefines part attribute data as text variables so that you can use them in this way. For example, you can embed part attribute text variables within your title block so that the information gets updated automatically as the part attributes change. Here is a list of text variables that are currently defined for part attributes.
part_number
part_class
part_designer
part_cost
part_supplier
part_description
part_keyword
part_manager
part_material
part_startdate
part_enddate
part_derived
part_<dimension label>
part_<user data label>
Editing Command
Line Expressions
Since command line expressions are considered driving parameters within features, you must edit the feature to edit the expression. You can use the History Editor to locate the feature and then right-click to edit it. You can also use the Redefine Feature command. See History Editing for more commands that work on a Part's History.
Referencing
Variables from Parts Associated with Drawing Sheets
You can reference variables from a part associated with the a drawing sheet without prefixing the variable name with the part name as stated in Variable naming Conventions above (this page). You can just use the variable name. Then, if the part referenced by the drawing sheet is changed, the sheet variable will automatically pull its value from the new part instead of the old.
This is convenient for setting up a title block to pull information from whatever part is associated with a drawing sheet. If you use the Replace Layout View Part command to change a part associated with a drawing sheet, you have to execute Regenerate Text (2D) command afterwards to update text strings that contain text variables.
General Notes
for Equations and Expressions
Using
the (Ctrl) and (Shift) Keys for Selection - When you select an item
from the scrolling list, the text font will change indicating that it
has been selected. As multiple items are selected, they are added to a
"pick list." The pick list can be processed by the various options
on this form. You can use the (Shift) key to select blocks of items. (Shift)+(Left-click)
will select all items between the picked item and the first item on the
active pick list -- all other items are unpicked. You can use (Ctrl)+(Left-click)
to unpick an item from the active pick list.
Referencing
External Variables - During equation editing, if you reference variables
that are external to the active part (i.e., those in the active part's
parent or child) be aware that the active part will not automatically
regenerate when/if the external variable is modified.
Using
Variable Names as Input - You can use the variable name of an equation
as input any time you are prompted to enter a value.
Spaces
are Supported in Expressions - You can use spaces in expressions (i.e.,
both "( v1 + 2 ) / v2" and "(v1+2)/v2" are acceptable).
Spaces are ignored by the expression evaluator.
IncludingFile Names in Variables or Dimensions - The Expression evaluator does not handle certain types of tokens. In particular variables and dimensions which are associated with file names which start with a numeric character or include other tokens (*, /, -, ...). VX has always supported braces to bypass this problem (e.g. [2001/Funky*Name a-go-go:variable]). VX now adds braces in automatically whenever a file name is included for variables or dimensions and is being inserted into an expression or equation.
