Defining Dimensional Constraints Parameters
You can control Dimensional Constraint geometry with mathematical equations and expressions.
Parametric equations include:
- The names of the Dimensional Constraints
- Expressions, in which you can use:
- Values
- User-defined variables, and variables that represent existing Dimensional Constraints
- Mathematical operators, functions, and constants
Expressions for Dimensional Constraints
When you create a Dimensional Constraint, an equation defines the dimension of an entity or between points on entities in the form name=value, for example d1=12.34.
You can replace the value by an expression: name=expression.
- Within the expression, you can use values, variables, mathematical operators, and mathematical functions and constants.
- The result of an expression is a value.
A variable can be one of the following:
- User-defined, for example length1=12.5
- An existing Dimensional Constraint name, for example d2=rad1
Use the Parameters Manager to define and edit expressions and variables.
You can also edit expressions in-place.
Dimensional Constraints Equation Examples
| Example |
Description |
| d1=rad1 |
Sets the variable d1 to the value of the variable rad1. |
| d2=rad2*2 |
Multiplies the variable rad2 by 2 and sets the variable d2 as the result. |
| length1=cos(ang1) |
Sets the user-defined variable length1 to the value of the cosine of angle ang1. |
| dist1=(length1 + d1) / 2 |
Sets the user-defined variable dist1 to the sum of the user-defined variable length1 and the variable d1 divided by 2. |
Constraint Names
Dimensional Constraints (both Dynamic and Annotation constraints) are identified by name, as well as user-defined variables used in expressions and formulas.
The Parameters Manager lists all Dimensional Constraints variables with their names, expressions, and values.
The naming conventions are:
| Meaning |
Default Name |
Constraints |
| Distance |
d1, d2, ..., dn |
Aligned, Horizontal, Vertical |
| Diameter |
dia1, dia2, ..., dian |
Diameter |
| Radius |
rad1, rad2, ..., radn |
Radial |
| Angle |
ang1, ang2, ..., angn |
Angular |
| User-defined |
user1, user2, ..., usern |
Used in expressions |
To rename constraint variable names:
- Specify a Dimensional Constraint.
- In the Properties palette, under Constraint, edit the Name.
- or -
- Specify a Dimensional Constraint.
- In the Parameter Manager palette, under Dimensional Constraints, edit the Name.
- or -
- Double-click a Dimensional Constraint.
- Edit the variable name in place.
Note: Constraint variable names must be unique.
Parametric Equations
Use operators and functions to define formulas and equations.
The evaluation of expressions follows standard mathematical rules.
Operators
You can use the following operators in expressions and formulas:
| Operator
|
Description |
+ |
Addition |
- |
Subtraction (or unary negation) |
* |
Multiplication |
/ |
Division |
^ |
Exponentiation |
% |
Floating point modulo |
. |
Decimal separator |
(expr) |
Parentheses to define expressions |
Functions
You can use the following functions in expressions and formulas:
| Function |
Syntax |
| Cosine |
cos (expr) |
| Sine |
sin (expr) |
| Tangent |
tan (expr) |
| Arc cosine |
acos (expr) |
| Arc sine |
asin (expr) |
| Arc tangent |
atan (expr) |
| Hyperbolic cosine |
cosh (expr) |
| Hyperbolic sine |
sinh (expr) |
| Hyperbolic tangent |
tanh (expr) |
| Arc hyperbolic cosine |
acosh (expr) |
| Arc hyperbolic sine |
asinh (expr) |
| Arc hyperbolic tangent |
atanh (expr) |
| Square root |
sqrt (expr) |
| Signum function (-1,0,1) |
sign (expr) |
| Absolute value |
abs (expr) |
| Truncate decimal |
trunc (expr) |
| Round to nearest integer |
round (expr) |
| Round down |
floor (expr) |
| Round up |
ceil (expr) |
| Largest element in array |
max (expr1;expr2) * |
| Smallest element in array |
min (expr1;expr2) * |
| Degrees to radians |
d2r (expr) |
| Radians to degrees |
r2d (expr) |
| Logarithm, base e |
ln (expr) |
| Logarithm, base 10 |
log (expr) |
| Exponent, base e |
exp (expr) |
| Exponent, base 10 |
exp10 (expr) |
| Power function |
pow (expr1;expr2) * |
| Random decimal, 0-1 |
random |
| Constant pi |
pi |
| Constant e |
e |
*) Uses the list separator (semicolon or comma) as defined in the OS format settings.
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Expression Evaluation
According to standard mathematical rules expressions are evaluated using the following precedence:
- Expressions within parentheses (innermost parentheses first)
- Standard operations order:
- Exponents
- Multiplication and division
- Addition and subtraction
- Operators of equal precedence from left to right.