Arithmetic and Logical Expressions

Any arithmetic expressions can be used in numerical inputs. Further processing of these expressions can also be linked to logical IF-THEN-ELSE conditions:

• Arithmetic operators
• Logical comparison expressions
• Mathematical basic functions
• IF-conditions
• Point, distance and angle entries

Only round brackets can be used as brackets, square or curly brackets are not permissible. You can use several nested brackets, but the brackets must be matched, i.e. every opening bracket must also have a closing bracket.

Arithmetic operators

The following operators can be used in an expression:

Instead of the operator ^, the function name XHY (x to the power of y) can also be used.

An arithmetic expression is evaluated according to the usual mathematical rules.

Logical comparison expressions

A logical comparison expression refers to a simple arithmetic comparison a1 op a2, where a1 and a2 are arithmetic expressions linked to a comparison operator op; op can be one of the following operators:

A logical comparison expression, however, can be formed from several simple arithmetic comparisons using the logical operators  AND and OR.

Logical comparison expressions are important, for example, if the value assignment to a variable is to be made dependent on certain conditions.

 Basic mathematical functions

Example: SQRT (A*A + B*B)  returns 

Although the trigonometric functions generally only process values in radians, inputs and results are processed and output in degrees within the HiCAD formula interpreter, depending on the angle unit defined. You use the ARC and GRD functions to convert between degrees and radians.

IF-conditions

The value assignment to a variable can depend on a condition. Two syntactic forms are possible:

• IF vglad THEN a or
• IF vglad THEN a ELSE b

where vglad stands for a logical comparison expression and a and b for any arithmetic expressions.

In the first form of the IF-condition, the value assignment is only performed if vglad is fulfilled, i.e. is true. In this case, the value of the expression a is assigned to the variable. In the other case, no value is assigned.

In the second form of the IF-condition, the value of the arithmetic expression is assigned to variable v if vglad is fulfilled; if not, the value of expression b is assigned.

The conditional value assignment will be used most within macro procedures and variants and can have extremely different forms. If, for example, you want the height of the text annotation to be selected depending on scale, a comparison of system variable @2 with a constant value generally suffices:

IF @2 < 100 THEN 2.5 ELSE 3

For scale numbers up to and including 100, annotation size 2.5 mm is selected and 3 mm for larger scales

Point, distance and angle entries

Arithmetic expressions can also be contained as a component in compound statements. For example, it is possible to use arithmetic expressions for point options A, R, P, W and D, which expect numerical arguments.

The following should be borne in mind for this application type as an argument of point options and as an argument after a distance and angle input:

• The character L directly after a point option or a distance or angle input is interpreted as the last distance or last angle and not as variable L.
• If variable L is to be used in this context, it must not be the first character of the arithmetic expression. This can easily be avoided by placing the variable in brackets or assigning it a plus/minus sign:

Example:

P L d is interpreted as a point option "polar coordinates with the angle last used and distance d", while the expressions P (L) d or P + L d use the value of variable L as the angle.

The same applies to options Z and FA which enable you to take distances and angles from the drawing.

Formulae

For all 3-D functions for which HiCAD requests the input of a numerical value, you can also enter a formula instead of a simple value. Formulae can be entered directly during the designing process, or subsequently in the feature list. The input of a value is therefore not always required, e.g. for the length of an edge (edge_length(e1)), or the distance between 2 point (distance_points(p1,p2)). For these formulae the variables (e1,p1,p2) must have been defined in the variables list of the part. One advantage of the working with formulae is that you do not need to know the exact value, and that the parameter will adjust itself to the defined variables.

Further information can be found in the Feature Technology Help and in the Automatisation with HiCAD Whitepaper in the ISD Wiki.