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If a parametric curve is needed to describe the style template, create it using symbolic expressions, for example:
You can use basic mathematical operations, functions and constants to create a symbolic expression in Renga STDL.
Operations that can be performed on variables, constants, and functions in symbolic expressions:
| Operation | Description |
|---|---|
+ | addition |
- | subtraction |
* | multiplication |
/ | division |
^ | exponentiation |
- | unary minus |
Mathematical functions that can be used in symbolic expressions:
| Function Name | Description |
|---|---|
| sin | sine with argument in radians |
| cos | cosine with argument in radians |
| tan | tangent with argument in radians |
| sind | sine with argument in degrees |
| cosd | cosine with argument in degrees |
| tand | tangent with argument in degrees |
| asin | arcsine with the result in radians |
| acos | arccosine with the result in radians |
| atan | arctangent with the result in radians |
| asind | arcsine with the result in degrees |
| acosd | arccosine with the result in degrees |
| atand | arctangent with the result in degrees |
| sqrt | square root |
| exp | exponential |
| ln | natural logarithm |
| lg | decimal logarithm |
| deg | function to convert radians to degrees |
| rad | function to convert degrees to radians |
| abs | absolute value |
In symbolic expressions, numbers can be represented as unnamed constants, specified as floating-point numbers (a sequence of digits separated by a dot), or as integers.
Symbolic expressions can also include the use of named constants:
| Constant Name | Description |
|---|---|
| M_PI | π - the ratio of a circle's circumference to its diameter |
| M_PI_2 | π / 2 |
| M_PI_4 | π / 4 |
| M_SQRT2 | √2 |
| M_E | e – the base of the natural logarithm |
| M_PHI | φ – the golden ratio |
| M_RADDEG | 180 / π – conversion factor from radians to degrees |
| M_DEGRAD | π / 180 – conversion factor from degrees to radians |
When creating symbolic expressions, the following limitations should be taken into account:
Because of these limitations, correct calculations for analytical expressions can only be performed for relatively simple mathematical expressions and functions. For example, calculating the value of sin(t)/t at zero can be inaccurate.