# orx-fcurve

FCurves are 1 dimensional function curves constructed from 2D bezier functions. 

The language to express Fcurves is similar to SVG's path language.

| Command               | Description                                                 |
|-----------------------|-------------------------------------------------------------|
| `m/M y`               | move the pen only in the y-direction                        |
| `h/H x`               | draw a horizontal line                                      |
| `l/L x y`             | line to (x, y)                                              |  
| `q/Q x0 y0 x y`       | quadratic bezier to (x,y) and control-point (x0, y0)        |
| `c/C x0 y0 x1 y1 x y` | cubic bezier to (x,y) and control-points (x0, y0), (x1, y1) |
| `t/T x y`             | quadratic smooth to (x, y)                                  |
| `s/S x1 y1 x y`       | cubic smooth to (x,y) and control point (x1, y1)            |

## Example Fcurves

`M0 l5,10 q4,-10` or `M0 l5 10 q4 -10`

`M0 h10 c3,10,5,-10,8,0.5 L5,5`

New lines are allowed, which can help in formatting the Fcurve
```
M0 h10
c3,10,5,-10,8,0.5
L5,5
```

# EFCurves

EFCurves are Fcurves with an additional preprocessing step in which scalar expressions are evaluated.

## Comments

EFCurves add support for comments using the `#` character. 

`M0 h10 c3,10,5,-10,8,0.5 # L5,5`


```
M0 h10               # setup the initial y value and hold it for 10 units.
c3,10,5,-10,8,0.5    # relative cubic bezier curve
# and a final line-to
L5,5
```

## Expressions

For example: `M0 L_3 * 4_,4` evaluates to `M0 L12,4`. 

`orx-expression-evaluator` is used to evaluate the expressions, please refer to its
documentation for details on the expression language used.

## Repetitions 

EFCurves add support for repetitions. Repetitions are expanded by replacing
occurrences of `|<text-to-repeat>|[<number-of-repetitions>]` with `number-of-repetitions` copies
of `text-to-repeat`.

For example:
 * `M0 |h1 m1|[3]` expands to `M0 h1 m1 h1 m1 h1 m1`
 * `M0 |h1 m1|[0]` expands to `M0`

### Nested repetitions

Repetitions can be nested. 

For example `|M0 |h1 m1|[3]|[2]` expands to `M0 h1 m1 h1 m1 h1 m1 M0 h1 m1 h1 m1 h1 m1`.

### Interaction between repetitions and expressions

`M0 |H_it + 1_ m1][3]` expands to `M0 H1 m1 H2 m1 H3 m1`



`M0 |H_index + 1_ m_it_]{1.2, 1.3, 1.4}` expands to `M0 H1 m1.2 H2 m1.3 H3 m1.4`



# References
 * https://x.com/ruby0x1/status/1258252352672247814
 * https://blender.stackexchange.com/questions/52403/what-is-the-mathematical-basis-for-f-curves/52468#52468
 * https://pomax.github.io/bezierinfo/#yforx