101 lines
3.1 KiB
Markdown
101 lines
3.1 KiB
Markdown
# orx-fcurve
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FCurves are 1 dimensional function curves constructed from 2D bezier functions.
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The language to express Fcurves is similar to SVG's path language.
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| Command | Description |
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|-----------------------|-------------------------------------------------------------|
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| `m/M y` | move the pen only in the y-direction |
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| `h/H x` | draw a horizontal line |
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| `l/L x y` | line to (x, y) |
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| `q/Q x0 y0 x y` | quadratic bezier to (x,y) and control-point (x0, y0) |
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| `c/C x0 y0 x1 y1 x y` | cubic bezier to (x,y) and control-points (x0, y0), (x1, y1) |
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| `t/T x y` | quadratic smooth to (x, y) |
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| `s/S x1 y1 x y` | cubic smooth to (x,y) and control point (x1, y1) |
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## Example Fcurves
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`M0 l5,10 q4,-10` or `M0 l5 10 q4 -10`
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`M0 h10 c3,10,5,-10,8,0.5 L5,5`
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New lines are allowed, which can help in formatting the Fcurve
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```
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M0 h10
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c3,10,5,-10,8,0.5
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L5,5
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```
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# EFCurves
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EFCurves are Fcurves with an additional preprocessing step in which scalar expressions are evaluated.
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## Comments
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EFCurves add support for comments using the `#` character.
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`M0 h10 c3,10,5,-10,8,0.5 # L5,5`
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```
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M0 h10 # setup the initial y value and hold it for 10 units.
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c3,10,5,-10,8,0.5 # relative cubic bezier curve
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# and a final line-to
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L5,5
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```
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## Expressions
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For example: `M0 L_3 * 4_,4` evaluates to `M0 L12,4`.
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`orx-expression-evaluator` is used to evaluate the expressions, please refer to its
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documentation for details on the expression language used.
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## Repetitions
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EFCurves add support for repetitions. Repetitions are expanded by replacing
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occurrences of `|<text-to-repeat>|[<number-of-repetitions>]` with `number-of-repetitions` copies
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of `text-to-repeat`.
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For example:
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* `M0 |h1 m1|[3]` expands to `M0 h1 m1 h1 m1 h1 m1`
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* `M0 |h1 m1|[0]` expands to `M0`
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### Nested repetitions
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Repetitions can be nested.
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For example `|M0 |h1 m1|[3]|[2]` expands to `M0 h1 m1 h1 m1 h1 m1 M0 h1 m1 h1 m1 h1 m1`.
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### Interaction between repetitions and expressions
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`M0 |H_it + 1_ m1][3]` expands to `M0 H1 m1 H2 m1 H3 m1`
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`M0 |H_index + 1_ m_it_]{1.2, 1.3, 1.4}` expands to `M0 H1 m1.2 H2 m1.3 H3 m1.4`
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# References
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* https://x.com/ruby0x1/status/1258252352672247814
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* https://blender.stackexchange.com/questions/52403/what-is-the-mathematical-basis-for-f-curves/52468#52468
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* https://pomax.github.io/bezierinfo/#yforx
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<!-- __demos__ -->
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## Demos
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### DemoFCurve01
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[source code](src/jvmDemo/kotlin/DemoFCurve01.kt)
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### DemoFCurve02
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[source code](src/jvmDemo/kotlin/DemoFCurve02.kt)
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### DemoMultiFCurve01
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[source code](src/jvmDemo/kotlin/DemoMultiFCurve01.kt)
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