# pif_BezierCurve

Generate sample points for drawing Bézier curves. [More]

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byond://Popisfizzy.pif_BezierCurve##version=1

Version 1.1.20160422
 Date added: Apr 12 2016 Last updated: Jan 2 2019

This project is available on GitHub!

Bézier curves are smooth parametric curves in arbitrary dimensions generated by a collection of n points. Their 'nice' behavior gives them many uses in computer graphics, and on top of that they look quite good too. They can also be naturally transformed by linear maps (i.e., linear transformations or matrix transformations) by simply transforming the n sample points.

Note: At this time, this library provides no means to actually draw the curve or produce an image of the curve, and instead simply outputs a list of points which the programmer must use to draw lines between in order to approximate the curve.

Example

Below is an example of how one could use this library to draw a Bézier curve for nine points with a "smoothness" (see documentation) of 50, where the points are: (0,0), (1,1), (2,2), (3,3), (4,4), (5,3), (6,2), (7,1), (8,0). This is assuming we have a DrawLine() method available that takes two points and draws a line between them.

```var    pif_BezierCurve/C = new(        0,0 , 1,1 , 2,2 , 3,3 , 4,4 , 5,3 , 6,2 , 7,1 , 8,0    )    list/Curve    last_x    last_yC.Smoothness(50)Curve = C.Curve()last_x = Curve[1]last_y = Curve[2]for(var/i = 1, i < C.Smoothness(), i ++)    var        new_x = Curve[2*i+1]        new_y = Curve[2*i+2]    DrawLine(last_x,last_y , new_x,new_y)    last_x = new_x    last_y = new_y
```

And below is what this curve looks like, along with the sample points used to generate it.

```Copyright (c) 2016-2019 Timothy "popisfizzy" Reilly

Permission is hereby granted, free of charge, to any person obtaining a copy
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The above copyright notice and this permission notice shall be included in
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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```

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