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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_y
C.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.
The MIT License
Copyright (c) 2016-2024 Timothy "popisfizzy" Reilly
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
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sell copies of the Software, and to permit persons to whom the Software is
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The above copyright notice and this permission notice shall be included in
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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