## by donb, published May 30, 2011

OpenSCAD Conic Bezier Curve by donb May 30, 2011
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# Summary

also known as Quadratic Bezier Curve
also known as Bezier Curve with 3 control points
also known as 'Conic Arcs' or 'Parabolic Segments'
By Don B, 2011, released into the Public Domain

What's it for

Bezier curves allow you to pick a small number of 'control points', then let the computer fill in a pretty curve between them. In this thing, 3 control points are used.

Notes

This is for 3-point bezier curves; there is another popular type, the 4-point 'Cubic', that this code doesn't do.

This is inspired by William Adam's cubic bezier Thingiverse OpenSCAD code. His code now also handles Conics; I guess I will leave this thing here as a sort of 'super simple' 'for dummies' version.

The first sample image shows a simple 3 control-point curved polygon, and a rod around which it can be rotated. The result of this rotation is shown in the big smooth object.

The next sample image shows the code itself; the module is only about 10 lines long thanks to OpenSCAD's built-in vector math.

http://www.thingiverse.com/thing:8443 by William A Adams (Cubic Beziers)
http://en.wikipedia.org/wiki/File:Bezier_2_big.gif by Phil Tregoning
http://en.wikipedia.org/wiki/B%C3%A9zier_curve by Wikipedia editors
http://www.freetype.org/freetype2/docs/glyphs/glyphs-6.html David Turner + Freetype team

Using the code

2. copy/paste the BezConic module to your own code
3. call it like this:

p0=[15,0];
p1=[1,14];
p2=[7,30];
linear_extrude() BezConic(p0,p1,p2,steps=20);

Fun Facts

BÃ©zier are named after Pierre BÃ©zier, who used the work of Paul de Casteljau to make curves on car bodies. Casteljau worked at Citroen and Bezier worked at Renault.

They are named 'conic' because 3-point Bezier's are basically parabolas. A parabola is basically the intersection of a cone with a plane (i.e. a conic section). Please see wikipedia for more info.

Conic Arc BÃ©zier Curves (3 control points) are used by TrueType fonts.

# Instructions

An example .stl file is included just for giggles.

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Here's a modified version of your module that will create a solid shape with a Bezier curve profile:

``````module bezier_solid( p0, p1, p2, steps = 5 ) {
stepsize1 = (p1-p0)/steps;
stepsize2 = (p2-p1)/steps;

rotate_extrude() {
for (i=[0:steps-1]) {
point1 = p0+stepsize1*i;
point2 = p1+stepsize2*i;
point3 = p0+stepsize1*(i+1);
point4 = p1+stepsize2*(i+1);
bpoint1 = point1+(point2-point1)*(i/steps);
bpoint2 = point3+(point4-point3)*((i+1)/steps);
polygon(
points=[
[0, bpoint1[1]],
bpoint1,
bpoint2,
[0, bpoint2[1]]
]
);
}
}
}``````

Exactlly right!

I had actually added the 3 point Beziers to my latest mesh/surface library, but didn't advertise. Rotation around any axis would be a very good thing. This combined with some surface normal goodness and you've got the makings of a killer new feature which I'm sure will be much used. Think of ho
w easy it is to create a vase of almost any shape!

lol redundancy. which one is your latest library? there are so many....

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