Rosio Pavoris a blog

If you’ve ever used a vector drawing program you’ve probably come across them. It turns out they’re conceptually a lot simpler than I expected them to be.
Wikipedia has great pictures that should be self-explanatory:

This is a linear “curve”, with only two guide points:

A quadratic curve has three guide points:

A cubic curve has four:

And a quartic curve has five:

Most vector graphic applications only go up to cubic, and represent more complicated curves as grafts of simpler ones.
My last exam was yesterday, though, so I had some free time, and I’ve been playing with Allegro recently, so I thought I’d write something that draws Bézier curves of arbitrary complexity. Behold.

First line is how you compile it on a typical system. You’ll need Allegro, obviously, which for Debian/Ubanto users is the liballegro-dev package. Others can get it here.

The guide points it uses are passed as command line arguments, with the first argument being the x coordinate of the first point, the second being the y coordinate of the first point, the third being the x coordinate of the second point, &c.
The origin (0, 0) is at the top left of the screen.

./bezier 10 10 50 320 310 230 200 10

This should give you something like:

The program will pause after drawing your curve, until you press a key. If that key is s, it will save the screen to a .pcx file, the name of which you can change in the #defines (default bezier.pcx; if you don’t like .pcx, Allegro also supports .bmp and .tga, and will determine file type based on the extension).

Other things you can customise should mostly be obvious. If LINES is 0 (or undefined), it will just draw pixels instead of trying to connect points with lines. If GUIDES is 1 it will mark the guide points in the color specified by GUIDECOL. GUIDECOL, FOREGROUND, and BACKGROUND are just RGB values in the range 0-255.
WIDTH and HEIGHT are the dimensions of the drawing field. This doesn’t have to be your resolution, but probably shouldn’t be higher. If you want a 100×100 image, 100 and 100 are perfectly legal values.
GRAIN is how often divide() recurses while trying to divide lines into sections. Higher values should give more accurate representations, but usually aren’t needed. STEPS is how many points this will actually give you. Don’t touch STEPS.

This isn’t hugely interesting, but it’s a nice enough toy that I thought I’d share it.