Donut math: how donut.c works (2011)

slightly disappointing - the effect is interesting but the implementation and derivation are sloppy.

using a z buffer is a little unexciting i was expecting something raytracy or voxely - maybe even scanliney... but thats too much to explain in this comment.

also using the matrices for deriving the torus equation... its much simpler to create a rotating basis intuitively with cos and sin then apply them again to create a circle going around... then rotate the torus as a separate operation before applying the 3d projection

e.g. start with

  x = R*cos(t);
  y = R*sin(t);

to define the big circle - note that ( cos(t), sin(t), 0 ) is the normal to that circle and use that to create the circles winding around with a second parameter:

  x = r*cos(t)*cos(u) + R*cos(t)
  y = r*sin(t)*cos(u) + R*sin(t)
  z = r*sin(u)

set u = n * t and then you get the torus shape with a single parameter where the spiral around the surface closes up on itself.

the 3d rotation of the whole object can be kept separate and done on a per axis basis (since using only two angle this is actually less operations as well)

you end up with the same result but no need to do any particularly challenging algebra.

And here's the beginning of a1k0n's MSP430 port:

https://gist.github.com/a1k0n/8582230

:)

I read that article awhile ago, used the character brightness representation idea to build a JavaScript image/webcam/video to ascii converter http://dph.am/jscii/ https://github.com/EnotionZ/jscii

I've ported it to Python:

https://gist.github.com/reeesga/8580649

How do I compile this? GCC complains:

    CFLAGS="-g -pipe" make -k donut
    cc -g -pipe    donut.c   -o donut
    donut.c:1:2: warning: data definition has no type or storage class [enabled by default]
    donut.c: In function ‘main’:
    donut.c:4:16: warning: incompatible implicit declaration of built-in function ‘printf’ [enabled by default]
    donut.c:5:12: warning: incompatible implicit declaration of built-in function ‘memset’ [enabled by default]
    donut.c:9:63: error: ‘s’ undeclared (first use in this function)
    donut.c:9:63: note: each undeclared identifier is reported only once for each function it appears in
    donut.c:10:18: error: expected ‘,’ or ‘;’ before ‘in’
    donut.c:11:32: error: ‘t’ undeclared (first use in this function)
    make: *** [donut] Errore 1
    
    Compilation exited abnormally with code 2 at Thu Jan 23 16:11:12

Definitely worth checking out! Some fascinating code and math to create animated ASCII art.

I ported this to Lua as a PNaCl demo: https://gonativeclient.appspot.com/demo/lua

Click the "Donut" button, and press enter.

Replace line printf("\x1b[H") with you system specific screen clearing function if you don't have POSIX.