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Cart [#48050#] | 2018-01-11 | No License | Embed
3

I made this the other day when just playing around with making an ellipse function for PICO-8 https://twitter.com/eggboycolor/status/949173853045043200 -- but I've decided to post on the BBS.

The core of the effect is a scanline-based ellipse drawing function, based on an algorithm that uses Bresenham style error calculation. The code for the ellipse function is described in a paper called "A Fast Bresenham Algorithm for Drawing Ellipses" by John Kennedy, and I've ported the pseudo-code to work with pico8.

Here's the ellipse function code:

-- based on:
-- "a fast bresenham type
-- algorithm for drawing
-- ellipses" by john kennedy
function ellipse(
 cx,cy,xr,yr,c,hlinefunc
)
 xr=flr(xr)
 yr=flr(yr)
 hlinefunc=hlinefunc or rectfill
 local xrsq=shr(xr*xr,16)
 local yrsq=shr(yr*yr,16)
 local a=2*xrsq
 local b=2*yrsq
 local x=xr
 local y=0
 local xc=yrsq*(1-2*xr)
 local yc=xrsq
 local err=0
 local ex=b*xr
 local ey=0
 while ex>=ey do
  local dy=cy-y
  hlinefunc(cx-x,cy-y,cx+x,dy,c)
  dy+=y*2
  hlinefunc(cx-x,dy,cx+x,dy,c)
  y+=1
  ey+=a
  err+=yc
  yc+=a
  if 2*err+xc>0 then
   x-=1
   ex-=b
   err+=xc
   xc+=b
  end
 end

 x=0
 y=yr
 xc=yrsq
 yc=xrsq*(1-2*yr)
 err=0
 ex=0
 ey=a*yr
 while ex<=ey do
  local dy=cy-y
  hlinefunc(cx-x,cy-y,cx+x,dy,c)
  dy+=y*2
  hlinefunc(cx-x,dy,cx+x,dy,c)
  x+=1
  ex+=b
  err+=xc
  xc+=b
  if 2*err+yc>0 then
   y-=1
   ey-=a
   err+=yc
   yc+=a
  end
 end
end

Could probably be optimized further.

The main difference from the original pseudo-code is just that rather than a "plot four ellipse points" function, I made the program a callback for each horizontal line segment to be drawn, and call that function twice for the top and bottom halves of the ellipse. This function defaults to rectfill but could be any function that takes (x, y, x2, y2, color), which is what I do for the wavy effect pictured in my cart. And if you poke certain settings, as you can see, fill patterns can be passed along too -- I guess really, you could interpret color any way you want for your particular scanline fill function.

Oh, also, it shifts the x and y radius down a bunch before squaring to avoid signed 16.16 fixed-point overflow.

And if you're more curious about the wavy effect, feel free to hit the view source (Code) button. I bet there are much cooler effects possible with a scanline based fill algorithm, but I was just trying to throw something together really quick.

P#48051 2018-01-10 20:08 ( Edited 2018-01-11 01:50)


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