bezier.p8.txt

-- pico8 bezier demo     https://github.com/ursetto
-- derived from https://twitter.com/freyaholmer/status/1063633408411295744

w1=40 w2=w1+16
p0={x=64-w1,y=90,c=8}
p1={x=64-w2,y=30,c=9}
p2={x=64+w2,y=30,c=10}
p3={x=64+w1,y=90,c=11}
◆={p0,p1,p2,p3}

cls()
t=0

-- t := 0..1.
function lerp(p1,p2,t)
 local x local y
 x = p1.x + (p2.x-p1.x) * t
 y = p1.y + (p2.y-p1.y) * t
 return {x=x,y=y}
end

function linep(p0,p1,c)
 line(p0.x,p0.y,p1.x,p1.y,c)
end
function circp(p,c)
 circfill(p.x,p.y,1,c) -- p.c?
end

function bezier(p0,p1,p2,p3,t)
 local x=bezier★(p0.x,p1.x,p2.x,p3.x,t)
 local y=bezier★(p0.y,p1.y,p2.y,p3.y,t)
 return {x=x,y=y}                 
end
function bezier★(x0,x1,x2,x3,t)
  -- returns a 1-d point
  -- p = p0*(-t^3+3t^2-3t+1)+
  --     p1*(3t^3-6t^2+3t)+
  --     p2*(-3t^3+3t^2)+
  --     p3*(t^3)
  -- p = p0*(1-t)(1-t)(1-t) +
  --     p1*3*t*(1-t)(1-t) +
  --     p2*3*t*t(1-t) +
  --     p3*t*t*t
   local omt = 1-t
   local omt2 = omt*omt
   local t2 = t*t
   return x0 * omt2 * omt +
          x1 * 3 * t * omt2 +
          x2 * 3 * t2 * omt +
          x3 * t * t2
end
function beziercurve(p0,p1,p2,p3,tmin,tmax,step,c)
   local t=tmin
   p = bezier(p0,p1,p2,p3,t)
   pset(p.x,p.y,c)
   t += step
   while (t < tmax) do
    pold = p
    p = bezier(p0,p1,p2,p3,t)
    --pset(p.x,p.y,c)
    linep(pold,p,c)
    t += step
   end
   t = tmax
   p = bezier(p0,p1,p2,p3,t)
   pset(p.x,p.y,c)
end

function _draw()
 cls()
 local p

 local t0=t/90  -- speed divisor
 -- convert 1..-1 to 0..1
 t0=(cos(t0+0.5)+1)/2

 -- draw the traversed curve
 -- up to the current point
 beziercurve(p0,p1,p2,p3,0,t0,0.02,1)

 for p in all(◆) do
  circp(p,p.c)
 end
 
 -- interpolate once
 pi0=lerp(p0,p1,t0)
 pi1=lerp(p1,p2,t0)
 pi2=lerp(p2,p3,t0)
 linep(pi0,pi1,5)
 linep(pi1,pi2,5)
 circp(pi0,6)
 circp(pi1,6)
 circp(pi2,6)

 -- interpolate again
 pii0=lerp(pi0,pi1,t0)
 pii1=lerp(pi1,pi2,t0)
 linep(pii0,pii1,5)
 circp(pii0,6)
 circp(pii1,6)

 -- interpolate once more
 piii0=lerp(pii0,pii1,t0)
 circp(piii0,12)


end

function _update60()
 t=t+0.5
end