Vince's Corner Takeout

[vince]

clean summary of all things bezier -- nth order curves, points, and derivatives

Code: (Select All)

sw = 800

sh = 600

screen _newimage(sw, sh, 32)



if _resize then

    sw = _resizewidth - 20

    sh = _resizeheight - 20

    screen _newimage(sw, sh, 32)

end if



n = 8

dim x(n - 1), y(n - 1)

x(0)=sw/2:y(0)=sh/7

x(1)=sw/3:y(1)=2*sh/7

x(2)=2*sw/3:y(2)=3*sh/7

x(3)=sw/5:y(3)=4*sh/7

x(4)=sw/2:y(4)=5*sh/7

x(5)=sw/5:y(5)=5*sh/7

x(6)=sw/2:y(6)=6*sh/7

x(7)=4*sw/5:y(7)=6*sh/7



cls

for i=0 to n - 1

    circle (x(i), y(i)), 3, _rgb(255,255,0)

next



preset (x(0), y(0))



ox = x(0)

oy = y(0)

dt = 0.02

for t=0 to 1 step dt

    bx = 0

    by = 0    

    

    dx = 0

    dy = 0

    

    for i=0 to n - 1

        bin = 1

        for j=1 to i

            bin = bin*(n - j)/j

        next

    

        p = bin*((1 - t)^(n - 1 - i))*(t^i)

        bx = bx + p*x(i)

        by = by + p*y(i)

                      

        q = bin*((1 - t)^(n - 2 - i))*(t^(i - 1))*(i - n*t + t)

        dx = dx + q*x(i)

        dy = dy + q*y(i)                

    next



    

    'hairline

    if abs(bx - ox)>1 and abs(by - oy)>1 then

        'line (ox, oy)-(bx, by), _rgb(55,55,55)



        ox = bx

        oy = by

    end if



    'point

    pset (bx, by), _rgb(255,0,0)



    'derivative vector

    m = sqr(dx*dx + dy*dy)

    line -step(7*dx/m, 7*dy/m), _rgb(0,255,0)



next

'line (ox, oy)-(bx, by), _rgb(55,55,55)