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Vince's Corner Takeout
#53
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)
Reply


Messages In This Thread
Vince's Corner Takeout - by bplus - 04-29-2022, 02:12 PM
RE: Vince's Corner Takeout - by vince - 04-29-2022, 09:34 PM
RE: Vince's Corner Takeout - by vince - 05-02-2022, 03:10 AM
RE: Vince's Corner Takeout - by bplus - 05-02-2022, 04:25 AM
RE: Vince's Corner Takeout - by vince - 05-02-2022, 11:16 PM
RE: Vince's Corner Takeout - by vince - 05-03-2022, 01:10 AM
RE: Vince's Corner Takeout - by bplus - 05-03-2022, 01:15 AM
RE: Vince's Corner Takeout - by vince - 05-03-2022, 04:26 AM
RE: Vince's Corner Takeout - by bplus - 05-03-2022, 03:32 PM
RE: Vince's Corner Takeout - by vince - 05-10-2022, 03:41 AM
RE: Vince's Corner Takeout - by vince - 05-10-2022, 03:57 AM
RE: Vince's Corner Takeout - by dcromley - 05-10-2022, 02:57 PM
RE: Vince's Corner Takeout - by vince - 05-10-2022, 08:14 PM
RE: Vince's Corner Takeout - by SMcNeill - 05-10-2022, 02:59 PM
RE: Vince's Corner Takeout - by vince - 05-11-2022, 01:13 AM
RE: Vince's Corner Takeout - by dcromley - 05-11-2022, 01:58 AM
RE: Vince's Corner Takeout - by vince - 06-01-2022, 09:05 AM
RE: Vince's Corner Takeout - by vince - 08-11-2022, 02:51 AM
RE: Vince's Corner Takeout - by bplus - 06-03-2022, 02:47 PM
RE: Vince's Corner Takeout - by triggered - 06-04-2022, 02:00 AM
RE: Vince's Corner Takeout - by vince - 06-07-2022, 02:02 AM
RE: Vince's Corner Takeout - by bplus - 06-07-2022, 02:15 AM
RE: Vince's Corner Takeout - by vince - 07-13-2022, 05:23 AM
RE: Vince's Corner Takeout - by BSpinoza - 07-14-2022, 04:54 AM
RE: Vince's Corner Takeout - by bplus - 07-14-2022, 04:35 PM
RE: Vince's Corner Takeout - by aurel - 08-11-2022, 01:02 PM
RE: Vince's Corner Takeout - by bplus - 08-11-2022, 04:22 PM
RE: Vince's Corner Takeout - by aurel - 08-11-2022, 05:33 PM
RE: Vince's Corner Takeout - by BSpinoza - 08-12-2022, 03:44 AM
RE: Vince's Corner Takeout - by vince - 08-11-2022, 08:42 PM
RE: Vince's Corner Takeout - by vince - 08-19-2022, 05:00 AM
RE: Vince's Corner Takeout - by bplus - 08-19-2022, 06:33 PM
RE: Vince's Corner Takeout - by vince - 08-23-2022, 10:04 PM
RE: Vince's Corner Takeout - by vince - 11-04-2022, 01:48 AM
RE: Vince's Corner Takeout - by vince - 03-31-2023, 11:07 PM
RE: Vince's Corner Takeout - by vince - 09-18-2023, 11:45 PM
RE: Vince's Corner Takeout - by Dav - 09-19-2023, 12:54 AM
RE: Vince's Corner Takeout - by bplus - 09-19-2023, 01:37 AM
RE: Vince's Corner Takeout - by GareBear - 09-19-2023, 03:56 PM
RE: Vince's Corner Takeout - by bplus - 09-19-2023, 04:47 PM
RE: Vince's Corner Takeout - by vince - 09-19-2023, 06:54 PM
RE: Vince's Corner Takeout - by bplus - 09-19-2023, 09:02 PM
RE: Vince's Corner Takeout - by vince - 01-13-2024, 07:15 PM
RE: Vince's Corner Takeout - by bplus - 01-13-2024, 07:59 PM
RE: Vince's Corner Takeout - by GareBear - 01-13-2024, 10:54 PM
RE: Vince's Corner Takeout - by vince - 02-16-2024, 04:01 AM
RE: Vince's Corner Takeout - by bplus - 02-16-2024, 02:27 PM
RE: Vince's Corner Takeout - by vince - 02-16-2024, 07:16 PM
RE: Vince's Corner Takeout - by Sprezzo - 02-17-2024, 03:04 AM
RE: Vince's Corner Takeout - by bplus - 02-17-2024, 02:44 PM
RE: Vince's Corner Takeout - by vince - 10-07-2024, 08:11 AM
RE: Vince's Corner Takeout - by bplus - 10-07-2024, 01:32 PM
RE: Vince's Corner Takeout - by vince - 10-11-2024, 12:05 AM
RE: Vince's Corner Takeout - by vince - 10-11-2024, 12:16 AM
RE: Vince's Corner Takeout - by PhilOfPerth - 10-11-2024, 03:51 AM
RE: Vince's Corner Takeout - by vince - 10-11-2024, 07:55 PM
RE: Vince's Corner Takeout - by PhilOfPerth - 10-11-2024, 11:30 PM
RE: Vince's Corner Takeout - by vince - 10-15-2024, 10:54 AM
RE: Vince's Corner Takeout - by bplus - 10-15-2024, 01:40 PM



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