Local ax=50,ay=50,bx=400,by=50,cx=350,cy=750,dx=750,dy=750
t1#=0
t2#=0
speed#=0 'Speed of clever speed changing version
x1#=ax
y1#=ay
x2#=ax
y2#=ay
While Not KeyHit(KEY_ESCAPE)
        SetColor 100,100,100
        bezier(ax,ay,bx,by,cx,cy,dx,dy) 'draw the curve
       
        ox1#=x1
        oy1#=y1
        ox2#=x2
        oy2#=y2
       
        'CLEVER SPEED CHANGING VERSION
        t1:+speed
        If t1>1 Then t1=0
        a#=t1
        b#=1-t1
        x1#=ax*b*b*b + 3*bx*b*b*a + 3*cx*b*a*a + dx*a*a*a
        y1#=ay*b*b*b + 3*by*b*b*a + 3*cy*b*a*a + dy*a*a*a
        SetColor 255,255,0
        DrawRect x1-3,y1-3,7,7

        'Calculate 'speed' of curve at this point.
        vx#=-3*ax*b*b + 3*bx*b*(b-2*a) + 3*cx*a*(2*b-a) + dx*3*a*a
        vy#=-3*ay*b*b + 3*by*b*(b-2*a) + 3*cy*a*(2*b-a) + dy*3*a*a
        d#=Sqr(vx*vx+vy*vy)

        'Watch out, magic ahead!

        speed#=1/d 'Make the ball moves less along the curve the 'faster' the curve is at this point, so the ball's *actual* cartesian velocity should stay roughly constant

        'You missed the magic! Go back!

        'Check what the actual speed is
        movedist1#=Sqr((ox1-x1)^2+(oy1-y1)^2)
        DrawText movedist1,0,0

        'Boring old version, t increments at a constant rate
        t2:+.001
        If t2>1 Then t2=0
        a#=t2
        b#=1-t2
        x2#=ax*b*b*b + 3*bx*b*b*a + 3*cx*b*a*a + dx*a*a*a
        y2#=ay*b*b*b + 3*by*b*b*a + 3*cy*b*a*a + dy*a*a*a
        SetColor 0,0,255
        DrawRect x2-3,y2-3,7,7

        'Check what the actual speed is
        movedist2#=Sqr((ox2-x2)^2+(oy2-y2)^2)
        DrawText movedist2,0,15

        Flip
        Cls
Wend

'DON'T BE DECEIVED! This is just a plain old bezier-drawing function, to show the curve the balls are moving along
Function bezier(ax#,ay#,bx#,by#,cx#,cy#,dx#,dy#)
        DrawLine ax,ay,bx,by
        DrawLine cx,cy,dx,dy
        ox#=ax
        oy#=ay
        For t#=0 To 1 Step .01
                a#=t
                b#=1-t
                x#=ax*b*b*b + 3*bx*b*b*a + 3*cx*b*a*a + dx*a*a*a
                y#=ay*b*b*b + 3*by*b*b*a + 3*cy*b*a*a + dy*a*a*a
                DrawRect x-1,y-1,3,3
                DrawLine ox,oy,x,y
                ox=x
                oy=y
        Next