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point on a bezier

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How could I get the coordinates of a point on a bezier line, given a value from 0 to 1? (0 is one endpoint, 1 being the other end.)

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What kind of Bezier curve fitting routine are you using? Most derivations give, as output, parametric equations that do exactly what you''re asking.

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Here''s what I''m doing right now. (its darkbasic code)
Circle travels back and forth over the line.

the increments aren''t equal, so the circle moves at inconsistent speeds.



sync rate 0
sync on

sw = screen width()
sh = screen height() - 80
speed# = 0.001

randomize timer()

x1 = rnd(sw)
y1 = rnd(sh) + 16
x2 = rnd(sw)
y2 = rnd(sh) + 16
c1x = rnd(sw)
c1y = rnd(sh) + 16
c2x = rnd(sw)
c2y = rnd(sh) + 16

mousemode = 0
control = 0

set text font "Arial"
set text size 16

repeat

cls

if inkey$()="a"
mousemode = 1
control = 1
endif

if inkey$()="b"
mousemode = 1
control = 2
endif

if inkey$()="1"
mousemode = 1
control = 3
endif

if inkey$()="2"
mousemode = 1
control = 4
endif

if mouseclick()=1
mousemode = 0
endif

if mousemode = 1
select control
case 1
x1 = mousex()
y1 = mousey()
endcase
case 2
x2 = mousex()
y2 = mousey()
endcase
case 3
c1x = mousex()
c1y = mousey()
endcase
case 4
c2x = mousex()
c2y = mousey()
endcase
endselect
endif

text 0,0,"A: " + str$(x1) + "x " + str$(y1) + "y"
text 0,20,"B: " + str$(x2) + "x " + str$(y2) + "y"
text 0,40,"C1: " + str$(c1x) + "x " + str$(c1y) + "y"
text 0,60,"C2: " + str$(c2x) + "x " + str$(c2y) + "y"
text 0,80, str$(t#)
center text screen width()/2,screen height()-20,"Bezier Curve - Press A/B/1/2 to move the points. Left Mouse to set"


if thing = 1
ttt# = ttt# + speed#
if ttt# >= 1 then thing=0
endif

if thing = 0
ttt# = ttt# - speed#
if ttt# <= 0 then ttt# = 0: thing=1
endif


Bezier(x1, y1, x2, y2, c1x, c1y, c2x, c2y, ttt#)
sync

until escapekey()

end

function Bezier(x1, y1, x2, y2, c1x, c1y, c2x, c2y, t#)

x as float
y as float

cx as float
bx as float
ax as float

cy as float
by as float
ay as float

x = x1
y = y1

cx = 3 * (c1x - x1)
bx = 3 * (c2x - c1x) - cx
ax = x2 - x1 - cx - bx

cy = 3 * (c1y - y1)
by = 3 * (c2y - c1y) - cy
ay = y2 - y1 - cy - by

text x1,y1,"a"
text x2,y2,"b"
text c1x,c1y,"c1"
text c2x,c2y,"c2"


x = ((ax * t# + bx) * t# + cx) * t# + x1
y = ((ay * t# + by) * t# + cy) * t# + y1

ink rgb(255,0,0),0
circle x, y, 10


ink rgb(255,255,255), 0
for t# = 0 to 1.05 step .05

x = ((ax * t# + bx) * t# + cx) * t# + x1
y = ((ay * t# + by) * t# + cy) * t# + y1

` First time through?
if t# = 0
oldx = x
oldy = y
endif

line oldx, oldy, x, y

oldx = x
oldy = y

next t#

endfunction

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What do you suppose the lines

x = ((ax * t# + bx) * t# + cx) * t# + x1
y = ((ay * t# + by) * t# + cy) * t# + y1

are doing?



Stevie

Don''t follow me, I''m lost.

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