Moving Along a Curve in 3D

[MartyPlumbo]

Does anyone out there know how to do the math to make an object in 3D space transform from point A through point B to point C, in a smooth curve?

To put it another way, I'd like a 3D object to move from one point in space to another, passing through a specified intermediate point, all using a regular arc.

Sort of like the cool 2D curve math on the Hairybobbies site ([url]http://www.geocities.com/hairybobby2000/mathhome.html[/url]), but now in 3D.

Anyone done this yet?

:-)

[paul]

I asked the same thing a year or two ago and saved the response from Paul
L...





Here is a parent script modified to work in 3d.

usage is:-

bezierCurver=script("3d

bezier").new(vector(0,0,0),vector(100,100,100),vec tor(-20,20,20),vector(120,

100,100))

then work out your time t as a value between 0 and 1

currentPosition=bezierCurver.getPosition(t)



read on for parent script (put it in a parent script cast member called "3d

bezier"



-- 3d bezier curve parent script

-- Paul Lemon (paull@pilotinteractive.co.uk)

property a,b,c

property start



on new me, istart, end, control1,control2

-- istart is a vector representing the start position in 3d space

-- end is a vector representing the end position in 3d space

-- control1 is a vector representing the first control point

-- control2 is a vector representing the second control point

start=istart

c=3*(control1-start)

b=3*(control2-control1) - c

a=end-start-c-b



return me

end

on getPosition me,t

-- returns a vector describing the beziers position at a point in time t

-- 0<= t <=1

t2=t*t

t3=t*t2

return a*t3 + b*t2 + c*t + start

end




on getOrientation me,t

-- returns a vector describing the direction(velocity) the beziers is

-- pointing in at time t

-- 0<= t <=1

t2=t*t

return 3*a*t2 + 2*b*t +c

end

on getspeed me,t

return=me.getOrientation(t).magnitude

end

"MartyPlumbo" <martyp@insightbb.com> wrote in message
news:bstv3f$8u6$1@forums.macromedia.com...

>
> Does anyone out there know how to do the math to make an object in 3D

space transform from point A through point B to point C, in a smooth curve?