Matrix Find Rotationpoint through translationdata

leslievdb

Hey guys

I have a bunch of keyframed points that translate over time. They translate according to the rotation of a fixed point (think of facialanimation tracker moving with a headbone), from those points i would like to find the original rotationpoint since i don't have that data.

My math skills arn't what they should be but i tried the following

- combine all points lengths and average them
- Take the arc tangent of the each point between two frames
- Convert spherical to Cartesian coordinates using the following formula






and the corresponding maxscript

fn drawLineBetweenTwoPoints pointA pointB =
(
  ss = SplineShape pos:pointA
ss.render_renderable  =false
  addNewSpline ss
  addKnot ss 1 #corner #line PointA

  addKnot ss 1 #corner #line PointB
  updateShape ss
  ss
)

average = 0
for i=1 to selection.count-1 do 
(
    [COLOR=Red]average += (length selection[i].pos)[/COLOR]
    --print average
)
lengte = ((average)/(selection.count))

xrot = 0
yrot = 0
zrot = 0

for i=1 to selection.count-1 do 
(
[COLOR=YellowGreen]    xrot += atan2 (at time 2 selection[i].pos.x)  (at time 1 selection[i].pos.x)
    yrot += atan2 (at time 2 selection[i].pos.y) (at time 1 selection[i].pos.y)
    zrot += atan2 (at time 2 selection[i].pos.z) (at time 1 selection[i].pos.z)[/COLOR]
)

xrot = xrot/selection.count
yrot = yrot/selection.count
zrot = zrot/selection.count

[COLOR=Orange]posx = lengte * sin zrot * cos xrot
posy = lengte * sin zrot * sin xrot
posz = lengte * cos zrot
[/COLOR] 
for i=1 to selection.count do 
(
    drawLineBetweenTwoPoints selection[i].pos [posx,posy,posz]
)

the result i got wasn't far from what the point could be but i think it was a lucky coincidence instead of my thoughtprocess actually being correct.

excuse my stupidity in case i'm doing some idiotic stuff here :P

mistra

since you're only working with rotations, perhaps you could calculate the sphere those points are on and find the center of that sphere.

all you need is 4 points and you're golden
link:
http://paulbourke.net/geometry/spherefrom4/