Hey all,
Plunging ever further into the depths of matrices and the fun math
issues one may need to solve while building some tools for the studio.
I'm trying to figure out how the SI Matrix3's are derived / set and am
hitting some walls. I have some Euler angles that I need to convert to
Matrix3's then set a Transform from the result.
Basically a Euler angle to Matrix3 operation. I need to solve this
without the built in methods as I need to convert data from external
sources to align with Softimage without the SDK available.
I've referenced many of web sites (wikipedia, educational institutions,
etc.) and all of the equations for multiplying the 3 matrices (x,y,z)
end up with results that are not consistent with Softimage's methods.
The only source that has proven to give me valid results is the 3D Math
Primer for Graphics and Game Dev book (Chapter 8.7). However it only
shows the solution for XYZ rotation order and even that I'm unsure how
they got the order in which they multiply the rows / columns.
If any of you smart people out there (Raf, Matt?) have a few free
minutes to review my below code and show me the error of my ways I'd
appreciate it. Maybe others could benefit too.
Create 2 nulls. Set one rotation to x = -45, y=45
Select 2nd null and run script.
Swap the commented "result" line and run again.
# Python
import math
si = Application
log = si.LogMessage
sel = si.Selection
def degToRad(value):
return value * (math.pi / 180)
x = -45
y = 45
z = 0
cx = math.cos(degToRad(x))
sx = math.sin(degToRad(x))
cy = math.cos(degToRad(y))
sy = math.sin(degToRad(y))
cz = math.cos(degToRad(z))
sz = math.sin(degToRad(z))
matX = XSIMath.CreateMatrix3()
matX.Set(0,1,0,0,cx,sx,0,-sx,cx)
matY = XSIMath.CreateMatrix3()
matY.Set(cy,0,-sy,0,1,0,sy,0,cy)
matZ = XSIMath.CreateMatrix3()
matZ.Set(cz,sz,0,-sz,cz,0,0,0,1)
result = XSIMath.CreateMatrix3()
# From most sites I referenced-ish
#result.Set(cz*cy, sz*cx + cz*sy*sx, sz*sx - cz*sy*cx, -sz*cy, cz*cx -
sz*sy*sx, cz*sx + sz*sy*cx, sy, -cy*sx, cy*cx)
result.Set(cy*cz + sy*sx*sz, sz*cx, -sy*cz + cy*sx*sz, -cy*sz +
sy*sx*cz, cz*cx, sz*sy + cy*sx*cz, sy*cx, -sx, cy*cx) # From Book
log(result.Get2())
xfo = XSIMath.CreateTransform()
xfo.SetRotationFromMatrix3(result)
sel(0).Kinematics.Global.PutTransform2(None, xfo)
# End Python
--
Eric Thivierge
===============
Character TD / RnD
Hybride Technologies
