Thanks everyone. Will take a look and retry with expanded notation without short cuts.
While i would bother Guillaume, he has some pressing work of his own and shouldn't be bothered to hold my hand through the math. Rather bother you guys who may have urgent work to be done that I'm oblivious to. :) Thanks for the generosity of replying. Will post results once I have the solution. On Aug 26, 2013 7:09 PM, "Matt Lind" <[email protected]> wrote: > I think he’s looking for the raw math sans Softimage API.**** > > ** ** > > As for working with texts and papers from online, you’ll need to pay > attention to what kind of vectors are used. Many use column vectors in > their matrices. Softimage uses row vectors. You cannot mix n’ match, you > must align all data to be consistently row vectors or consistently column > vectors. You can convert a matrix to/from row aligned via a transpose > (flip entries across main diagonal).**** > > ** ** > > I would also advise using more parenthesis to ensure order of operations > are enforced in your computations. You’d be surprised how often silly > mistakes result from this.**** > > ** ** > > As a learning exercise I would advise doing it all long hand by building a > matrix for the initial transformation of the null then multiply it in turn > by each rotation vector (euler angle) because a transformation is > essentially a series of matrix and vector multiplications performed in a > specific order (XYZ in this case). The algorithm you are using is an > abbreviated version because many terms simplify during the computations. > If you do it long hand you should get the correct result. From that you > can trace your steps backwards to find your error in your initial attempts. > **** > > ** ** > > Matt**** > > ** ** > > ** ** > > ** ** > > ** ** > > *From:* [email protected] [mailto: > [email protected]] *On Behalf Of *Vladimir > Jankijevic > *Sent:* Monday, August 26, 2013 3:46 PM > *To:* [email protected] > *Subject:* Re: SI Matrix3 and Maths**** > > ** ** > > if you want to do it the hard way you can do it like this:**** > > ** ** > > # Python**** > > import math **** > > x = -45.0**** > > y = 45.0**** > > z = 0.0**** > > ** ** > > def degToRad(value):**** > > return value * (math.pi / 180)**** > > **** > > ** ** > > 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))**** > > ** ** > > ** ** > > rotationX = XSIMath.CreateMatrix3( 1,0,0,**** > > > 0,cx,sx,**** > > > 0,-sx,cx)**** > > > **** > > rotationY = XSIMath.CreateMatrix3( cy,0,-sy,**** > > > 0,1,0,**** > > > sy,0,cy)**** > > > ** > ** > > rotationZ = XSIMath.CreateMatrix3( cz,sz,0,**** > > > -sz,cz,0,**** > > > 0,0,1)**** > > > **** > > > **** > > rotationXY = XSIMath.CreateMatrix3( rotationX.Value(0,0) * > rotationY.Value(0,0) + rotationX.Value(0,1) * rotationY.Value(1,0) + > rotationX.Value(0,2) * rotationY.Value(2,0),**** > > > rotationX.Value(0,0) * rotationY.Value(0,1) + rotationX.Value(0,1) * > rotationY.Value(1,1) + rotationX.Value(0,2) * rotationY.Value(2,1),**** > > > rotationX.Value(0,0) * rotationY.Value(0,2) + rotationX.Value(0,1) * > rotationY.Value(1,2) + rotationX.Value(0,2) * rotationY.Value(2,2),**** > > > **** > > > rotationX.Value(1,0) * rotationY.Value(0,0) + rotationX.Value(1,1) * > rotationY.Value(1,0) + rotationX.Value(1,2) * rotationY.Value(2,0),**** > > > rotationX.Value(1,0) * rotationY.Value(0,1) + rotationX.Value(1,1) * > rotationY.Value(1,1) + rotationX.Value(1,2) * rotationY.Value(2,1),**** > > > rotationX.Value(1,0) * rotationY.Value(0,2) + rotationX.Value(1,1) * > rotationY.Value(1,2) + rotationX.Value(1,2) * rotationY.Value(2,2),**** > > > **** > > > rotationX.Value(2,0) * rotationY.Value(0,0) + rotationX.Value(2,1) * > rotationY.Value(1,0) + rotationX.Value(2,2) * rotationY.Value(2,0),**** > > > rotationX.Value(2,0) * rotationY.Value(0,1) + rotationX.Value(2,1) * > rotationY.Value(1,1) + rotationX.Value(2,2) * rotationY.Value(2,1),**** > > > rotationX.Value(2,0) * rotationY.Value(0,2) + rotationX.Value(2,1) * > rotationY.Value(1,2) + rotationX.Value(2,2) * rotationY.Value(2,2))**** > > > **** > > rotationXYZ = XSIMath.CreateMatrix3(rotationXY.Value(0,0) * > rotationZ.Value(0,0) + rotationXY.Value(0,1) * rotationZ.Value(1,0) + > rotationXY.Value(0,2) * rotationZ.Value(2,0),**** > > > rotationXY.Value(0,0) * rotationZ.Value(0,1) + rotationXY.Value(0,1) * > rotationZ.Value(1,1) + rotationXY.Value(0,2) * rotationZ.Value(2,1),**** > > > rotationXY.Value(0,0) * rotationZ.Value(0,2) + rotationXY.Value(0,1) * > rotationZ.Value(1,2) + rotationXY.Value(0,2) * rotationZ.Value(2,2),**** > > > **** > > > rotationXY.Value(1,0) * rotationZ.Value(0,0) + rotationXY.Value(1,1) * > rotationZ.Value(1,0) + rotationXY.Value(1,2) * rotationZ.Value(2,0),**** > > > rotationXY.Value(1,0) * rotationZ.Value(0,1) + rotationXY.Value(1,1) * > rotationZ.Value(1,1) + rotationXY.Value(1,2) * rotationZ.Value(2,1),**** > > > rotationXY.Value(1,0) * rotationZ.Value(0,2) + rotationXY.Value(1,1) * > rotationZ.Value(1,2) + rotationXY.Value(1,2) * rotationZ.Value(2,2),**** > > > **** > > > rotationXY.Value(2,0) * rotationZ.Value(0,0) + rotationXY.Value(2,1) * > rotationZ.Value(1,0) + rotationXY.Value(2,2) * rotationZ.Value(2,0),**** > > > rotationXY.Value(2,0) * rotationZ.Value(0,1) + rotationXY.Value(2,1) * > rotationZ.Value(1,1) + rotationXY.Value(2,2) * rotationZ.Value(2,1),**** > > > rotationXY.Value(2,0) * rotationZ.Value(0,2) + rotationXY.Value(2,1) * > rotationZ.Value(1,2) + rotationXY.Value(2,2) * rotationZ.Value(2,2))**** > > xfo = XSIMath.CreateTransform()**** > > xfo.SetRotationFromMatrix3(rotationXYZ)**** > > ** ** > > Application.Selection(0).Kinematics.Global.PutTransform2(None, xfo)**** > > ** ** > > ** ** > > On Mon, Aug 26, 2013 at 6:05 PM, Matt Lind <[email protected]> > wrote:**** > > Don't you have Mr LaForge and Mr. LeClaire at your disposal? I would > think they could answer in a heartbeat. > > > Anyway, an alternate way of dealing with this problem is to export the > axis vectors instead of computing the rotations. This ensures you get a > match and you don't have to deal with math. > > > Matt**** > > > > > > -----Original Message----- > From: [email protected] [mailto: > [email protected]] On Behalf Of Eric Thivierge > Sent: Monday, August 26, 2013 2:46 PM > To: [email protected] > Subject: SI Matrix3 and Maths > > 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 > > > > **** > > ** ** >
