Formula? What you talkin' 'bout Willis?
Eric Thivierge =============== Character TD / RnD Hybride Technologies On August-27-13 2:54:24 PM, Matt Lind wrote:
Which begs the question – why is that formula in the user’s guide and not the sdk guide? I’ve wondered about that for years. Matt *From:*[email protected] [mailto:[email protected]] *On Behalf Of *Grahame Fuller *Sent:* Tuesday, August 27, 2013 11:52 AM *To:* [email protected] *Subject:* RE: SI Matrix3 and Maths Just to clarify, that’s the order of the matrices in the multiplication, which in a row-vector world corresponds to performing the transformations interactively in the opposite order. If there’s non-uniform scaling involved and hierarchical scaling is on, it’s more complicated. For the gruesome details, scroll to the bottom of this page: http://download.autodesk.com/global/docs/softimage2014/en_us/userguide/index.html?url=files/transforms_ScalingObjects.htm,topicNumber=d30e51306. If there’s no non-uniform scaling then everything works out the same as for classic scaling. gray *From:*[email protected] <mailto:[email protected]> [mailto:[email protected]] *On Behalf Of *Daniel Brassard *Sent:* Tuesday, August 27, 2013 2:29 PM *To:* [email protected] <mailto:[email protected]> *Subject:* Re: SI Matrix3 and Maths BTW, the order of operation on the matrices is important. For Softimage you scale, rotate then translate (SRT like the order in the MCP, easy way to remember). Any other way and you will have unpredictable results. On Tue, Aug 27, 2013 at 2:12 PM, Daniel Brassard <[email protected] <mailto:[email protected]>> wrote: A pretty good explanation of row vector and transform Matrix here. http://msdn.microsoft.com/en-us/library/windows/desktop/bb206269(v=vs.85).aspx On Tue, Aug 27, 2013 at 1:39 PM, Grahame Fuller <[email protected] <mailto:[email protected]>> wrote: I'm pretty sure it's the row versus column vector issue. In a nutshell, most of the CG world, including Softimage, treats vectors as rows, i.e., 1x3 matrices. The rest of the world, including most references you'll find for math, physics, robotics, etc., treats vectors as columns, i.e., 3x1 matrices. In a row-vector world, you construct your transform by inserting your X,Y,Z basis vectors into a matrix as rows. The order of multiplication for transforms is Mchild x Mparent, and when multiplying a vector and matrix the vector goes on the left and the matrix on the right. In a column-vector world, it's the opposite. You construct your transform by inserting your X,Y,Z basis vectors into a matrix as columns. The order of multiplication for transforms is Mparent x Mchild, and when multiplying a vector and matrix the vector goes on the right and the matrix on the left. In particular, note that the row-vector transform is transposed (mirrored across the diagonal) from the column-vector transform. So if the formulas for your individual rotation matrices matX, matY, and matZ came from a reference that uses column-vectors, you need to transpose the matrices. To calculate the various rotation orders, you just need to multiply the matrices in different orders. In a row-vector world, you use reverse order, for example, if you want XYZ order then you calculate matZ x matY x matX. Luckily matrix multiplication is the same in both row-vector and column-vector worlds, so you can save some processor time by figuring it out long-hand and stuffing the final values into the full transform matrix directly, like in the code sample you showed, but of course it's easy to make a typo or other mistake. gray From: [email protected] <mailto:[email protected]> [mailto:[email protected] <mailto:[email protected]>] On Behalf Of Eric Thivierge Sent: Monday, August 26, 2013 8:21 PM To: [email protected] <mailto:[email protected]> Subject: Re: SI Matrix3 and Maths Thanks Raf I saw that today. It's a problem somewhere with my matrix multiplication I think. Tried a bunch of different combos but I'm thinking it's what Matt touched on either the row / column mixing or a mistake in the shorthand somewhere. -------------------------------------------- Eric Thivierge http://www.ethivierge.com On Mon, Aug 26, 2013 at 8:15 PM, Raffaele Fragapane <[email protected] <mailto:[email protected]><mailto:[email protected] <mailto:[email protected]>>> wrote: The rotation order matters. It's as simple as each rotation pushing a gimbal along by a linear distance of trigonometric functions of that angle in turns, in the rotation order... order. Wikipedia has the matricial forms: http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations What's not working from that? Or if you haven't looked at it, shame on you!
