I remember reading the Shilov books at the bookstore for evaluation. I found the terminology a little technically heavy making it a challenging read as I didn't have the technical background at the time. Because of the lack of illustrations you really must have it all contained in your head as you progress through the book or else you can get lost. I'd be more inclined to check that book out now vs. when first getting exposed to the subject.
My first linear algebra textbook was "linear algebra with applications", by Otto Bretscher (3rd edition). It started OK, but after the first few chapters it ran afoul of any sense or structure. The exercises and problems were ridiculously hard and abstract in comparison to the material presented in the chapter. It was fun to be challenged mentally, but this book went too far as it felt like a mystery novel where the key piece of evidence wasn't introduced until the end after the case was solved. Even the teacher dumped the book half way through the semester. Out of frustration I bought Linear algebra by Howard Anton (7th edition) because he authored the school's calculus books and at least made some sense, but his linear algebra book was all number crunching and lacked theory. Disappointed again I tried Kohlman-Hill because it had advertised material for computer science majors, but it turned out to be fluff. There were also a few others in the mix I can no longer remember. I did well in school, but I didn't have much fun with linear algebra mostly because there was a void between theory and practice. Theory was just that, and the books covering the practice often used terms and techniques not found in the theory books, or required significant computer science background to make use. That made it difficult to jump in. When I picked up the Gerald Farin book at Siggraph 2006, I felt like I found the bridge to connect the two worlds. The examples aren't as deep as a traditional textbook, but are very intuitive and directly applicable to 2D and 3D graphics. The main benefit of the book is it explains concepts of linear algebra in the context of computer graphics in a way that doesn't require a computer science background. My only complaint is the book can be a little thin in some areas covering specific use cases and not mention important edge cases to look out for. Then again I have the 1st edition of the book, perhaps the 3rd edition fills those holes. Matt From: softimage-boun...@listproc.autodesk.com [mailto:softimage-boun...@listproc.autodesk.com] On Behalf Of Grahame Fuller Sent: Thursday, August 15, 2013 12:57 PM To: softimage@listproc.autodesk.com Subject: RE: just not normal Matt, maybe it was the same textbook? :) I forget the author but as I recall it was a grey hardback with pinkish/purplish printing on the front. "True vector" I obviously not a technical term, but I find it's useful to distinguish things like force and velocity from the data type that's called a vector in ICE, but is really just a 3-tuple and might actually contain a position, or scaling factors, Euler angles, etc. In physics, you are taught that vectors have direction and magnitude but no position (which is why you can add them geometrically by moving them tip-to-tail). That makes them different from positions, in fact I have read that in some systems (MATLAB maybe?) positions and vectors are separate data types. gray From: softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com> [mailto:softimage-boun...@listproc.autodesk.com] On Behalf Of Daniel Brassard Sent: Thursday, August 15, 2013 2:31 PM To: softimage@listproc.autodesk.com<mailto:softimage@listproc.autodesk.com> Subject: Re: just not normal MIT Courseware Linear Agebra with videos http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ On Thu, Aug 15, 2013 at 1:51 PM, Matt Lind <ml...@carbinestudios.com<mailto:ml...@carbinestudios.com>> wrote: Tell me, Gray - what is a 'true' vector? I've never heard of that term. ;-) As for the textbooks, I only recommend the Gerald Farin book for the same reason as you - the textbook I used in college was awful. Awful enough I purchased 5 different linear algebra textbooks to figure it all out as most come with the same 8 topics, but only explain 2 or 3 of them well, and rarely come with examples directly applicable to what we do here. The Farin book complements a traditional linear algebra course by illustrating the subset of concepts applicable to the case of working in 2D or 3D computer graphics. If you have a linear algebra background, you'll breeze through the book pretty fast. However for somebody getting their feet wet in the subject, it's really good for introducing concepts and guiding the reader on the right track for pursuit of further knowledge. Hindsight being 20/20, I would be more interested to learn the subject if I had the Farin book before my college textbook. The Farin book, by the way, is a reworking and simplification of his previous book whose name escapes me at the moment, but is based on linear algebra for CAD and CG co-written with Dianne Hansford. Matt From: softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com> [mailto:softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com>] On Behalf Of Grahame Fuller Sent: Thursday, August 15, 2013 9:18 AM To: softimage@listproc.autodesk.com<mailto:softimage@listproc.autodesk.com> Subject: RE: just not normal Joey, ICE doesn't convert locations directly. It can display them as vectors for debugging purposes but under the hood they are really a triangle ID + barycentric coordinates. Or perhaps you meant true vectors? The list of attributes that ICE will convert to the self's reference frame is here: http://download.autodesk.com/global/docs/softimage2014/en_us/userguide/index.html?url=files/ICE_trees_GettingandSettingDatainICETrees.htm,topicNumber=d30e274098 (scroll down to "Reference Frames", right before "Setting Data"). You can trust ICE to use the correct math, 3x3 or 4x4 matrices, depending on whether the attribute is a true vector or position, but if it's a custom attribute then it's up to you to know what it is and take the appropriate action. The book that Matt mentioned looks interesting as an intuitive, geometrical approach. For a more technically oriented book I'd recommend Shilov's "Linear Algebra" - when I was at uni the assigned textbook was awful but Shilov's just clicked with me. gray From: softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com> [mailto:softimage-boun...@listproc.autodesk.com] On Behalf Of Matt Lind Sent: Wednesday, August 14, 2013 7:52 PM To: softimage@listproc.autodesk.com<mailto:softimage@listproc.autodesk.com> Subject: RE: just not normal It will differentiate how to handle orientation vectors differently from position vectors which is the solution to the problem you said you couldn't solve on your own. Matt From: softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com> [mailto:softimage-boun...@listproc.autodesk.com] On Behalf Of Ponthieux, Joseph G. (LARC-E1A)[LITES] Sent: Wednesday, August 14, 2013 4:49 PM To: softimage@listproc.autodesk.com<mailto:softimage@listproc.autodesk.com> Subject: RE: just not normal I'm certain that it would be very useful, but what I am more interested in is what ICE is pre-computing that changes what might be normal expectations such as the example provided with locations. With ICE, positions are converted to global using 4x4 matrices and locations are converted to global using 3x3 matrices. Will a linear algebra book be able to tell me that, in context to ICE? -- Joey Ponthieux LaRC Information Technology Enhanced Services (LITES) Mymic Technical Services NASA Langley Research Center __________________________________________________ Opinions stated here-in are strictly those of the author and do not represent the opinions of NASA or any other party. From: softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com> [mailto:softimage-boun...@listproc.autodesk.com] On Behalf Of Matt Lind Sent: Wednesday, August 14, 2013 7:39 PM To: softimage@listproc.autodesk.com<mailto:softimage@listproc.autodesk.com> Subject: RE: just not normal The documentation you're searching for is a linear algebra textbook. I think you'll find the subject very useful and directly applicable to your work on many fronts. "Practical Linear Algebra: A Geometry Toolbox" by Gerald Farin is a decent starting point as it discusses the fundamentals in plain english, but it's intended to complement a linear algebra course, not replace it. Matt From: softimage-boun...@listproc.autodesk.com<mailto:softimage-boun...@listproc.autodesk.com> [mailto:softimage-boun...@listproc.autodesk.com] On Behalf Of Ponthieux, Joseph G. (LARC-E1A)[LITES] Sent: Wednesday, August 14, 2013 4:23 PM To: softimage@listproc.autodesk.com<mailto:softimage@listproc.autodesk.com> Subject: RE: just not normal WOW! What a difference two nodes make! I converted the 4x4 Matrix down to a 3x3 Matrix omitting Translation in the process, and plugged that into Multiply Vector by Matrix and...EVERYTHING WORKS! The flipping is gone. I had solved the problem by taking three points on the surface, converting to global position on each, then deriving a "normal" vector from them. It was rock solid and this solution has the same results as that. My preference was to get the normal from the location, that way if the object surface is irregular it will always work as expected. This solves that problem very elegantly! I'm curious, but is there any documentation anywhere that gives better detail on how locations vs positions etc affect global space conversion? I would have never guessed how to solve this even though I knew about the local to global conversion from the docs. Thanks! -- Joey Ponthieux LaRC Information Technology Enhanced Services (LITES) Mymic Technical Services NASA Langley Research Center __________________________________________________ Opinions stated here-in are strictly those of the author and do not represent the opinions of NASA or any other party.
