Path: chuka.playstation.co.uk!news From: James Undery Newsgroups: scee.yaroze.programming.3d_graphics Subject: Re: Matrices Date: Thu, 12 Jun 1997 13:20:02 -0700 Organization: PlayStation Net Yaroze (SCEE) Lines: 37 Message-ID: <33A059F2.6CA35F83@glam.ac.uk> References: <01bc7723$05437940$LocalHost@default> NNTP-Posting-Host: 193.63.132.194 Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Mailer: Mozilla 4.0b5 [en] (Win16; I) X-Priority: 3 (Normal) Jon Prestidge (alias Moose) wrote: > All the books and source-codes I've looked at so far (except Yaroze stuff) > seem to use 4x4 matrices for 3D work, where as the only structure (ie > MATRIX) used in the Yaroze stuff is a 3x3 matrix. Why? However I've > noticed that in most examples in books where 4x4 matrices are used > (translating,scaling,rotating etc), the last row and column seem largley > redundant - is this anything to do with it?... or what? Most academic texts store will store 3D points using a 4D vector, the fourth 'dimension' is a scaling factor for the other three. The 4x4 transformation matrices will only use the last row of the last column to alter this scaling factor, that is 1 0 0 0 x 0 1 0 0 y 0 0 1 0 z 0 0 0 a s will scale a vector by a factor of a in all directions (x,y,z), rather than a 0 0 x 0 a 0 y 0 0 a z which is the 3x3 version of the same transformation. I used to know why this was a 'good idea', but the reason escapes me now. unit vectors... simplified transformation matrices ... Any good book using the 4x4 matrices should explain how they relate to 3x3 matrices, and the advantages and disadvantages of both methods. (Not including we have to use libps or write a lot more code.) I hope this makes some sense. James