Maths - Affine Conversion - Multivector to Matrix

Definition of terms:

Since we want to consider the possibility that there is also a translation from the centre, and that the rotation may not be about the centre but may be about some arbitrary point, then the matrix has to be increased from 3x3 to 4x4 so that it can specify the position and orientation. (as explained here).

The Multivector is based on 3D vectors and it can specify the position and orientation.

I am still working on this - can you help?

metadata block

see also:

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics). This book is intended for mathematicians and physicists rather than programmers, it is very theoretical. It covers the algebra and calculus of multivectors of any dimension and is not specific to 3D modelling.

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

Dark Basic Professional Edition - It is better to get this professional edition

This is a version of basic designed for building games, for example to rotate a cube you might do the following:
make object cube 1,100
for x=1 to 360
rotate object 1,x,x,0
next x

Game Programming with Darkbasic - book for above software

Discussion about using Darkbasic for physics simulation

Can you help?

Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page.

progam

I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here:

http://sourceforge.net/projects/mjbworld/

This site may have errors. Don't use for critical systems.