Maths - Isometry Properties of 4d Multivectors

I'm not really very happy with the method developed in this section to handle 3D isometries. It works but it uses the bivector for both rotation and displacement. I would be much happier if the displacement were represented by a vector. I think the above approach could cause problems if we start to use this terminology for physics.

We can use a 3D multivector to represent isometries by using this form:

multivector = scalar part of quaternion + vector representing translation + bivector part of quaternion.

but we would have to combine subsiquent transforms using the addition operation rather than the multipication operation. Also I'm not sure this would properly handle rotations which follow translations.

To do all the things that I would like I think we need to go to geometric algebras based on 5D vector spaces?

 

 


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.

flag flag flag flag flag flag 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.

 

Terminology and Notation

Specific to this page here:

 

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

Copyright (c) 1998-2017 Martin John Baker - All rights reserved - privacy policy.