PDA

View Full Version : R: Homogeneous transform? What one? For sure not that one.



Paolo De Leva
07-07-2005, 07:50 PM
Let's consider not only the many thousands (are you sure they are so
many?) biomechanists and software engineers trained to use the "incorrect"
terminology, but also the many thousands students in mathematics,
engineering, physics, computer science, biomechanics, and many other
disciplines based on mathematics, who actually attended a serious math
course in which they learned the formal definition of the expression
"homogeneous transformation".

Let's also consider the decades of literature concerning matrix
algebra.

Let's also consider that we have technical dictionaries which give
in formal terms the correct definition of the expression "homogeneous
transformation", and we'd better use them before writing textbooks.

Let's also consider that the applications of matrix algebra are not
limited to computer graphics and biomechanics. An "homogeneous
transformation" is just a "linear function". Do you happen to imagine how
many millions of applications are there for linear functions, besides those
in computer graphics or biomechanics?.

Let's also consider that even a 3x3 rotation matrix is a homogeneous
matrix (the "second reason" in my original posting about this topic) and I
find it hard to accept it's not, just because many people like to use the
same exotic name with the pretension to uniquely indicate their beloved 4x4
matrix. Is there anyone who likes the term orthonormal and want to use it to
indicate a 4x4 matrix? Why not? It's more exotic than "homogeneous" and
actually not many know its true meaning.

In the next days, I will post a comment which will show how little
transformation matrices are understood and how poorly they are explained to
students by those who also use incorrect terminology. I am not saying they
don't explain well how to build and use transformation matrixes. They do it,
in some cases brilliantly. But one thing is to correctly explain how these
matrices must be built and used (and many can do it), another thing is to
thoroughly explain, i.e. to give an insight about how and why they do work,
in a visual way (and, most unfortunately, only a few are willing and able to
do it)... didn't I already write a similar phrase before in one of my
previous postings?

With regards,

Paolo de Leva
Sport Biomechanics
University Institute of Motor Sciences
Rome, Italy



-----Messaggio originale-----
Da: * Biomechanics and Movement Science listserver
[mailto:BIOMCH-L@NIC.SURFNET.NL] Per conto di Andersen, Clark R.
Inviato: giovedý 7 luglio 2005 18.05
A: BIOMCH-L@NIC.SURFNET.NL
Oggetto: Re: Homogeneous transform? What one? For sure not that one.

Unfortunately, considering the decades of literature referring to 4X4
homogeneous transformation matrices, along with the many thousands of
engineers and software developers trained to use that description, I
believe that at this point the only realistic option is to expand the
definition to include the actual usage of the phrase, beyond pure
mathematics, as that usage is not likely to change. This is the nature
of the evolution of language.

Clark Andersen
Department of Orthopaedics and Rehabilitation
Division of Biomechanics and Bone Physiology Research
The University of Texas Medical Branch
Galveston, Texas