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: giovedÃ¬ 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

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