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

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  • R: Homogeneous transform? What one? For sure not that one.

    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

    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: giovedì 7 luglio 2005 18.05
    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