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

Paolo De Leva
07-13-2005, 08:19 PM
Dear subscribers,

Here is some bibliographic data, confirming that the ambiguous and
etymologically inappropriate expression "homogeneous transformation
matrices" is widely (mis)used, as several subscribers already pointed out.
The information was kindly provided by Frank Borg:

"It could be that the concept of the *homogeneous transformation
matrix* (HTM) originates from computer science; e.g.:

VanArsdale, D., "Homogeneous Transformation Matrices
for Computer Graphics",
Computers & Graphics, vol. 18, no. 2, 177-191, 1994


"By HTM they apparently mean matrices that represent affine
transformations (rotation+shear+translations) in terms of homogeneous
coordinates (as you have described)."

We can still recommend the use of alternative terminology, although
many will defend the ambiguous terminology by minimizing the weight of our
arguments and opposing to it the supporters' weight: "thousands of people
uses that terminology!".

As I wrote in my previous posting, we are also free to use less
questionable terminology.

In textbooks, a warning should be included about the double meaning
of the expression "homogeneous transformation", and about the fact that
affine (i.e. not-necessarily-homogeneous) transformations can be performed
and are typically performed with these matrices.

Personally, I'd rather use the new expression "cool matrices :-)"
than the etymologically inappropriate and ambiguous expression HTM.

Luckily, terminological ambiguity is not frequent in scientific

Although their format is bad-looking, asymmetric, skewed,
not-uniform, heterogeneous (i.e. not-homogeneous), these are truly "cool"
matrices, anyway. They are quite useful for computer graphics applications.
Not indispensable for simple roto-translations, such as those most
frequently used in biomechanics.

With my kindest regards,

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