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

http://www.silcom.com/~barnowl/HTransf.htm)".

"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

language.

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

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

http://www.silcom.com/~barnowl/HTransf.htm)".

"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

language.

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