Quaternions (derives from Re: Of cuneiform tablets and computer encoding)

From: William Overington (WOverington@ngo.globalnet.co.uk)
Date: Wed May 01 2002 - 06:13:00 EDT

>> I am thinking of including in this encoding system facilities for
>> expressing rotations in quaternion format. This could potentially be very
>> useful so as to use quaternions to express the position and orientation
>> of the stylus used for making the wedge shaped depressions in the clay
>> tablet.

> Quaternions. What on earth do you mean by using quaternions?
> Is it just me, or would that be like using some kind of higher math to
> describe how to write Han characters with a brush?

Thank you for your enquiry.

My first thoughts concerning your enquiry were that I should first make sure
that I know what are Han characters. I have thus been having a look at the
start of Chapter 10 of the Unicode specification. I mention this so that
the limitations of my answer as regards Han characters are evident. My only
knowledge of writing Han characters with a brush is that I have seen the
occasional art programme on television where an artist has been drawing
traditional characters with a brush.

In answer to your question, it is broadly like using higher mathematics to
describe how to write Han characters with a brush, yet a much simpler
prospect, for cuneiform is written with a stylus, and, although I am unsure,
at the present stage of my own knowledge in this area, as to whether such a
stylus is absolutely rigid or can bend a little under the pressure of being
pushed into clay, a model of a rigid stylus is not unreasonable, whereas for
painting characters as well as the rigid paint brush handle there are also
matters such as the size and shape of the brush, the flow of the brush and
the amount of ink in the brush and the flow characteristics of the ink that
would need to be considered.

Quaternions are a part of mathematics that has traditionally been seen as
being very advanced, specialised and obscure. However, modern computer
graphics displays of three-dimensional objects has altered that to a large
extent. My own view is that quaternions deserve to be more popular.
Certainly, they are not part of basic mathematics, yet using them for
three-dimensional calculations is, as it happens, not too difficult at all.
My view is that if someone can carry out calculations using sines and
cosines and can use complex numbers to the extent of being able to multiply
two of them together and divide one complex number by another, then getting
started in quaternions is just a matter of learning that there are four
parts to them rather than the two of complex numbers and of learning how to
add, subtract and multiply two of them together and of learning how to
divide one by another. Certainly, those calculations can be tedious by
hand, yet with computer software, once one understands how to use
quaternions and can call a function each time that one needs to carry out a
calculation involving two quaternions, the calculations are no problem at

For a clay tablet with cuneiform writing, quaternions could be used to store
the three-dimensional coordinates of the vertices of the wedges and also the
orientations of the facets of the wedge shaped indentations thus produced
and also any rotation operations of a stylus made while producing a wedge
shape in the clay. It would also be possible to use quaternions to
describe, and thus potentially demonstrate within a 3d graphics system, the
technique of making a wedge, in particular of making what is called a corner
wedge. Certainly, quaternions would not be needed for transcribing clay
tablets as such, yet could be useful in, say, making an animated movie
showing how a particular sign consisting of a number of wedge indentations
would have been made. Thus, in my graphics encoding system I am hoping to
include quaternion facilities. Quite how anyone interested in using my
graphics encoding system applies that feature to his or her research, if at
all, remains to be seen, I am simply adding it in to the design because it
occurs to me that it might be useful and because I feel that it makes the
design of the graphics encoding system comprehensive.

The thing that fascinates me about the cuneiform studies area is its
interdisciplinary nature, using linguistics, physics, engineering and
computer science in order to achieve quality results by using linguistic
skills, laser scans and three-dimensional computer modelling.

Returning to your question about using mathematics to describe the method of
drawing Han characters with a brush, I never cease to be amazed at the
things that I learn serendipitously in this newsgroup and I therefore wonder
if anyone knows whether an artist has been filmed using two or more
synchronized cameras while drawing Han characters with a brush, the brush
having special markings on its body so that its position and orientation
with respect to the paper can be digitized and encoded in a computer so that
a computerized precise record of an artist drawing the characters exists.

William Overington

1 May 2002

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