direction cosine matrix calculation

[Tai-HoonKIM]

Dear all,

I am struggling with the calculation of direction cosine matrix.
My goal is to get eigenvalue for each cell using 3 by 3 window.
eigenvalue will be calculated from the direction cosine matrix. Unfortunately I am good at this kind of stuff.
Please give me a any little tiny of idea for this.

you may see (McKean and Roering, 2004, Geomorphology 57, 331-351) for more clear understanding (I attached part of it because of the amount limit).


Thank you in advance

[Tai-HoonKIM]

Dear William Huber,

Thank you for your comment. Unfortunately I am new to some programming in ARCGIS. so I couldn't understand what you recommended. Especially, these parts;

(2) From those, compute the three "directional cosine" grids.

(3) Compute the six squares and products of those three grids.

(5) Construct the coefficients of the characteristic polynomial from T: these are somewhat involved by straightforward algebraic combinations of the coefficients of T.

and what is name of other programs which enable this process efficiently?
I am sorry to bothering you and thank you again for your kind response.

Tai-Hoon

[Tai-HoonKIM]

Dear William Huber,

thank you for your instant response.

I did;
1. calculate 3 direction cosine layers (x, y, z directions)
2. calculate 6 (actually 9) layer which are components of a matrix (x^2, y^2, z^2, xy, xz, yz).
3. sum 6 layer with neighborhood method simulating window moving calculation.

so I have 6 layers (sum of x^2, y^2, z^2, xy, xz, yz with 9cells, i.e., 3 by 3).
but I couldn't understand the remainder.
if you don't mind could you show a simple example for this?
I am very sorry for disturbing you again.

Tai-Hoon

[Tai-HoonKIM]

Thank you very much, William Huber.
Yes, I will try to use other software. as you told this is ridiculus for solving.

Tai-Hoon