Compact syntax for 0-matrix?
Kirby Urner
urner at alumni.princeton.edu
Tue May 30 20:01:28 CEST 2000
Boris Borcic <borcis at geneva-link.ch> wrote:
>Mmm.. I am playing along lines a bit similar to yours,
>(e.g. polyhedra), and I have found Numeric quite useful
>for one particular bit : doing away with the complexities
>of specifying projective transforms by combinations of
>rotations, translations, scalings, etc..., using rather
>the 3-transitivity of the projective group, to specify
>a transform by choosing 3 points together with 3 target
>points to which the transform should map them. I find
>this hugely more transparent (this is 2D; in 3D, i guess
>you'd need 4 points).
>
>Numeric serves to solve the corresponding linear
>equations - of course, you could also code it.
>
>Boris
>Numeric serves to solve the corresponding linear
>equations - of course, you could also code it.
>
>Boris
Polyhedra are my focus as well, but I need to keep
it simple and transparent. I do rotation, translation
and scaling, but don't try to conflate these to single
operations.
I simply catalog points as vectors in a dictionary
and walk through it, applying whatever transformation.
In the case of rotation "in place", I move the poly
to the origin, rotate, and put it back.
I've done rotation using both matrices and quaternions.
A next step for me might be to implement rotation
using some Clifford Algebra (as per some recent posts
on that topic).
For a look at my Polyhedra with Python, check links
from http://www.inetarena.com/~pdx4d/ocn/cp4e.html
I use Povray as my back end ray tracer -- OpenGL
in Tk would be another approach, but wouldn't look
as good.
Kirby
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