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[help-3dldf] Re: Polyhedra and ellipses
From: |
Laurence Finston |
Subject: |
[help-3dldf] Re: Polyhedra and ellipses |
Date: |
Wed, 8 Dec 2004 12:19:03 +0100 (MET) |
On Tue, 7 Dec 2004, Martijn van Manen wrote:
>
> I'll try to answer some of your questions in another
> installment. What I would like to say though is that the
> number of fun and exciting polyhedra is rather endless.
> I'll make some selection.
I've made a start on the Archimedean polyhedra with the truncated
octahedron. They ought to keep me busy for a while.
> Ofcourse there are "smart" methods
> of finding the vertices and the edges and so on.
> Those mathematicians in the nineteenth century produced
> formula after formula. There are endless and sometimes
> pointless calculations.
This sounds promising.
> What you should maybe figure out is how to construct a nice
> data structure for them, so that afterwards you can traverse it
> and find intersections with lines and planes. The people in
> computational geometry love the "doubly connected edge list".
> You might want to implement it.
Once I have a basic understanding of the methods I'll be able to figure
out a data structure to use.
> For the tangencies of two ellipses, or two quadrics, I'll
> give you some methods too.
Thanks. I plan to implement classes for parabolae and hyperbolae, so I
may implement a base class `Conic_Section'. If
appropriate, I'll implement a function for finding intersections of
`Conic_Sections' and overload it with specializations for two
`Ellipses', an `Ellipse' and a `Parabola', etc. If `Quadric' is a better
name, I'll use it; I don't know the its definition yet.
Laurence