In article ,
Bill Rogers wrote:
On Wed, 16 Jun 2004 02:32:30 +0000,
(Robert Bonomi) wrote:


Sheesh, kind of a tall order :-) The math is a little long to
explain here, but you can see it if you think of the hexagon as a
series of six equilateral triangles, each one of which is a 30-60-90
triangle

nit #1 -- 'equilateral' and '30-60-90' are mutually exclusive.

etc....

It's a wonder they haven't invented the computerised saw. Just punch
in the number of sides, angle of sides etc., and the blade and miter
adjust themselves. Perhaps they have, and it's not in the Orange
Giant yet?

There *IS* a whole _class_ of that kind of equipment.

It's called 'CNC tooling'.

The machine itself just takes a list of positioning and cutting commands.

"Front-end" systems, however, can take a 3-d representation of the part
to be made, and the rough stock, and 'figure out' the entire command-list
to "remove everything that's not part of the thing being made".

The things those kind of machines can do _is_ downright scary.

As for this particular 'problem', any half-way decent '3-D' CAD program
will let you start with a vertical plank, tilt it to the desired angle,
chop the top and bottom off parallel to the ground, and chop the sides
to a vertical radial from the 'center'. Viola!, you've got the object
you need. add some 'centerlines' for reference, and you can just have
the software 'read' the angles needed.

The same approach works for compound miter settings for molding corners -
'the corner looks like _this_', the boards go like 'this', 'the join is
the plane _here_', and 'the _back_side_ of the molding is like _this_.'

Then pull the piece of molding out of the model, rotate it so it's flat
on it's back, and just have the s/w 'show' the angles. set the saw to
match, and "awaaaaay we go!".