Re: Drawing outline of 3D shape
- To: mathgroup at smc.vnet.net
- Subject: [mg67647] Re: Drawing outline of 3D shape
- From: "MS" <mark.stankus at gmail.com>
- Date: Mon, 3 Jul 2006 06:38:09 -0400 (EDT)
- References: <e88871$92c$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
MS wrote:
> Hello,
>
> Is there a program to draw the outline of a 3D shape.
> So a sphere would be drawn as a circle.
> A half sphere would be drawn as a arc (where the round
> part goes from visible to not visible) and a circle (highlighting
> the flat part of the half sphere.
>
> Mark Stankus
I received a few responses. I know how to draw such
a figure in any particular case. What I am looking for
is a program which takes a description of a solid and
draws the figure based on that. For example,
DrawOutlineOfShape[{x,y,z}, x^2 + y^2 + z^2 <=1 && z >=0]
The idea (in terms of mathematics)
would be to determine the interior of the set (from topology)
(see http://mathworld.wolfram.com/Interior.html) and the boundary
(see http://mathworld.wolfram.com/Boundary.html). Then determine
(based on the viewpoint) what is hidden and what is not, draw the
appropriate curve and also draw the place where the different pieces
come together (where the surface is not locally a manifold).
I have some initial ideas. Is anyone interested in contributing
to the development?
Mark