On Mon, 12 Jul 1999 13:00:02 -0700, Josh English
<eng### [at] spiritonecom> wrote:

>A smooth mesh should hold the same positions in space a a non-smoothed
>mesh, so the distance to the surface should be the same.
>I'm not sure how the normal vector would affect an electrostatic field.
>You need to calculate the closest point between the mesh and your
>arbitrary point to determine the strength of the field.
>
>Joshua
>eng### [at] spiritonecom

Distance to the mesh is not a problem. The problem is elsewhere. 

Electrostatic field line start at the surface of the charged object
pointing at the direction of the normal and extend to infinity
retaining their direction (in a closed system, anyway). If the mesh is
unsmoothed this can be represented as infinite straight triangular
prisms starting at the faces of the mesh. Obviously there's no way to
cover the whole space this way unless the faces are infinitesimally
small. This is of course unacceptable.

On the other hand, a closed smooth mesh would generate a continuous
field because the normal blends smoothly (well, more or less). The
intensity of the field at a point A in space depends not on the
distance to the mesh but rather on the distance to that point of the
mesh whose normal points at A. That's what makes it complicated. If it
were a primative then the problem is relatively easily solved by the
Gauss equations. The gradient to a smoothed mesh, however, is
something beyond the scope of my math abilities.

So here I state the problem again, more clearly. Given a closed smooth
mesh M and a pont in space P outside the mesh, find the point(s) on M
whose normal(s) point at P.


Peter Popov
ICQ: 15002700

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