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Subject: Re: How to project a point onto a surface?

hyperandey@shaw.ca wrote:

> The model I am working with is 3D membrane structure. This
> structure has been meshed with triangular elements before I carry on
> the search of geodesic line. The surface is defined as discrete
> points not analytically defined surface. That's why I come up this
> method to search geodesic line on this kind of special surface.

There's not really anything special about that surface. It's a
triangle mesh, and that's that.

> My question is how to locate the triangular element on the surface
> in which each segment node will be projected based on segment node
> x, y coordinates and how to work out the z coordinate of projected
> segment node on this triangular element based on its node
> coordinates.

And Dave's answer was that this is probably not a very good way of
getting at the geodesic connection between points. I'll give you two
reasons for this assessment:

1) You hadn't mentioned anything about this being an explicit surface
of the type z=f(x,y) before. If that's indeed the case, the surface
*is* special, but the fact you didn't explicitly state this makes one
wonder whether you know that this would be a special requirement.
I.e. you may be relying on this without knowing it's an assumption
that you must check.

2) The probability that the projection of the actual geodesic
connection onto the x/y plane, even if the surface is z=f(x,y),
is quite small. Probably a lot smaller than you realize.

In summary: the idea that the straight line in (x,y) would have
anything to do with the 3D geodesic is flawed. What Dave's been
trying to tell you is that you're looking at the wrong end of the

> Certainly if you can give me another ideas to generate
> geodesic line in meshed surface, It would be appreciated.

Dave already did that.

Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)
Even if all the snow were burnt, ashes would remain.


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