Re: Projecting a point to a triangular mesh surface

Hans,

Thank you for pointing out the ambiguity in my problem statement.
You are absolutely correct, there are many different ways of interpreting
the problem as I defined it.
Allow me to rephrase. . .
Let M be a triangular surface mesh and Ti a triangle within the mesh that
has a normal Ni.
Let P(x,y,z) be the point to project. I wish to find a point Q that is
within the domain of Ti or its boundary,
such that the normal Ni at point Q passes through the point P.
There could be many such points that fulfill this condition, and I wish to
find the closest one that minimizes
the distance d(P, Q).

There are no holes in the mesh surface and the surface is closed, every edge
of the mesh is shared by exactly two triangles.

There can potentially be many triangles in the mesh and one or many points
to query, so an exhaustive search is out of the question.

Pramod

"Hans-Bernhard Bröker" <HBBroeker@xxxxxxxxxxx> wrote in message
news:es9us6$iho$00$1@xxxxxxxxxxxxxxxxxxxx
Pramod wrote:
Can anyone point me to a text or research publication that describes an
efficient algorithm for projecting a point to the nearest position on a
triangular mesh surface.

I would be surprised if anyone could, given that the problem is so
inadequately defined. "Projection of a point onto it" is not a concept
that applies to any surface other than a plane or a sphere in an obvious
way. So before you can get a solution, you'll have to specify more
precisely what the problem is.

I guess what you really want is the points' nearest neighbour in the
surface.



.

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