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**Up:** Direct Triangulation of 3D Surfaces
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##

Projection

An important aspect of direct discretization techniques consists in
the need to project 3D points to the surface (or its boundary curve)
to satisfy the surface constraint. This is generally a non-trivial
task further complicated by the fact that there is not always
the unique solution (consider for example projection of the centre of
a sphere to that sphere). It is therefore important to project only
points close to the real surface and to employ an appropriate projection
algorithm which ensures that the ``expected'' solution is obtained.
The proximity of points subjected to projection can be achieved by
curvature-based mesh density control typically restricting the element
spacing to a value smaller than the minimum radius of curvature. In
the case of parametric surfaces and curves, the projection may be
accomplished very efficiently in an iterative manner. The starting
point of the iteration then ``guarantees'' that the obtained solution
is the expected one.

**Subsections**

** Next:** Curve Projection
**Up:** Direct Triangulation of 3D Surfaces
** Previous:** Octree Control Space
*Daniel Rypl *

2005-12-07