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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