The central notion of our approach
is the parameterization of space by distances from the
material features ( geometries, where material
properties are known ) - either exactly or approximately.
Functions of such distances provide a systematic and
intuitive means for modeling desired material distributions,
as they appear in design, manufacturing, analysis and
optimization of components with varying material properties.
Two possible difficulties may arise in relying on distance
functions: (1) computational cost; (2) loss of
differentiability at equidistant points. Both of these
limitations of the exact distance functions may be overcome
by replacing them with various smooth approximations,
while preserving most of the attractive properties of
the distance functions. In particular, we construct
approximate distance functions of geometries with the
technique originally described by Rvachev [1,2].
Examples below show exact and approximate distance functions
constructed with our approach.
Figures: (a) The
exact distance field of a S-shaped B-spline curve.
(b) An approximate distance field of the same curve.
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| (c) |
(d) |
Figures: Approximate
distance fields of a B-spline surface and a solid.
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