Page 56 - Geometric Modeling and Algebraic Geometry

3 Real Line Arrangements and Surfaces with Many Real Nodes 53
construction would only yield 96 nodes which is less than the number 99 found in
[15].
Notice that it is not clear that line arrangements are the best plane curves for
our purpose, and we may ask: Is it possible to exceed the number of critical points
on two levels of the line arrangements F A 2 (x, y) using irreducible curves of higher
,d
degrees? Either in the real or in the complex case? This is not true for the real folding
polynomials. E.g., those associated to the root system B 2 consist of many ellipses
and yield surfaces with fewer singularities (see [3]).

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