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By Arora S., Karakostas G.

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Geom. 9 (1993), 387–426. [3] B. Baumgart. A polyhedron representation for computer vision. In “Proc. Natl. Comput. , 1975”, 589–596. [4] T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein. to Algorithms. Second edition, McGraw Hill, Boston, 2001. Introduction [5] D. P. Dobkin and M. J. Laszlo. Primitives for the manipulation of threedimensional subdivisions. Algorithmica 4 (1989), 3–32. [6] L. J. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams.

Searching graphs is a core topic in computer science and descriptions of Depth-first Search can be found in most algorithms texts, including [1] and [4]. [1] A. V. Aho, J. E. Hopcroft and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Massachusetts, 1973. 44 II Surfaces [2] E. Brisson. Representing geometric structures in d dimensions: topology and order. Discrete Comput. Geom. 9 (1993), 387–426. [3] B. Baumgart. A polyhedron representation for computer vision.

It will be convenient to identify antipodal points on the sphere and think of a direction as a pair (u, −u). Formally, this means we replace the sphere by the two-dimensional projective plane but we don’t have to be this formal yet. The pair (u, −u) crosses the curve T iff u crosses T or −T . Recall that the winding number is defined for a closed curve and a point in the plane. Here we have a closed curve and an antipodal point pair on the sphere. Assuming u and −u are not on the curve, we let the winding number be the net number of counterclockwise turns formed by T around the directed line defined by u.

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