Article · Wikipedia archive · Last revised Jun 15, 2026

Double wedge

In geometry, a double wedge is the the symmetric difference of two half-spaces whose boundaries are not parallel to each other. For instance, in the Cartesian plane, the union of the positive and negative quadrants forms a double wedge, and more generally in two dimensions a double wedge consists of the set of points within two vertical angles defined by a pair of lines. In projective geometry double wedges are the projective duals of line segments.

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In geometry, a double wedge is the (closure of) the symmetric difference of two half-spaces whose boundaries are not parallel to each other. For instance, in the Cartesian plane, the union of the positive and negative quadrants forms a double wedge, and more generally in two dimensions a double wedge consists of the set of points within two vertical angles defined by a pair of lines. In projective geometry double wedges are the projective duals of line segments.12

References

References

  1. de Berg, Mark; Cheong, Otfried; van Kreveld, Marc; Overmars, Mark (2008), Computational Geometry: Algorithms and Applications (3rd ed.), Springer, p. 178, ISBN 9783540779735.
  2. Karasik, Y. B.; Sharir, Micha (1993), "The power of geometric duality and Minkowski sums in optical computational geometry", in Yap, Chee (ed.), Proceedings of the Ninth Annual Symposium on Computational Geometry, San Diego, CA, USA, May 19–21, 1993, Association for Computing Machinery, pp. 379–388, doi:10.1145/160985.161168; see section 6, "Reporting all empty double wedges for a point set", p. 384