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1.1 The motivation

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1.1 The motivation. Most of the objects we encounter in the real world are curved objects in the three dimensional Euclidean space. Curves are frequently encountered in maps.

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1.1 The motivation

  • Most of the objects we encounter in the real world are curved objects in the three dimensional Euclidean space. Curves are frequently encountered in maps.
  • Many problems from different fields involve proximity queries like finding the nearest neighbour, finding all the neighbours, quantifying or qualifying the neighbour-liness of two objects.
  • The Voronoi diagram (of semi-algebraic sets) is the solution to those proximity problems.
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CIRCLE

CUBIC

1.4 The Delaunay graph

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(x,y)

r

R

C4

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