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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

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1 1 the motivation

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.


1 1 the motivation

1.2 The Voronoi diagram


1 1 the motivation

CIRCLE

CUBIC

1.4 The Delaunay graph


1 1 the motivation

1.5 The Delaunay empty circle

criterion


1 1 the motivation

1.7 The problem


1 1 the motivation

(x,y)

r

R

C4


1 1 the motivation

6.2 An example


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