Convex Hull of Grid Points below a Line or a Convex Curve

  • Hélymar Balza-Gomez
  • Jean-Michel Moreau
  • Dominique Michelucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)


Consider a finite non-vertical, and non-degenerate straight-line segment s = [s 0; s 1] in the Euclidian plane \( \mathbb{E}^2 \). We give a method for constructing the boundary of the upper convex hull of all the points with integral coordinates below (or on) s, with abscissa in [x(s 0); x(s 1)]. The algorithm takes O(log n) time, if n is the length of the segment. We next show how to perform a similar construction in the case where s is a finite, non-degenerate, convex arc on a quadric curve. The associated method runs in O(k log n), where n is the arc’s length and k the number of vertices on the boundary of the resulting hull. This method may also be used for a line segment; in this case, k = O(log n), and the second method takes O(k 2) time, compared with O(k) for the first.


Grid Point Convex Hull Intersection Point Recursive Call Fibonacci Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Hélymar Balza-Gomez
    • 1
  • Jean-Michel Moreau
    • 1
  • Dominique Michelucci
    • 1
  1. 1.École Nationale Supérieure des Mines de Saint-ÉtienneSaint-Étienne cedex 2

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