Fig 1.
A small example of 2D points with integer coordinates.
Left: (x, y) integer points on a 2D grid with p = 5. Center: Points with minimum and maximum y values for each x coordinate. Right: A polyline.
Fig 2.
Percentage of reduction of points of four datasets of 2D points with integer coordinates.
The result of two methods of reductions are shown: The one of Akl and Toissant as presented in [8] and the one proposed here.
Fig 3.
Speedup factor as a function of p/n for a random set of circles and superellipses.
A set of n points in a box of p × q were preconditioned first by the method proposed here and the convex hull found by the algorithm in [8] as available from CGAL [10].
Fig 4.
Speedup factor for a dense dataset.
The points of a dataset of 13 mammals were first preconditioned with the method proposed here and then the convex hull was computed with seven algorithms.
Fig 5.
Speedup factor for a typical image dataset.
The points of a dataset of 49 brain images were first preconditioned with the method proposed here and then the convex hull was computed with six algorithms.
Fig 6.
Speedup factor as a function of p/n for a sparse dataset.
The points of seven homerange datasets were first preconditioned with the method proposed here and then the convex hull was computed by Chan’s algorithm.
Fig 7.
Speedup factor in OpenCV as a function of box size for a dense dataset.
The points of each mammal in the datasete was first preconditioned with the method proposed here and then the convex hull was computed by OpenCV convexHull function.