Finding the Smallest Triangles Containing a Given Convex Polygon

For a given convex n-gon P an O(n log2 n) algorithm finds all local minima (with respect to area) among the triangles containing P. No areas are computed, for the algorithm is based on a simple geometric characterization of the local minima.

[1]  G. Toussaint.  Solving geometric problems with the rotating calipers , 1983 .

[2]  Godfried T. Toussaint,et al.  On the multimodality of distances in convex polygons , 1982 .

[3]  Leonidas J. Guibas,et al.  Finding extremal polygons , 1982, STOC '82.

[4]  David P. Dobkin,et al.  Efficient uses of the past , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[5]  Leonidas J. Guibas,et al.  The power of geometric duality , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[6]  Alok Aggarwal,et al.  An Optimal Algorithm for Finding Minimal Enclosing Triangles , 1986, J. Algorithms.

[7]  David G. Kirkpatrick,et al.  The Ultimate Planar Convex Hull Algorithm? , 1986, SIAM J. Comput..

[8]  Raimund Seidel,et al.  Constructing arrangements of lines and hyperplanes with applications , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[9]  David P. Dobkin,et al.  On a general method for maximizing and minimizing among certain geometric problems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).