Triangle / Circle spanning multiple points

Question

I have a set of points in 2D. I want to find:

• the smallest triangle covering all points
• the smallest circle covering all points.

Is there any algorithm? I came across a convex hull so that it matches convex polygons for many points. But I want a circle and a triangle.

Thanks in advance

Answer 1

If you are referencing the region at least, then the following algorithms could potentially be useful.

Triangle

linear (.. O (n)) , ,

. . , , , Springer, . 1-16, 2014 .

, :

J. , . , . , . , , Journal of Algorithms, vol. 7, . 2, pp. 258-269, 1986 .

: .

++ :
https://github.com/IceRage/minimal-area-triangle

(3.0) OpenCV.

:

G. , , (ESA), Springer, pp. 325-338, 1999.

++ :
http://www.inf.ethz.ch/personal/gaertner/miniball.html.

Answer 2

O (n), . . http://en.wikipedia.org/wiki/Smallest-circle_problem http://prografix.narod.ru/source/orourke1986.pdf. . , , , .