Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating extent measures of points
Journal of the ACM (JACM)
Minimal enclosing parallelepiped in 3D
Computational Geometry: Theory and Applications
How to get close to the median shape
Proceedings of the twenty-second annual symposium on Computational geometry
How to get close to the median shape
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing
IEEE Transactions on Signal Processing
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We develop a combinatorial algorithm for determining a minimum volume simplex enclosing a set of points in ${\cal R}^3$. If the convex hull of the points has $n$ vertices, then our algorithm takes $\Theta(n^4)$ time. Combining our exact but slow algorithm with a simple but crude approximation technique, we also develop an $\varepsilon$-approximation algorithm. The algorithm computes in $O(n + 1/\varepsilon^6)$ time a simplex whose volume is within $(1 + \varepsilon)$ factor of the optimal for any $\varepsilon 0$.