The R*-tree: an efficient and robust access method for points and rectangles
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Direct spatial search on pictorial databases using packed R-trees
SIGMOD '85 Proceedings of the 1985 ACM SIGMOD international conference on Management of data
The R+-Tree: A Dynamic Index for Multi-Dimensional Objects
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Fast oriented bounding box optimization on the rotation group SO(3,ℝ)
ACM Transactions on Graphics (TOG)
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Principal component analysis (PCA) is commonly used to compute a bounding box of a point set in R^d. The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimum-volume bounding boxes. We present examples of discrete points sets in the plane, showing that the worst case ratio of the volume of the PCA bounding box and the volume of the minimum-volume bounding box tends to infinity. Thus, we concentrate our attention on PCA bounding boxes for continuous sets, especially for the convex hull of a point set. Here, we contribute lower bounds on the approximation factor of PCA bounding boxes of convex sets in arbitrary dimension, and upper bounds in R^2 and R^3.