Computational geometry: an introduction
Computational geometry: an introduction
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Solving the Collision Detection Problem
IEEE Computer Graphics and Applications
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Matrix computations (3rd ed.)
Trust-region methods
Optimized view frustum culling algorithms for bounding boxes
Journal of Graphics Tools
Determining the minimum-area encasing rectangle for an arbitrary closed curve
Communications of the ACM
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Convergence of the Nelder--Mead Simplex Method to a Nonstationary Point
SIAM Journal on Optimization
Incremental Algorithms for Collision Detection Between Polygonal Models
IEEE Transactions on Visualization and Computer Graphics
Efficient collision detection of complex deformable models using AABB trees
Journal of Graphics Tools
On Optimality of OBBs for Visibility Tests for Frustum Culling, Ray Shooting and Collision Detection
CGI '98 Proceedings of the Computer Graphics International 1998
Computational geometry.
Approximating extent measures of points
Journal of the ACM (JACM)
Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3-D Technology) (The Morgan Kaufmann Series in Interactive 3D Technology)
Introduction to Derivative-Free Optimization
Introduction to Derivative-Free Optimization
Bounds on the quality of the PCA bounding boxes
Computational Geometry: Theory and Applications
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Consensus Optimization on Manifolds
SIAM Journal on Control and Optimization
A virtual training system using a force feedback haptic device for oral implantology
Transactions on Edutainment VIII
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An exact algorithm to compute an optimal 3D oriented bounding box was published in 1985 by Joseph O'Rourke, but it is slow and extremely hard to implement. In this article we propose a new approach, where the computation of the minimal-volume OBB is formulated as an unconstrained optimization problem on the rotation group SO(3,ℝ). It is solved using a hybrid method combining the genetic and Nelder-Mead algorithms. This method is analyzed and then compared to the current state-of-the-art techniques. It is shown to be either faster or more reliable for any accuracy.