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Kinetic triangulation : ウィキペディア英語版
Kinetic triangulation
A Kinetic Triangulation data structure is a kinetic data structure that maintains a triangulation of a set of moving points. Maintaining a kinetic triangulation is important for applications that involve motion planning, such as video games, virtual reality, dynamic simulations and robotics.〔
==Choosing a triangulation scheme==
The efficiency of a kinetic data structure is defined based on the ratio of the number of internal events to external events, thus good runtime bounds can sometimes be obtained by choosing to use a triangulation scheme that generates a small number of external events.
For simple affine motion of the points, the number of discrete changes to the convex hull is estimated by \Omega(n^2),〔 thus the number of changes to any triangulation is also lower bounded by \Omega(n^2). Finding any triangulation scheme that has a near-quadratic bound on the number of discrete changes is an important open problem.〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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