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INTRODUCTION 75
where the exponent x is given by
x< 1 (3.7)
The author is not aware that any such contact detection algorithm exists. In addition,
there is no proof that such an algorithm is possible. However, before 1995 the same was
true for linear contact detection algorithms, when it was not clear that such an algorithm
would be feasible, until the first robust linear contact detection algorithm was designed
in the form of the Munjiza-NBS contact detection algorithm.
RAM efficiency means that the total memory required for the contact detection
algorithm to store all its data should be as small as possible. The total memory
required for some algorithms may, for instance, depend upon the spatial distribution of
discrete elements, and the total number of discrete elements.
The ideal situation is that the total RAM requirements M depend only upon the total
number of discrete elements, and are proportional to the total number of discrete elements
M ∝ N (3.8)
The optimal contact detection algorithm is in general dependent upon the problem
to be solved. The properties of different contact detection algorithms make them suited
for different types of problems, such as dense packing and loose packing, as shown in
Figure 3.1. In addition, one algorithm may be better suited for quasi-static problems,
where the relative motion of individual discrete elements is restricted, (Figure 3.2), while
the altogether different algorithm is suited for dynamic problems where individual discrete
elements move significantly, as shown in Figure 3.3.
Figure 3.1 Packing density: (left) dense packing; (right) loose packing.
Figure 3.2 Typical quasi-static problem.
