Contact Modeling and Collision Detection in Human Joints - 3D Multiscale Physiological Human - page 184

Fig. 8.2 a Cylindrical segmentation of the space without objects, b with rotating objects , c the
corresponding table cells for storing list of the fixed polygons in each ring segment [ 3 , 13 , 14 ]
(Reprinted from Journal of Biomechanics, Vol. 42, Arbabi E, Boulic R, Thalmann D, Fast collision
detection methods for joint surfaces, pp. 91-99, Copyright (2009), with permission from Elsevier)
cell of the table, the polygons which have a chance to collide with the mobile vertex
(during rotation) are found. Among the found polygons the one with the smallest
angular distance to the mobile vertex is saved. The mobile vertex is checked to see
whether it is penetrating the saved polygon or not. If yes, the mobile vertex and the
saved polygon are returned as a penetrating pair.
Thismethod does not only return the penetratingmobile vertices, but it also returns
the corresponding penetrating fixed triangles in the angular direction, which conse-
quently provides the curvilinear penetration depth of the vertices without applying
any additional computations.
8.2.3 Radial Segmenting Collision Detection
Maciel et al. proposed a ray-based sampling method for detecting collision among
rotating or sliding objects [ 18 ]. This method returns the pairs of penetrated mobile
vertices and their corresponding penetrated fixed triangles. The method could be
shown to be faster than many other general methods and also to be suitable for
evaluating human joints. However, it also suffers from some weaknesses in accuracy
and in processing stages.
Later, Arbabi et al. proposed another method working by radial segmentation of
the object's spatial occupancy [ 14 ]. The collision is found by comparing the position
of the vertices and the polygons occupying the same radial segment (see Fig. 8.3 )
[ 14 ]. Generally, the method is inspired by the work done by Maciel et al. [ 18 ].
However, an important part of the method, i.e. the strategy used for creating and
filling the table, is different from this work. The proposed new strategy not only
makes the method return accurate collision answers (vs. the approximated answer of
[ 18 ]), but also increases the speed of table updating significantly. Arbabi et al. also