Biomedical Engineering Reference
In-Depth Information
Fig. 8.3
Checking whether the mobile vertex (
yellow dot
on the
dark gray
rough 2D mesh) is
penetrating the fixed polygon (
green dashed line
on the
light gray
2D mesh). Both of the
green
fixed triangles
(
dark dashed line
and
light dotted line
) are inside the
gray
spatial cell (segmented
by
black radial lines
). However, only the
dark green triangle
(
dashed line
) is intersected by the
vector connecting the origin (
red dot
) to the mobile vertex. The signed radial distance between the
dark green triangle
and the vertex is calculated by subtracting the
red vector
(
short vector
) from
the
blue
one (
long vector
)[
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)
investigated the effect of the mapping function (to map from Cartesian coordinates
to radial segments) on the processing time to check the importance of simplicity of
the function versus uniformity of its output's distribution [
14
]. The main steps of the
algorithm are listed as follows:
1. Radial segmentation of the space around the fixed object;
2. Creating one table for the fixed object based on the radial segmentation;
3. Storing a list of all the fixed polygons in the corresponding table cells;
4. Comparing the position of each mobile vertex with all the fixed polygons stored
in the corresponding cell of the table;
5. Finding the polygon which has a chance to collide with the mobile vertex;
6. Checking the radial distance between the vertex and the found polygon;
7. If the mobile vertex is penetrating the fixed polygon, return them as a penetrating
pair [
13
,
14
].
8.2.4 Testing and Comparison
To evaluate the proposed methods for collision detection during rotation (striking
and sliding), Arbabi et al. compared the performance of the proposed methods with
the performance of the previous methods in different scenarios [
13
,
14
]. Based on
the results, it could be seen that the total processing time of the proposed cylindrical
and radial segmenting methods can be respectively up to about one and two orders of
magnitude faster than the other methods. Both of these methods are able to be used
