366
V. L. Kondarattsev et al.
Fig. 24.6 Train set accuracy evaluation
3D models. In this chapter, we propose our own heuristic algorithm for the descriptive representation of 3D models based on the ray casting method and a method
for comparing such descriptive representations. There are also many other ways to
construct descriptors for 3D models. For example, a whole group of methods is based
on calculating the moment characteristics of a polygon mesh. The most relevant work
devoted to the construction of moment descriptors is [16], in which authors used
three-dimensional Zernike moments. Comprehensive information about methods of
constructing descriptive representations (descriptors) for 3D models can be found in
the doctoral dissertation [2].
In order to describe the descriptors constructing algorithm, let ‘us first introduce
all the necessary operators and concepts in Sect. 24.5.1. Description and search are
discussed in Sect. 24.5.2. Section 24.5.3 provides a description of experiments.
24.5.1 Constructions and Operator
Rays whose lengths will be used to construct a descriptive representation of the
mesh will be emitted from points of the unit icosphere Ico n,m =
V
ico
n , P
ico
m
, where
V
ico
n are the icosphere mesh vertices and P
ico
m are the icosphere mesh polygons [17].
Icosphere’s main feature, which we will use, is that all its vertices belong to the
surface of a two-dimensional sphere x
i
∈ S 2 (S 2 is the surface of a two-dimensional
sphere).