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Fig. 24.7 Constructing R set for opposite icosphere vertices v i and v
i
Let us describe the algorithm for converting a polygonal model M n,m in its
descriptive representation D
M n,m
.
Constructing the descriptors. The input of the algorithm is a polygonal model
M n,m with its surface I
M n,m
, number of vertices of icosphere is equal to 2N . As
a result, the algorithm returns descriptive representation of the model as a matrix
D 4×N .
Steps of the algorithm are the following:
1. The model is placed inside a unit icosphere by scaling and sequentially combining
the origin of coordinates with the geometric center of the model’s minimum
volume bounding box:
2. All vertices of the icosphere form N pairs of opposite vertices v i , v
i , i =
1, . . . , N , which corresponds to the guide vectors u i , u
i . Sets of ray lengths
are calculated for each such pair:
R(u i , I ) =
r
1
i , r
2
i , . . .
,