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Ch22-I044963.fm Page 107 Tuesday, August 1, 2006 3:32 PM
3:32 PM
Tuesday, August
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Ch22-I044963.fm
1, 2006
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gas)
This is a pure space and is defined as a space including a specified point.
Thus, both spaces are defined as a geometrical data. Therefore it is possible handle the space as a
target for attaching design information and the intention. The expression of the space which relates
directly to an object with substance is possible to treat the relational design information between the
target object, space and pure space is possible to treat the single design information as a point. Fig.3-
(1) shows the space which shows tracks of object and Fig. 3-(2) shows a case of personal computer
and shows the space of air flow for cooling and Fig. 4 shows a example of pure space.

H r lp • ~ ' "
t
P '* ^If 1
••lib" -m* 1

(1) Tracking space (2) The space of air flow for cooling
Figure 3: Example of the space

Figure 4: Example of closed space

Moreover, to handle the air flow and a closed space accentually, it is necessary for the mechanism to
evaluate the space conditions, opening, closing or penetrating. For example, Fig. 4 shows a
suspension part and the space in which oil is filled. The capability to check the open or closed state of
this space is very important. It explains the judgment of the opening and closing space, as follows. For
simplicity, all of the parts are solid models.

Proposition: Determination the open or closed state of space
Judgment
First, we show several definitions
P : Point included in space to be judged , Bi (i=l,2,,,,n): Parts which compose the suspension
H : The minimum hexahedron including the all parts
He : The hexahedron which expands +e (>0) for each coordinate. BD(He) : Boundary set of He
Then, if we take the differences of all parts from He, in general it becomes several solids.
U Sj = He - [J Bi
i - I i - i
So, point P is included in Sk for some k. At that time, we can judge the state of space including
point P as follows.
Tf b e Sk for some b e BD(He)