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In terms of the ASSF representation, a ``contact'' is one item on the list of
things that are in contact with a particular feature. Each item on this list
refers to a second shape feature (on a different object) that is in contact
with this one. The qualitative state information implicit in this
representation of a contact includes the names of the two objects that are in
contact, the relative size of the features which are in contact, the relative
orientation of the objects which they belong to, and the qualitative shapes of
the features, and their neighbouring features.
The most important of these qualities for the purposes of sliding analysis is
the shape of the two features. Different sliding behaviour can be observed for
each of the differently shaped feature pairs described in the following list:
- 1.
- Contact between two vertices only. This results in each vertex
appearing on the contact list associated with the other.
(See figure 5.1)
Figure 5.1:
Vertex to Vertex Contact
|
- 2.
- Contact between a line segment and a vertex. Each appears on the
contact list of the other. (See figure 5.2)
;
Figure 5.2:
Line Segment to Vertex Contact
|
- 3.
- Contact between two line segments of the same length, which are
exactly aligned. Each line segment appears on the contact list of the
other. In addition to this, the vertices at each end of each segment
appear on the contact list associated with the vertices at each end of
the other segment. (See figure 5.3)
;
Figure 5.3:
Aligned Line Segments Contact
|
- 4.
- Contact between two overlapping line segments. In this case, the
contact list of each line segment includes the other line segment, and
also the vertex at one end of the other. Each vertex also has the
other line segment on its contact list. The side of the line segment
on which the contacting vertex appears separates two types of overlap
contact - either both vertices are clockwise from the contacting
segment when the boundary of the object is being traversed, or both
are anticlockwise. (See figure 5.4)
;
Figure 5.4:
Overlapping Line Segments Contact
|
- 5.
- Contact between two line segments, where one is longer than the other,
and the longer one extends past the shorter at both ends. In this
case the contact list of the longer will include the shorter segment,
and also the vertex at each end. The contact list of the shorter will
have only one entry - the larger line segment.
(See figure 5.5)
;
Figure 5.5:
Large Line Segment to Small Line Segment Contact
|
- 6.
- Contact between a vertex and a convex curve. Each appears on the
contact list of the other. (See figure 5.6)
;
Figure 5.6:
Vertex to Convex Curve Contact
|
- 7.
- Contact between a vertex and a concave curve. Each appears on the
contact list of the other. (See figure 5.7)
;
Figure 5.7:
Vertex to Concave Curve Contact
|
- 8.
- Contact between a line segment and a convex curve. Each appears on the
contact list of the other. The vertices at the ends of the line
segment will not be in contact with the curve.
(See figure 5.8)
;
Figure 5.8:
Line Segment to Convex Curve Contact
|
- 9.
- Contact between a line segment and a concave curve is not possible,
but the vertices at each end of the line segment can be in contact
with a concave curve. (See figure 5.9)
;
Figure 5.9:
Line Segment to Concave Curve Contact
|
- 10.
- Two convex curves can contact each other. (Concave curves cannot.)
(See figure 5.10)
;
Figure 5.10:
Convex Curve to Convex Curve Contact
|
- 11.
- A concave and convex curve can contact each other only if the angle of
the convex curve is smaller than the concave curve.
(See figure 5.11)
;
Figure 5.11:
Concave Curve to Convex Curve Contact
|
In addition to the actual shape of two features in contact, it is apparent
from the above list that the shape and contact status of neighbouring features
is also relevant in distinguishing between qualitative contact states. The
shape of neighbouring features becomes more important, however, when
considering the ways in which the contact state can change as the objects
slide past each other.
Next: Contact State Transitions
Up: A Program for Reasoning
Previous: A Program for Reasoning
Alan Blackwell
2000-11-17