In terms of curve analysis, a topic segment is a point, a straight line or a series of consecutive straight lines. Topic segments should not have shared points. The boundary between two consecutive topic segments is defined as the starting point of the second topic segment.
The topic segment is a point: see (b) in the figure above. When the line is only composed of two points, say p1.p2 and p2.p3, the point p2 is taken as a single point topic segment. The boundary is itself. The point p3 will be a boundary for the following topic segment.
The topic segment is a line: there are some different cases in this situation. (a) has two topic segments, one is 'dominated/dominant' pattern, and the other is 'drifting'. For 'dominant/dominated' pattern topic segments, the point at the end of line can not be boundaris except the starting point. So p2 can not be a boundary. The boundary in the case (a) is p3, which is the starting point of the following 'drifting' segment. (c) has two 'drifting' segments, each of which is composed of more than one points, we use the peak point p2 as the boundary of two topic segments.The last case (d) is a topic segment of 'interrupted' pattern. The boundary should be p1.
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In order to get the information about boundaries of topic segments, we need simplify the method. That is:
1. if the segment currently concerned is a dominated/dominant pattern, all of points in the segment can not be taken as the starting point of other segments.
2. if there are not only one points in the segment line, the boundary might be the starting point when there are no any segments before it. Or else, the point next to the starting point of the segment is taken as the boundary.
3. If there are only two nodes in the segment which are end points of the line. The peak point would be a boundary which is also the single point segment. The point next to the peak would be the boundary for the following topic segment.
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