think-cell technical report TC2003/01 A GUI-based Interaction ...

5.2 An Application of Dynamic Programming IMPLEMENTATION
5.2.4 Advanced Gridline Matching Considerations
In practice, there are a lot more issues involved with gridline matching than the
basic matching discussed in the previous sections. For example, which exactly is
the list of destination gridlines? Depending on the user input, some subset of the
available gridlines from the destination slide must be chosen. The precise semantics
of mouse input – typically a point or a rectangle – must be defined. In case of a
single point, it is unclear where the input of destination gridlines stops. One possible
implementation would take all available destination gridlines and treat the entire
last row of the cost matrix as valid solutions. Figure 46 exemplifies the optimal
solution in this case, where the minimum cost value from the last row of the matrix
is taken as the starting point for the reconstruction.
SOURCE
DEST
Dest.
Source
s 1 s 2 s 3 s 4 s 5
d 1 d 2 d 3 d 4 d 5 d 6
1
2
3
4
5
Solution
MergeGridlines(…)
SOURCE
DEST
(a) Gridlines being matched
1 2 3 4 5 6
0
SOURCE
7
SOURCE
11
SOURCE
26
SOURCE
58
DEST
20
SOURCE DEST IDENTIFY IDENTIFY DEST DEST
96 131 81 97 105 139
s 1 s 2 s 3 s 4 s 5
d 1
d 2
Solution
DEST DEST DEST DEST DEST
23 77 165 317 428
SOURCE IDENTIFY DEST DEST IDENTIFY DEST
29 31 46 59 178 210
DEST SOURCE DEST SOURCE IDENTIFY IDENTIFY
18 35 41 61 74 199
SOURCE DEST IDENTIFY SOURCE SOURCE DEST
24 29 55 79 115 171
SOURCE SOURCE DEST IDENTIFY DEST DEST
70 89 133 83 109 147
(b) Optimal path reconstruction
Figure 46: Matching a dynamic number of destination gridlines
IDENTIFY
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Depending on the interpretation of the mouse pointer location as a reference
point for the insertion, it might be necessary to run the optimization algorithm
in two directions. In any case, gridlines must be matched for both dimensions,
vertically and horizontally. This adds a new dimension to the complexity of the
matching problem: The relationships between source and destination shapes that
are established in one dimension may have an influence on the costs calculated for
the other dimension. My approach to this interdependency is to iteratively try
a small number of different solutions in either dimension and then decide for the
ultimate best guess. This approach does not always yield the actual optimum, but
it has the advantage to find a “good” solution in polynomial time.
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