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41 lines
2.2 KiB
C
41 lines
2.2 KiB
C
/*
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* curvefit.h
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* scorealign
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*
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* Created by Roger B. Dannenberg on 10/20/07.
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* Copyright 2007 by Roger B. Dannenberg. All rights reserved.
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*
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* Dynamic programming does a good job of getting a rough alignment
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* that is very good in a global sense, but there are often short-term
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* "digressions" where the optimal path wanders off the "true" path.
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* These digressions are hard to correct with simple smoothing. This
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* module is intended to assert a "steady tempo" constraint to improve
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* the path. It starts with the dynamic programming path, which is likely
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* to be close to the correct path. The DP path (in pathx[] and pathy[])
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* is divided evenly into segments of approximately line_time seconds
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* along the x axis. For a segment from x1 to x2, linear regression is
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* performed on the DP path from x1 to x2. This specifies an initial
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* line segment. Next, the end-points are joined by averaging: if
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* the segment from x1 to x2 ends at y-end and the segment from x2 to x3
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* starts at y-start, then the end of line x1--x2 and the beginning of
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* line x2--x3 are adjusted to (y-end + y-start)/2. Now the fun starts:
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* the endpoints of all the lines are adjusted up and down in order to
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* minimize a distance function. The distance function estimates the
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* integral of the distance matrix value along the line. Since the line
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* falls between discrete points in the matrix, interpolation is used.
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* The end result is converted back into a discrete path. (Maybe in the
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* future, the pathx[]/pathy[] representation should be generalized to
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* allow for non-integer path coordinates.) The resulting path will
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* have steady tempo at least within each segment. What I hope will
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* happen is that when there are chord changes or melody changes, there
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* will be "narrow" pathways in the distance matrix. Getting the
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* alignment wrong at these transitions will cost a lot. Other places
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* are not so critical, which is why I think DP wanders off the true
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* path. The straight-line path will ensure that for the most part, the
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* score alignment is determined by the transitions, and where alignment
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* is not critical, the alignment will avoid any rubato or over-fitting.
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*/
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void curve_fitting(Scorealign *sa, bool verbose);
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