Queries the selected DTW object for the time along the y-direction given the time along the "x-direction".
When the input time is in the interval [xmin, xmax], the returned time will be in the interval [ymin, ymax], where [xmin, xmax] and [ymin, ymax] are the domains of the two "objects" from which the DTW-object was constructed.For input times outside the domain we assume that the two object were aligned.
We like to have a "continuous" interpretation of time for the quantized times in the x and y direction; we make the path a piecewise linear monotonically increasing function. There are special cases:
1. The local path is in the x-direction only. We calculate the y-time from the line that connects the lower-left position of the begin cell of this path to the upper-right position of the last cell.
2. The local path is in the x-direction only. We calculate the y-time from the line that connects the lower-left position of lowest cell to the upper-right position of the highest cell.
3. A cell is both part of a path in the x- and the y-direction. We then calculate the intersection point of the paths in the x- and the y-directions. The y-times in this cell are now calculated from the two line segments that originate from this intersection point.
© djmw, June 3, 2011