DTW: Get y time from x time...

Queries the selected DTW object for the time along the y-direction given the time along the "x-direction".

Setting

Time (s)
the time along the x-direction.

Behaviour

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.

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© djmw, June 3, 2011