question:
My question is if it is possible to derive a system of equations describing or approximating a certain contour of a simply connected domain, (through or approximately through a set of points), such as the one in the figure below, and if so, if there are any tools or common practices for this.
All (constructive) input is appreciated, thanks in advance.
Context:
I am trying set up a running animation using inverse kinematics, and for that I would like to model the position of the foot over time. The countour of the previous picture is also obtained by tracing the foot in the frames from the short running animation flipbook in the picture below.
attempts:
my initial idea was to trace shape "point by point", and plotting the x and y values of all points against the point number. The point number could then be seen as the "time" axis. One might then be able to obtain (an approximation of) the equations by using the fourier transform on the curves obtained for x and y. However, the (constant) interval of the points might "warp" the resulting time axis, resulting in a frequency spectrum that may be less desirable. (desirable meaning less frequencies with a high amplitude). I can not think of any way to work around this.
For this one would also need software to perform such a trace, but I do not know if there is software available for this. In the worst case I would even be willing to write a small c or matlab program.