Assume we have $X=[\mathbf{x},\mathbf{y}]$, where, $\mathbf{x}=x_1,x_2,...$ and $\mathbf{y}=y_1,y_2,...$, representing a curve (sampled) in Cartesian coordinates. The question is whether or not we can find out the winding number by only using $X$?
Can winding number be calculated given a vector of points (samples of a curved line)?
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geometry
analysis
computational-mathematics
computer-algebra-systems
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0Without more information/assumptions, no. The function could get arbitrarily 'windy' at the uncountably many other points that have not been sampled. – 2017-01-23
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1If you assume that you connect these points via straight line segments, then yes. Otherwise, no. – 2017-01-23
1 Answers
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Ok. I found a MATLAB code that does the job very well. It is written in a way that the steps are easy to follow algorithmically: