How to Export Contour Plot as Shape File if Output is of Data Type 'Double'?

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Good morning!

I'm trying to export a contour plot as a shapefile. However, there seems to be a problem with the shapewrite function. The error reads, "error using shapewrite: expected input number 1, S, to be one of these types: struct, mappoint, geopoint, mapshape, geoshape. Instead its type was double." The second error reads, "error in shapewrite>parseInputs (line 639) validateattributes(S,...)." The last error reads, "error in shapewrite (line 80) [S, basename, dbfspec] = parseInputs(varargin{:})."

My initial code is:

shape = ncread('file.nc', 'var', [1,1,1], [inf,inf,1])
contourf(var')
x = contourf(var')
shapewrite(x, 'var.shp')

Note: the first two lines of code produce the contour plot and the last two lines are my attempt to convert the contour plot to a shapefile.

Again, I am trying to convert the contour plot to a shapefile so that I can work with the SHP in ArcGIS. Any help would be greatly appreciated. Thank you in advance!