In d3, how to get the interpolated line data from a SVG line?

I display a line chart with D3 with roughly the following code (given the scale functions x, y and the float array data):

 var line = d3.svg.line()
         .interpolate("basis")
         .x(function (d, i) { return x(i); })
         .y(function (d) { return y(d); });
 d3.select('.line').attr('d', line(data));

Now I want to know the vertical height of the line at a given horizontal pixel position. The data array has lesser data points than pixels and the displayed line is interpolated, so it is not straight-forward to deduce the height of the line at a given pixel just from the data array.

Any hints?