如何有效地在python中找到图形的顶部边界线

Question

I have a set of graphs from which I want to find an outline graph (Black line in this figure.)

Finding the maximum of each graph at all points on the x-axis is not possible because the x-values are not same for all the graphs. The points are accurate to a couple of decimal places. this figure might be able to help understand better.

I tried converting each graph to a polygon and using shapely cascaded_union and then cropping off the bottom. It works for a small number of graphs, but when the number of graphs becomes large. It takes a lot of time.

Is there some other efficient way to do this?

Answer 1

Sort all your points by their x coordinate.

Your final output will have a finite number of pixels. You can compute the range of x values that fall within each pixel(small range but not 0). So split your points into buckets. Since they are already sorted, you just need to advance through the list until the values belongs to the next range.

For each pixel column compute the maximum y value you find. Add a point at the (x, y) for the black line.

The complexity of this will be o(N logN).

If you have gaps on the x axis you can choose to either skip it and have a gap in the black line or simply interpolate between the neighbouring values. If you plot the blackline as a collection of line segments you can just skip generating a point for that column and let the renderer do the interpolation for you.

If your original points are too rare (they skip pixels) your line may look jagged (jumping up and down). You can avoid this by adding interpolated values for the functions that don't have a point in that range. Linear interpolation should work just fine. Make sure you generate try to generate a point at the beginning and the end of the interval and take the larger y-value.