Which is the result of comparing two curves?
I call Delta, a real number, the result of the comparison of the two curves. where p are points from the first curve and q are points from the second curve. Now you have to choose a suitable distance function depending on your problem: the function has two points as arguments and returns a real number.
What should the similarity be between two points?
If the points overlap, similarity should be 100%. You are comparing trajectories, or curves. This is a studied topic. Procrustes analysis and dynamic time warping, as EMS says, are tools of the trade. Once you’ve aligned the curves you’ll want to measure the distance, say the Fréchet distance.
How to calculate the distance between two curves?
This solution uses a two-dimensional array. The cost would be the distance between two points. The final value of the array DTW [n, m] contains the cumulative distance. DTW is similar to Jacopson’s answer. Frechet distance calculates the farthest that the curves separate.
How to compare two curves F and G?
I need to compare two curves f (x) and g (x). They are in the same x range (say -30 to 30). f (x) may have some sharp peaks or smooth peaks and valleys. g (x) may have the same peaks and valleys. If so I want a measure on how well these features coincide without visual inspection.
How to measure the offset between two curves?
Do this on floor, or on a window pane to create a transparency effect and then take a digital caliper (or similar – ruler, etc.) and measure the offset between the two curves at as many points as you can. The differences are your error.
What’s the best way to overlay a curve?
I think the best way is to overlay the new curve over the old one – such as putting the new curve on paper and laying it over the old curve. Do this on floor, or on a window pane to create a transparency effect and then take a digital caliper (or similar – ruler, etc.) and measure the offset between the two curves at as many points as you can.