Question

I have two paths in 3D and I want to “average” them, if there’s such a thing.

I have the xyz pairs timestamped at the time they were sampled:

    ms   x   y   z
    3   0.1 0.2 0.6
    12  0.1 0.2 1.3
    23  2.1 4.2 0.3
    55  0.1 6.2 0.3

Facts about the paths:

• They all start and end on/near the same xyz point.
• I have the total duration it took to complete the path as well as individual vertices
• They have different lengths (i.e. different number of xyz pairs).

Any help would be appreciated.

Answer 1

Expanding on @6502’s answer.

If you wish to retrieve a list of points that would make up the average path, you could sample the avg function at the instances of the individual input points. (Stretched toward the average length)

def avg2(T1, waypoints1, T2, waypoints2):
    # Collect the times we want to sample at
    T = (T1 + T2) / 2
    times = []
    times.extend(t*T/T1 for (t,x,y) in waypoints1)  # Shift the time towards
    times.extend(t*T/T2 for (t,x,y) in waypoints2)  #   the average
    times.sort()

    result = []
    last_t = None
    for t in times:
        # Check if we have two points in close succession
        if last_t is not None and last_t + 1.0e-6 >= t:
            continue
        last_t = t

        # Sample the average path at this instance
        x, y = avg(t, T1, waypoints1, T2, waypoints2)
        yield t, x, y