Blender script to generate a NURBS curve from a camera's path.

create_nurbs_camera_path.py

import bpy
from mathutils import Vector

# Create the curve data
# https://blender.stackexchange.com/a/6751
curveData = bpy.data.curves.new('CameraCurve', type='CURVE')
curveData.dimensions = '3D'
curveData.resolution_u = 2
curveData.bevel_depth = 0.01 # curve radius in meters
polyline = curveData.splines.new('NURBS')
polyline.points.add(bpy.context.scene.frame_end)

# Loop over camera poses and add coords to curve
# https://blender.stackexchange.com/a/58922
camera = bpy.data.objects["Camera"]
sensorHeightMet = camera.data.sensor_height * 0.001 # used to hide curve tube from camera frame
frame = bpy.context.scene.frame_start
while frame <= bpy.context.scene.frame_end:
    bpy.context.scene.frame_set(frame)
    pos = camera.matrix_world.decompose()[0] # https://blender.stackexchange.com/a/38210
    rot = camera.matrix_world.decompose()[1].to_matrix()
    camUp = Vector((rot[0][1], rot[1][1], rot[2][1])) # camera Up vector
    # lower curve to avoid showing inside of curve tube close to camera
    pos = pos - camUp * sensorHeightMet * 3 # empirical factor if sensor height is not enough
    # map coords to spline
    polyline.points[frame].co = (pos[0], pos[1], pos[2], 1)
    frame += 1

# create object and add to main collection
curveOB = bpy.data.objects.new('CameraCurve', curveData)
bpy.data.collections['Collection'].objects.link(curveOB)