how to make an object follow a curve with the same speed as another animated object

Question

Say I have an object which has an animation.

I have another object which is constrained to a curve. I want it to follow the curve BUT I want it to do it at the same speed as the animated object.

here I am manually moving the object to show what I mean. I want the cube to move along the path, but with the same variations in speed that the moving camera has.

Doing this will essentially let me deform a motion path like you would do with a mesh. I don't know much about coding so if the answer includes writing some kind of script, I would really appreciate it if you gave an example :)

EDIT: batFINGER phrased it well in the comments: "for every frame if Free object moves d units, the path object will move d along the curve"

Also, preferably I would also like to do this live in blender.

Answer 1

Bake the displacement.

Given

I used a gltf camera path which I exported from a video game, so Its just a keyframe animation

Here is a quick baking script,

Whenever the animation of the camera has been changed, run the script to bake some simple physics.

• Set scene to first frame of action save the location as previous location
• For each frame of camera action
• Calculate the distance from frame location to previous location and store
• Set the location as previous.

From the data bake in 3 animations on custom properties

• "speed" The amount of distance travelled that frame

• "disp" The accumulative displacement

• "offset" The frame displacement as a fraction of total

• The values of the 3 are keyframed into the camera action

• The cube in GIF has a follow path constraint to circle, the relative offset is being driven by cameras custom property "offset" added by script. Baked in graph editor

Here is a test script, assuming the animated object is scene camera, and it is animated by active action

import bpy
import numpy as np
context = bpy.context
scene = context.scene
cam = scene.camera
action = cam.animation_data.action
frames = np.arange(*action.frame_range)

def gloc(ob):
    return ob.matrix_world.to_translation()



locs = []
scene.frame_set(frames[0])
ploc = gloc(cam)
for f in frames:
    print(f)
    scene.frame_set(f)
    loc = gloc(cam)
    s = (loc - ploc).length
    locs.append(s)
    ploc = loc


def flatten(a, b):
    c = np.empty((a.size + b.size,), dtype=b.dtype)
    c[0::2] = a
    c[1::2] = b
    return c

def fcurve(fcurves, datapath, data):
    cam[datapath] = 0.0
    fc = fcurves.find(datapath)
    if fc:
        fcurves.remove(fc)
    fc = fcurves.new(datapath)
    fc.data_path = f'["{datapath}"]'
    fc.keyframe_points.add(len(frames))

    fc.keyframe_points.foreach_set(
            "co",
            flatten(frames, data)
            )
    fc.convert_to_samples(*action.frame_range)           

# per frame speed    
speed = np.array(locs)
fcurve(action.fcurves, "speed", speed)

# displacement
disp = np.cumsum(speed)
fcurve(action.fcurves, "disp", disp)
# Offset of total displacement

offset = disp / disp[-1]

fcurve(action.fcurves, "offset", offset) 

Note, GIFs shown are not moving two objects same distance each frame, rather the same offset fraction along their asscociated paths per frame. To make it 1:1 distance would require calculating the length of the constraint curve

Answer 2

Edit: sorry it looks like I misunderstood your question as your object A follows a curve path. Anyway I leave my original answer.

Let's say the cone is the object A that goes straight ahead and the cube is the object B that is following a curve.

First, you can do it with Curve modifier and Copy Location constraint:

• Create a plane, give it a Curve modifier (with the curve as Object) and a Copy Location constraint (with the cone as Target)
• Select the cube, shift select the plane, select 3 vertices of the plane and CtrlP to parent the cube to the plane vertices
• Animate the cone, the plane will go along the curve and the cube will follow the plane

You can also do it with Drivers:

Give your cube a Follow Path constraint, enable its Follow Curve option, right click on Offset value and choose Add Driver:

In the pop-up panel, choose the object the cube is supposed to follow, in Expression choose a variable, here *-40 -50 (-0 is here so that it begins at the right position), you can right click on Offset to Open Drivers Editor, press V to make a linear curve, rotate the curve, test the animation:

Here is what it gives for me: