Is there a way to grow this curve at a constant velocity?

Question

Hello, I would like to be able to grow the curve shown in the gif above at a constant velocity. For the straight edges of the curve, I just don't like how they grow super quickly. It looks a bit too choppy.

I assume that the curve growth velocity is dependent upon the density of the curve's vertices. There are fewer vertices throughout these straight edges, therefore the curve will grow faster along those edges. I think an even distribution of vertices throughout the curve with small distances between them to maintain detail could possibly solve this, but I don't know how to do that.

To create the animation, I started off with my mesh symbol. I converted it to a curve, added a nurbs path and scaled it down, set the curve's bevel object as the small nurbs path, set the curve type to 2D, unchecked the curve's cyclic-u property, and then keyframed the end value from 0 to 1 under start & end mapping to animate the growth. I also added a few vertices to the curve to patch the slit caused by unchecking cyclic - U.

I found that animating the curve using this method had the best topology on the symbols I'm creating these curves out of. I would prefer to maintain the sharp corners of the symbol if possible.

EDIT: So, to remove slanted tips caused by changing the mapping end & start to spline, I end up having to subdivide the long segments of the curve. I wrote a script that does this if anyone else out there needs it. The pseudocode is as follows: "for each of the curve's segments, if the segment length is greater than some amount, subdivide that segment with some number of cuts"

import bpy

curve = bpy.context.scene.objects["Latex Figure"]

matrix = curve.matrix_world 

bpy.context.view_layer.objects.active = curve

bpy.ops.object.mode_set(mode = 'EDIT')

i = 0
range = len(curve.data.splines.active.points)
while i < range:
    point0 = curve.data.splines.active.points[i].co
    point0 = matrix @ point0

    if i == range - 1:
        point1 = curve.data.splines.active.points[0].co
    else:
        point1 = curve.data.splines.active.points[i + 1].co
        
    point1 = matrix @ point1
         
    d = (point1 - point0).magnitude
    
    someAmount = .1
    
    numCuts = int(2 * d/someAmount)
    
    if d > someAmount:
            
        bpy.ops.curve.select_all(action='DESELECT')
        
        curve.data.splines.active.points[i].select = True
        if k == r - 1:
            curve.data.splines.active.points[0].select = True
        else: 
            curve.data.splines.active.points[k + 1].select = True
      
        bpy.ops.curve.subdivide(number_cuts = numCuts)
        
        i += numCuts + 1
        range += numCuts
         
    else:
        i += 1
        
        
bpy.ops.object.mode_set(mode = 'OBJECT')        

Answer 1

If you set the 'Mapping' Start / End to 'Spline' on a Bezier curve..

.. then the curve's length is mapped from 0-1. (Or, at least, a reasonably sampled approximation of it). You can put linearly-interpolated key-frames on those fields.

BTW.. if you want a round profile, you can use the native bevel. You may not need a separate bevel object.

In your particular case, the object-level scale of your curve is way out of whack, at 600. CtrlA > applying scale brings it to 1, but then you have to correct the radius to compensate. Here, I've brought the radius of the control-points to 0.1 (in the N panel, in Edit Mode). When that's done, you don't have to convert the curve type. It works as a NURBS.

The front of the sweep is diagonal along some of the straight sections. It's interpolating between the directions of the control points at the end of the segments. Inserting a couple more control points entirely in the straight, towards the ends of the segments, will fix that, if you need to.

Answer 2

With animation nodes you can easily turn the curve in a curve with equal distance vertices like this:

if you extend the animation nodes setup like this, you got constant speed:

by adding a map range node you can get increasing speed:

Note: with a little math you can exchange the map node with some math nodes and you can make the velocity more configurable...