Color a mesh based on progress along a 'spline' (read - series of unconnected transforms). Colors can be adjusted using curves. Do this in edit mode with a VertexColor shader/your custom one to see results live. WARNING: This affects the mesh directly so make sure to save a backup.

SplineVertexColors.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class SplineVertexColors : MonoBehaviour {

	#region Types
	public enum Mode
	{
		ChannelCurves,
		Gradient
	}
	#endregion

	#region Serialized
	public MeshFilter m_MeshFilter;
	public Transform[] m_SplinePoints;

	public Mode m_Mode = Mode.ChannelCurves;

	[Header("Mode - Channel Curves")]
	public AnimationCurve m_RedCurve = AnimationCurve.Linear(0f,0f,1f,1f);
	public AnimationCurve m_GreenCurve = AnimationCurve.Linear(0f,0f,1f,1f);
	public AnimationCurve m_BlueCurve = AnimationCurve.Linear(0f,0f,1f,1f);
	public AnimationCurve m_AlphaCurve = AnimationCurve.Linear(0f,0f,1f,1f);

	[Header("Mode - Gradient")]
	public Gradient m_Gradient;

	[Header("Debug")]
	public bool m_DrawVertexSplineConnections = true;
	#endregion

	#region Lifecycle
	private void Update()
	{
		UpdateMeshColors();
	}
	#endregion

	#region Methods
	private void UpdateMeshColors()
	{
		var mesh = m_MeshFilter.sharedMesh;

		Vector3[] vertices = mesh.vertices;
		Color[] colors = new Color[vertices.Length];

		for( int i = 0; i < vertices.Length; i++ )
		{
			float vertProgress = GetVertexProgress( vertices[i] );

			if( m_Mode == Mode.ChannelCurves )
			{
				colors[i] = new Color( m_RedCurve.Evaluate( vertProgress ), m_GreenCurve.Evaluate( vertProgress ), m_BlueCurve.Evaluate( vertProgress ), m_AlphaCurve.Evaluate( vertProgress ) );
			}
			else
			{
				colors[i] = m_Gradient.Evaluate( vertProgress );
			}
		}

		mesh.colors = colors;
		m_MeshFilter.sharedMesh = mesh;
	}

	private float GetVertexProgress( Vector3 vertexPosition )
	{
		float minDistanceSqr = Mathf.Infinity;
		int minDistanceIndex = -1;

		Vector3 vertexWorldPosition = transform.TransformPoint( vertexPosition );

		for( int i = 0; i < m_SplinePoints.Length; i++ )
		{
			float distanceSqr = Vector3.SqrMagnitude( m_SplinePoints[i].position - vertexWorldPosition );
			if( distanceSqr < minDistanceSqr )
			{
				minDistanceIndex = i;
				minDistanceSqr = distanceSqr;
			}
		}

		if( m_DrawVertexSplineConnections )
		{
			Debug.DrawLine( vertexWorldPosition, m_SplinePoints[minDistanceIndex].position, Color.blue );
		}

		return (float)minDistanceIndex/(float)(m_SplinePoints.Length-1);
	}
	#endregion
}