Determine arc-length of a Catmull-Rom spline
- by Wouter
I have a path that is defined by a concatenation of Catmull-Rom splines. I use the static method Vector2.CatmullRom in XNA that allows for interpolation between points with a value going from 0 to 1.
Not every spline in this path has the same length. This causes speed differences if I let the weight go at a constant speed for every spline while proceeding along the path. I can remedy this by letting the speed of the weight be dependent on the length of the spline. How can I determine the length of such a spline? Should I just approximate by cutting the spline into 10 straight lines and sum their lengths?
I'm using this for dynamic texture mapping on a generated mesh defined by splines.