Im working on a program that makes use of catmull rom splines. I start with a list of points (ex. (50, 50), (75, 125), (200, 50) and (225, 300)) and then later calculate additional points for the spline.
I would like to calculate the normal at each of these main points, but I am not sure how to proceed.
How would I go about calculating the normals?
On a Catmull-Rom spline, the tangent at the point $P_i$ is in the direction of the vector $P_{i+1} - P_{i-1}$. To get the normal vector, just rotate this vector by 90 degrees. If you rotate the vector $(u,v)$ by 90 degrees, you get the vector $(-v,u)$.