I have a series of unit normals/tangents that are sampled at a regular intervals along the x dimension but I do not have their heights/y-component. For example:
I would like to integrate the gradients into a curve, but am a bit stuck because it is unclear to me how to appropriately estimate the gradient from these normals/tangents. Can anyone recommend a paper/source that would help describe how I could reconstruct a 1D curve based upon these unit normals? I'm not currently interested in 3D reconstruction, merely this simple test case of reconstructing a 1D curve. Thanks for any help you can provide!
In any textbook on differential geometry of curves and surfaces you will find a treatment of the Frenet-Serret equations, which is a system of differential equations which determines a curve from its curvatures. You have (a sampling of) unit normals so you can compute a sampling of curvature and do the usual things to approximate the solution.
The equations are usually stated for curves in 3d, but their special case for curves in the plane is excatly the same.