Curvature of a 1D curve in a 2D or 3D space

Calculates the local radius of curvature as well as the cumulative arc length and the curvature vector along a 1D curve in 2D or 3D space

Function circumcenter finds the radius R and the center of the circumscribed circle of a triangle in 3D space.

Function curvature calls circumcenter for every triplet , , of neighboring points along the curve. The curvature is defined as . The curvature vector is , where is the unit vector in the direction from to the center of the circle.

Note that this local calculation is sensitive to noise in the data.

The syntax is:

[L,R,K] = curvature(X)

X: array of column vectors for the curve coordinates. X may have two or three columns.

L: Arc length

R: Curvature radius

K: Curvature vector