Hi mukesh,
The regular cubic spline is using angle as the independent variable to define x and y parametrically in the usual way, x = cos(theta), y = sin(theta).
cscvn picks its own independent variable, which is not angle. Instead, the process is [1] as you proceed along the defined (x,y) points in order, find the euclidean distance between each pair. [2] take the square root of each distance [3] cumulatively sum those up to define the break points. The (x,y) points stay the same so they will still be on the resulting spine curve. In this case the distance between each pair of points is sqrt(2), so the break points are
[0 1 2 3 4]*sqrt(sqrt(2))
which is what you show above.
