Channel problem: Given a (2D or 3D) polygonal channel, generate a spline that traverses the channel and stays strictly inside.

The user can specify: degree and smoothness of the spline, the location of the spline breakpoints.

In the examples below, the channels are in a semi-transparent gray so that the spline curve and its control points in space are visible. The overlay of semi-transparent channel walls creates darker and lighter regions - this is just an artifact of projection.

Note that the control polygon does not generally stay inside the channel - so that a fit based on bounding the control polygon would not be able to generate these solutions to the fitting problem.

Single degree 3 Bezier curve in a sharp-cornered 2D channel	Degree 3 Bezier spline in a 2D mazewith many sharp corners
The single degree 3 Bezier curve above is subdivided once (left) and twice (right). Note that the control polygon does not stay inside the channel - so that a fit based on bounding the control polygon would not be able to generate this solution to the fitting problem even after two subdivisions.
Degree 3 Bezier spline in a tighter helical structure