Mathematics: Curves, Surfaces, Volumes

Support for B-splines and NURBS objects.
Abstract base classes for implicit curves and surfaces.
Determing the surface represented by a quadratic polynomial equation of 3 variables.
Computation of the Frenet frame for 2D or 3D curves. Computation of the Darboux frame for 3D surfaces.
Bézier and polynomial curves.
Natural spline curves that have free boundary conditions, clamped boundary conditions or that are closed. The NaturalSplineCurve class implemented only natural cubic splines; this class will be deprecated. New classes have been added for both cubic and quintic splines.
Tension-continuity-bias spline curves.
Least-squares fitting of point sets by B-spline curves and surfaces.
Computing geodesics (shortest path between points) on a surface is a differential geometric topic that involves Riemannian geometry. The algorithm for constructing geodesics that is implemented in these source files uses a multiresolution approach.
Reparameterize a curve by arclength. This is used to move along a curve with a specified speed function.