A normalized basis for reduced Clough–Tocher splines

We present the construction of a suitable normalized B-spline representation for reduced cubic Clough–Tocher splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. Geometrically, the problem can be interpreted as the determination of a set of triangles that must contain a specific set of points. This leads to a natural definition of tangent control triangles. We also consider a stable computation of the Bézier control net of the spline surface.

Research highlights► Clough–Tocher splines. ► Normalized B-splines. ► Control triangles. ► Bezier control net.