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 Bezier control net of the spline surface.
Speleers, H. (2010). A normalized basis for reduced Clough-Tocher splines. COMPUTER AIDED GEOMETRIC DESIGN, 27(9), 700-712 [10.1016/j.cagd.2010.09.003].
A normalized basis for reduced Clough-Tocher splines
Speleers H.
2010-12-01
Abstract
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 Bezier control net of the spline surface.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
