Shape Preserving Spline Curves and Surfaces

Curves and surfaces design is an important research topic of CAGD (Computer Aided Geometric Design) and CG (Computer Graphics). The basic ingredient of CAGD and CG is the construction and manipulation of curves and surfaces. A common requirement is data fitting whether exact (interpolation) or approximate and a common solution is spline function. In CAGD/CAD systems in order to control the shape of the the curve it is very important to choose the appropriate basis functions. Based on their good properties the classical Bernstein basis functions play a significant role in CAGD/CAD systems. As a unified mathematical model with many desirable properties polynomial B-splines are popularly used on the grounds of flexibility and efficiency in modelling free form curves and surfaces. In this bookwe have studied the approximation properties of different types of splines with shape parameter.