Cubic Trigonometric Polynomial B-spline Curves and Surfaces with Shape Parameter

摘要

A cubic trigonometric polynomial B-spline curve with a shape parameter analogous to cubic B-spline curve, is presented in this work. Each polynomial B-spline curve segment is generated by four consecutive control points; we can design different curves by adjusting shape parameter value. With the increasing of shape parameter A value, the curve comes near the control polygon; for equidistant knots and A = 1, the curve is C3 continuous. The ellipses and circles can be represented exactly using cubic trigonometric polynomial B-spline curve. Finally, we study B-spline surfaces with a shape parameter in this work.