| Popis: |
This chapter focuses on parametric cubic spline curves. Theoretical analysis and applications have shown that, in the case of small deflection, the curve represented by the interpolatory cubic spline function is satisfactory in the sense that the curve is very close to the one that is drawn by using a wooden spline. Two drawbacks of spline functions used in computational geometry that have been shown by an example discussed in the chapter are: (1) in the case of large deflection, the interpolatory cubic spline may lose fairness, and (2) the interpolatory curve represented by the cubic spline function is dependent on the choice of coordinate systems in which the data points and the end conditions are evaluated. In other words, the interpolatory curve is not geometrically invariant. Affine invariants and geometric properties of plane parametric cubic curves are discussed in the chapter. Also, several kinds of spline curves formed by segments of parametric cubic curves are reviewed. |
