Abstract
The parametric cubic segment is the most commonly used curve segment in computer-aided design. Most CAD systems have what is called a spline routine to automate the definition of curves built up from several parametric cubic segments. A spline routine simplifies the work of curve fitting, since it relieves the designer from manually determining tangents at joints, ie common points between adjacent curve segments. However, spline routines severely limit the number of shapes it is possible to create by the parametric cubic spline. Here, a detailed derivation and description is given of a matrix formulated algorithm for cubic curve fitting with well and easily controlled conditions at curve segment joints. The algorithm is equally suited to modify the shape of curves manually and by computer routines, eg routines for numerical optimization of shape. This is illustrated in several examples. The algorithm derived is also well suited to interactively smooth data in curve design.
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