Discussion on Minimal Curvature Variation in Cubic Hermite Curve Construction

In the fields of computer aided geometric design, computer graphics and so on, curvature variation minimization has been widely used for constructing curve and surface. This paper investigates the minimal curvature variation in constructing the cubic Hermite curve that interpolates the given positions and unit tangent vectors at two points, while the magnitudes of the tangent vectors are unknown. The computation of this problem is very hard to handle and a very time-consuming task. To reduce the computing cost, simpler models are used to approximate it, but the existing simpler models can't give a good approximation, and hence make the curves constructed have unsatisfactory shapes. So a new model is presented in this paper. In the new model, the magnitude of each tangent vector is expressed as polynomial function of the tangent vector angles, which is easy to compute, and the shapes of constructed curves are visually similar to the ones constructed by minimizing the accurate curvature variation.