Further Research On A Kind Of Particular Curves And Surfaces

The thesis is composed of five chapters.At first, after reviewing the history of the curves and surfaces in CAGD, the author briefly introduces the main content.The second chapter researches a kind of distance-based approximatedpiecewise cubic Hermite spline which is G~1 continuous, that is, we derive a kind of distance-based approximated tangent and use the tangent to construct bound condition of piecewise cubic Hermite spline. We add a tension parameter in every piece of the curve to control the curve; study the relationship between tangent vector and self-intersection; we present approximation condition that curve approximates control polygon. At last some examples are given to compare Cardinal with Distance-based approximated Hermite interpolation.The third chapter mainly introduces the properties of Bézier curve and by transforming the parametric representations of derivative vector curve(of Bézier curve) to their implicit representations, a simple and practical sufficient condition for determining the regularity of Bézier curve is presented. At last, we introduce generalized Bézier curve.In the fourth chapter, the Bézier surface is presented, we also do a further research on a kind of particular surface which is based on Bézier blending function.Finally, in the fifth chapter, we make a summary and give expections.