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中文摘要：
FB-样条曲线是C-B样条曲线和H-B样条曲线的统一和推广。文章利用包络理论和拓扑映射的方法,讨论了FB-样条曲线的奇拐点和曲线性质,并给出了依据控制多边形判断FB-样条曲线出现1个或2个拐点、1个尖点、1个二重点以及处处为凸的充分必要条件;最后给出了FB-样条曲线的奇点、拐点以及二重点在λ-μ平面上的分布图。
英文摘要：
FB-spline curves are the unification and extension of C-B spline curves and H-B spline curves. This paper discusses singularities, inflection points and convexity of FB-spline curves in terms of their control polygons, and gives the necessary and sufficient conditions for testing when FB-spline curves have one or two inflection points, or a cusp, or a loop, or none of the above points by the envelope theory and the topological mapping method. At last, all kinds of distribution of singularities, inflection points, loops and cusps on FB-spline curves on the λ-μ plane are illustrated.
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