【摘要】 离散细分法是构造曲线曲面的一类重要方法,而在实际应用中要求某些细分法是保形的,即初始控制点是凸的,那么要求细分最终生成的曲线或曲面也要求是凸的.用构造法构造了一类在等距离意义下矩形域上生成线性保凸曲面的细分法,该细分法具有插值性、局部性、线性不变性,齐次性和仿射不变性,并用数学归纳法证明了该类细分法的线性保凸性、收敛性和光滑性.更多还原

【Abstract】 A class of convexity-preserving subdivision scheme is proposed and its convergence and smooth properties are proved by mathematical induction. The subdivision scheme is interpolatory, local, invariability and affine invariant. If these original data satisfy convexity property, the final curves and surfaces obtained by the subdivision scheme also maintain the convexity property. The subdivision scheme is useful because only original convexity data can be obtained and the final curves/surfaces are required to be convex in some industrial application.更多还原