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中文摘要：
为了使得插值曲线保单调，设计了两类新的平面参数曲线及其保单调插值算法．计算奇异混合函数，把三角／双曲多项式B样条曲线与奇异多边形通过奇异混合函数混合，无需解方程组或繁琐的迭代，得到自动插值给定平面点列且C^2（或G^1）连续的带形状参数的复合曲线，尤其能得到摆线、螺旋线、双曲线、悬链线等各类超越曲线．通过把插值曲线的导矢分量转化为类Bernstein多项式，并且利用Bernstein多项式非负的充要条件，得到插值曲线单调的充要条件，获得形状参数合适的取值范围．该方法简单方便，所得参数范围保证丁插值曲线保单调．
英文摘要：
Monotonicity-preserving interpolation algorithms for two new kinds of plane parameter curves were investigated. Dispensing with solving any system of equations or using any iterative computation, a C^2 （or G^1） continuous spline curve, such as cycloid or catenary, was generated automatically by blending the parametrized singular polyline and the trigonometric/hyperbolic polynomial B spline curve. By converting every component of the first derivative of the interpolating curve into Bernstein polynomial, the non-negativity conditions of Bernstein polynomial could be used to get the necessary and sufficient conditions for the monotonicity of interpolation curves and the range of the shape parameter. The shape parameter obtained makes the blending curve monotonicity-preserving.
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