针对基于点和平面间对偶性的可展曲面设计方法中的不足,提出两种带多局部形状参数的可展曲面设计新方法.首先构造一组含有两个形状参数的三次调配函数,并由此调配函数定义一种带多局部形状参数的B样条曲线族.基于3D射影空间中点和平面间的对偶性原理,利用这种带多形状参数的B样条调配函数生成具有带多参数B样条基的控制平面,并由该控制平面进行包络和脊线可展曲面的设计,同时给出在带多参数B样条基下两种可展曲面的参数表示形式.该方法生成的可展曲面不仅具有灵活的局部形状可调性,而且保留了B样条曲面的许多特性.特别是当形状参数都取1时,所生成的可展曲面即为可展B样条曲面.分析所设计的两种可展曲面的形状与性质,给出具体的应用实例.实例表明所提方法不仅简单有效,而且易于控制可展曲面的形状,是可展曲面设计的有效新途径.%To solve the problems in adjusting and controlling shapes of developable surfaces, two explicit and efficient methods of computer-aided design for developable surfaces with multiple local shape parameters are proposed. A class of novel quasi-B-spline basis functions with two shape parameters is presented to construct B-spline curves with multiple shape parameters, which is an extension of the classical cubic uniform B-spline basis functions. Following the idea of duality between points and planes in 3D projective space, the corresponding developable quasi-B-spline surfaces with multiple shape parameters are represented using control planes with quasi-B-spline basis functions. The developable quasi-B-spline surfaces inherit the outstanding properties of the B-spline surfaces, with good performance in adjusting the local shapes by changing the two shape parameters. In the particular case where shape parameters are both equal to 1, the developable quasi-B-spline surface is a developable B-spline surface. In addition, some properties of the developable quasi-B-spline surfaces and applications in developable surfaces design are discussed. Modeling examples illustrate that the developable quasi-B-spline surfaces provide two valuable ways for the design of developable surfaces.
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