|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|158782||2017||11 صفحه PDF||سفارش دهید||8463 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Advances in Engineering Software, Volume 114, December 2017, Pages 235-245
In this paper, two explicit methods are presented for the computer-aided design of developable Î»-BÃ©zier surfaces associated with shape parameter. Based on the duality between points and planes in 3D projective space, a developable Î»-BÃ©zier surface associated with a shape parameter is designed by using a set of control planes with Î»-BÃ©zier basis functions. The shape of developable Î»-BÃ©zier surface can be easily adjusted by modifying the value of the shape parameter. When the shape parameter takes on different values, a family of developable Î»-BÃ©zier surfaces can be constructed, which keeps most of beneficial properties of traditional BÃ©zier surfaces. In order to tackle the problem that an engineering complex developable surface is usually hard to be constructed by using a single developable surface, we also derive the necessary and sufficient conditions for G1 continuity, Farin-Boehm G2 continuity and G2 Beta continuity between two adjacent developable Î»-BÃ©zier surfaces. Finally, the properties and applications of developable Î»-BÃ©zier surfaces are discussed. The modeling examples show that the proposed method is effective and easy to implement, which greatly improve the problem-solving abilities in engineering appearance design by adjusting the position and shape of developable surfaces.