Research On Modeling Method Based On Developable Surface

With the development of digital technology and the improvement of construction standard,nonlinear architecture has become one of the main trends in contemporary architecture.Non-Euclidean geometry has been studied deeply in the field of mathematics and computer graphics at present.,Free-form surfaces can be easily obtained in common architectural modeling software(Rhino,CATIA).However,Free form brings a series of difficult problems in the actual construction process of construction projects,including subdivision of free-form surface,numerical optimization and so on.On the one hand,the designer can optimize complex surface by flat panel in the process of surface optimization.On the other hand,single-curved surface which can be bended by plane plate can replace freeform surface.The object of this paper is this kind of surface which called developable surface.A developable surface is a surface on which Gausian curvature is 0 at any point on the surface.This kind of surface can be expanded into a plane without drawing,shrinking,wrinkling or tearing.Construction efficiency can be improved and cost can be controlled by using the developable surface in architecture design.The developable surface is mainly used in the field of shipbuilding and garment design and works of Frank.Gehry and Santiago.Calatrava.In recent years,more and more computer graphic researches turned to the modeling method of developable surface,which provides method guidance for the application of developable surface in architectural design.The modeling tool of developable surface based on Rhino platform is not complete at present.The purpose of this paper is to design a set of modeling tools of developable surface based on Rhino platform,which is convenient for user to model developable surface better.Research background and significance of developable surfaces in the field of architecture are introduced in the first chapter.The mathematical definition of developable surface and its application in construction projects are introduced in the second chapter.In the third chapter,five digital modeling methods of developable surface on different platforms are summarized.In the fourth chapter,the author introduces the developable surface modeling tools based on three different logic.Each tool is divided into four steps:generating the initial developable surface,developing the plane,cutting the surface and combining the surfaces.The tool is designed to generate the basic type of developable surface and combine to get a more plentiful model.The tool uses parameters as few as possible to control the result,helping the designer to control its shape more freely in the modeling of the developable surface.In the fifth chapter,we summarize the three modeling methods and point out the shortcomings,and make prospects for possible improvements in the future.