| It is crucial for manufacturers to make a decision quickly from many concept sketches in the early stage of automotive styling,which has substantial effects on the downstream engineering,the time-to-market,the competitiveness of product and the investment. Therefore,the developing model should be finalized as early as possible.The number of 3-D models developed from sketches is,however,limited because of the cost and time involved in the 3-D modelling process,and the 2-D sketches give little real 3-D information at early stages,limit the variety at late stages and opportunity for management intervention.In the past decades,people paid more attention to 3-D modelling quickly from 2-D sketches.Many measures have been tried to reconstruct 3-D models by applying the existing CAD systems. Some researchers focused on the issues of "2-D to 3-D" and "Shape from X"(X stands for the different sources of 2-D).The regular geometries,such as cube,cylinder and sphere, have been now successfully reconstructed into 3-D models.However,the free-form surface reconstruction is still difficult especially from the automotive sketches-the non-realistic images.The automotive styling software from 2-D to 3-D mentioned in this paper,which is designed to transform reversely the 2-D automotive sketches quickly into 3-D surface models,can solve the problem above.It involves 2-D multi-stroke identification function, 2-D automotive sketches to 3-D surface models transforming function,3-D parametric modelling function,etc.With the multi-functional combination and mature 2-D to 3-D transforming technology,nowadays,this software can be advanced in domestic market.As the research approach develops,2-D to 3-D transforming technology is gradually becoming mature day by day.Although there are plenty of research on transformation technology from 2-D sketch to 3-D surface model directly in foreign countries,people in our country rarely fulfil any achievement in this field,even nobody knows this new technology. Therefore,the developing process of this 2-D to 3-D software is actually an exploration in the darkness by oneself,which needs to solve new problems constantly.Nowadays,a part of functions in this software is still incomplete and some function modules require to be improved,also interface of this software needs to be expanded and beautified.Nevertheless, the most obvious flaw of this software is:When we execute 3-D parametric modelling module and construct complex model using this module in the form of Coons surface, surface blending effect is not quite perfect,which results in discontinuousness of model appearance and has bad effect on styling.This is a troublesome problem,so this paper is mainly about how to blend two parametric surfaces smoothlyIn this 2-D to 3-D software,parametric surface is expressed in the form of Coons surface.Recently,there are a variety of Coons surface applied in the Engineering field,such as bilinear blend Coons surface,partial bi-cubic blend Coons surface,bi-cubic blend Coons surface,C-Coons surface,Gordon surface and so on.Especially,we use Gordon surface to construct parametric surface model in the software,but taking fitting algorithms into consideration,we finally choose bi-cubic blend Coons surface as the blend surface of two existed surface,due to its mature and steady technology.In this 2-D to 3-D transforming software,parametric model is demonstrated in the form of Coons surface.This type of surface has such features below:we can take the specific boundary conditions as the basis,which includes four boundaries,four cross-boundary derivatives,cross-boundary curvatures,etc.Then we interpolate the limited data information of boundaries,and there are infinite points on the boundaries.According to the conditions offered above,we can use blending function to form the surface.Thus,when constructing complex compound surfaces,we can make use of any kinds of parametric curves,which are taken as four boundaries,so as not only to expand application range of the surface,but also simplify the constructing method of the surface.Before blending parametric surface in this software,we have to make some process on the surface in parametric modules.That is because when the parametric models are shown in the form of Coons surface,we take aesthetics into consideration and beautify the joint of four boundaries on parametric surface.In order to enhance the parametric modelling effect, we create round corn at the joint,which is also helpful to form some specific styling surface. All the surfaces of parametric modules are with round corns,but when we blend surface, they bring us into trouble.That is because curvature of boundary change a lot at the round corn,and it is difficult to fit two surface boundaries.So before we blend the parametric surface,in order to get ready for fitting boundaries,we should return the joint part to its original pattern.Most researches on Coons surface blending algorithms was carried out in the field of Computational Mathematics.Except for complex formula deduction and repeated interpolations and approximations,there is little value of reference in engineering application. So it is essential for us to introduce a simple and flexible Coons surface blending method according to its own features.Based on Coons surface features in parametric modules, following measures are taken to blend surface:First,we should fit four side boundaries of surface which is ready for blending,and change them into two side boundaries of blended surface.This work includes returning the round corn,where adjacent boundaries of blend surface meet other boundaries,to its original pattern,setting data points,and fitting boundaries.Second,referring to the constructing method of parametric surface,we choose two adjacent boundaries,two fitted side boundaries,as four boundaries of Coons surface, and construct surface in the same time.At last,making reference to the parametric approaches adopted in these models,we can easily parameterize the blending surface and unify the parametric surface with other surface which is waiting for blending.With the methods mentioned above,we can conveniently and rapidly blend parametric surface in this 2-D to 3-D software,and make the blended surface parameterized in the way which other parametric modules present.That is to say we can change some specific parameters to fulfil geometric shape adjustment function.Realization of blending parametric surface speeds the commercialization of this 2-D to 3-D software,and at the same time builds a bridge between 2-D sketch design and 3-D modelling.Besides,lots of algorithms in this software are of guidance meanings and referring values for the further research in this field. |
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