The Research Of N-sided Surface And The Generation Of Blending Surface Basing On Finite Element Mesh

Surface Modeling is one of important contents of Computer Aided Geometry Design (CAGD) and Computer Graphics (CG), which derive from external form lofting technology, such as automobile, airplane, shipping etc., Surface Modeling research mainly about showing, designing, displaying and analysis with the circumstances of computer graphics system. Nowadays with the development of more than three decades, now Surface Modeling has formed geometric theory system which is constructed with two mediums, i.e. rational B-spline surface parameterized design and hidden algebra surface as main part, interpolation, approximation, fitting as its framework. With the theory of Surface Modeling improving day by day and the demands of industry designing, how to construct N-sided surface become the task with which experts and engineers are concerned more and more, it is the focus all the while that surface designers pay attention to how to construct the N-sided surface which is continuous with its conterminous surfaces and how to make the constructed surface apt to operate in available CAD/CAM system now. In the available ways of Surface Modeling, it is no doubt that Non-Uniform Rational B-Spline (NURBS) is the most extensively popular technology in the mordern Surface Modeling. Outstanding advantages of NURBS: it can express quadratic regular curve and surface exactly, thus it can use united mathematics measure to show regular surface and free surface; it has weight factor that could have an effect on the shape of surface in order to control and operate the shape easier and easier; NURBS is the directly expanding of Non-Rational B-Spline in four-dimention, majority characterastic and corresponding calculation of Non-Rational B-Spline curve and surface also hold good for NURBS curve and surface in order to succeed and develop. Owing to these outstanding advantages of NURBS, International Standard Organization (ISO) issued STEP international standard concerning manufactured goods data exchange in 1991, which let NURBS as the unique mathematics description method that define geometric shape of manufactured goods. Consequently NURBS become the most important foundation in the developing tendency of Surface Modeling technology. The thesis exactly use NURBS to research N-sided surface construction in the Surface Modeling field. In accordance with fixed N-sided which is with n strip B-spline curves as boundary, make N-sided parameter field divide into n individual small four-sided parameter field by way of dividing up. Because of now available CAD/CAM system is based on triangle field and four-sided field, therefore with the way of Gregory construction N-sided surface construct N-sided Coons surface first.The thesis used the experience of the theorem which let Coons type B-spline surface convert into NURBS surface, it also give the method of surface conversion to the structure certification of theorem. Then according to the theorem of surface conversion to give surface conversion way to let Coons type B-spline surface to converse NURBS surface which is apt to operate in available CAD/CAM system, and it clear up singularity of Coons type B-Spline surface on the vertex. To construct N-sided surface in NURBS have the advantages as follows: 1. Define the boundary curve and strided boundary derived vector of N-sided surface can be given in B-spline curve; 2. Strided boundary derived vector of boundary curve can be given individual, while it don't need satisfy any binding conditions like consistency; 3. According to adopting NURBS surface to construct N-sided surfacewhich is G 1 continuous almost everywhere of entirety in order that we can let the method that is on the ground of system of CAD/CAM of NURBS operate. Because the blending surface has extensive use very much in project,and it is the popular topic of research in Surface Modeling, so the thesis is engaged in creating blending surface research to the project Computer Aided Geometric Design (CAGD). It mainly research about the way of forked pipes creating blending surface that column with column intersect and column with cone intersect. In the light of the partition of Finite Element and founding mathematics model to the forked pipes.It has given the calculation of creating Blending Surface and program procedure to construct Blending Surface in the AutoCAD system. The way mainly utilize uniform cubic B-Spline and combine with blending surface which is between column with column and column with cone in the rolling-ball construction forked pipes. The main procedure of utilizing calculation to construct blending surface as follows: 1. Construct the offset surfaces of two base surfaces (original surfaces), the distance between offset surface and base surface is equal to radius of the rolling ball. 2. Compute the intersection of the offset surfaces in order to make sure the center track of rolling ball and point of tangency track of the rolling ball with the original surface. 3. Construct uniform Cubic B-Spline curve between rolling ball and point of tangency of original surface to replace the arc which is swept over by rolling ball. 4. Along the track of center and two points of tangency, utilize uniform Cubic B-Spline interpolation to construct the mesh of blending surface which is between column side with column side and column side...