The Research On Deformation Basing On The Surface Mesh

With the enhancement increasingly requirement of computer graphical displayabout the authenticity, real-time character and interaction, with this trend ofgeometry designing being close with variety , particularity and topological structurecomplexity is obvious day by day, with the pace of graph industry and manufacturemarching toward integrated and networked mode become more rapid, theresearch field of surface modeling technology has been extended from traditionalexpressing surface , surface intersection and putting surface together to shapeblending , reconstruction , simplification , conversion , offset for surface . Thecontent of this paper is Free-Form Deformation algorithm based on surface mesh.Today in the industrial designing and analysing, the technology using the finiteelement method to imitate huge and complicated industrial design has been alreadyripe. And it is an important link of building the finite element model that the 3Dsolid model is divided automatically into the finite element mesh. The forms of themesh gained will influence directly the precision and scale of calculating. But whenwe analyze and calculate the finite element mesh of the 3D solid model, the solidmodels designed generally are not satisfied with the actual demand. At that time wemust carry out some deformations on the finite element mesh in detail. Thetraditional method is that we give the suggestions for revision to CAD designers, thedesigners revise the 3D model, and then carry on mesh dividing and the finiteelement calculation again. If it can't meet the demands yet, we need repeatabove-mentioned course, it is very tedious obviously. Then we can think of naturallythat if we can revise the 3D mesh until meeting the demands, and then return the 3Dmesh revised to CAD designers. Designers will perfect the 3D model according toamended information. Through this way only one time we can succeed. This is theproject background of the Free-Form Deformation algorithm based on surface meshin this paper. Namely the question is that when a mesh point on the surface mesh ismoved, how do other mesh points change? The Free-From Deformation (FFD ) algorithm was raised by Sederberg andParry of Brigham Young University. It is a new method of Free-FromDeformation. The basic thought of this algorithm is that first of all we needconstruct a cuboid control frame formed by 3D control points, and then embed theobject researched into the cuboid, and moving these control points make the cuboiddesform, and then the object is deformed too. But the control frame in FFD only canbe cuboid, but the shape of the object is complex and varied, this limit theapplication of FFD greatly. The Dirichlet Free-Form Deformation (DFFD ) algorithm is based on FFDalgorithm, presented by Moccozet. Though this algorithm has still kept the set ofcontrol points that surround the object researched, this set is greatly differentfrom that in FFD algorithm. The difference is that they have not any topologicalrelation between them, and they only are a set of 3D points including object totally.DFFD has not only abandoned the topological structure among the control pointsbut also used Sibson local coordinate system. Sibson neighbours of a point are thesepoints that adjoint the point and they gained by Delaunay trianglation . Sibson localcoordinate of the point is the result that Sibson neighbours of the point influence thepoint. The key thought of DFFD algorithm is that seeking Sibson neighbour of thepoint that need deformed on the set of control points of the object researched, andmoving one or several Sibson neighbours. Because of being influenced by its Sibsonneighbours, we can get the movement situation of this point. The expression is:?X = ut?Pt . (where, ut are Sibson neighbours of X point, ?Pt is movement ∑distance of ut , ?X is movement distance of X point) Though DFFD algorithm is more intuitionistic and flexible, it has shortage inoperation. That is that it make control frame deform through moving control points,thereby make the object deformed. This is a kind of indirect deformation method.So it is very difficult to control the shape of the object accurately. We want to cancontrol deformation accurately by moving points of surface directly for actual need. For the above reasons, I improve DFFD algorithm in this paper, and present anew deformation algorithm---Direct DFFD algorithm. This algorithm can be moresuitable to practical application. Suppose that X is a mesh point on the mesh ofsurface. We investigate mesh of the whole surface after X is changed. At first wemark all the mesh point besides X as control point. In order to make the controlpoint set totally surround the mesh of whole surface, we need add a cuboid outsideall the control points ( 8 assistant points). Then according to mapping method wecan get Delaunay triangulation of 3D mesh points, and thereby gain Sibsonneighbours of X point, and then get Sibson neighbours of each Sibson neighbours ofX point. Because Sibson neighbour is symmetrical, Sibson neighbours of eachSibson neighbour of X must include X point. At last we calculate corresponding...