Research On Deformation Technology Of Surface Based On FEM

It is well known that shape modeling of any complicated objects is a time-consuming process withrepeated modification and editing. Therefore, flexible and natural deformation technology has beenwidely concerned. Based on FEM, research on deformation technique of surface is investigated in thispaper. The main research contents and achievements are as follows:In order to solve the deformation of skeleton semantic mesh, a deformation algorithm driven byskeleton-rigid frame model is proposed. The skeleton of the mesh extracted with light intersectionmethod is composed of straight line segments. The skeleton-rigid frame model is constructed bydefining each line segment as a beam element. The mapping between mesh vertex and skeleton-rigidframe model is established. By finite element method, the control equations of deformation under loadand geometric constraint are constructed. The deformation of skeleton-rigid frame model is computedby solving the equations. The mesh surface attached to the skeleton is deformed with skeleton. Arotation field is created by shape function of beam element to revise the deformation result. Comparedwith the existing physically based deformation technology, this algorithm is without sub-stepcalculation and improves the convenient usability.For the deformation of the shape of product surface, a mesh deformation algorithm driven bymesh-rigid frame model is proposed. The original mesh is simplified to a coarse base mesh at a certainextent, and the mapping relationship between original mesh and base mesh is established. Themesh-rigid frame model is constructed by defining each vertex of base mesh as a node. By finiteelement method, the control equations of deformation under load and geometric constraint areconstructed. The deformation of skeleton-rigid frame model is computed by solving the equations.According to the mapping relationship, the deformation result of initial mesh is calculated out. Theelastic modulus of elements corresponding to features of mesh is increased to preserve form feature indeformation process. The algorithm is not only suitable for freedom design under load, but alsosuitable for fine design under geometry constraint. Using mesh simplification method to create basemesh, the algorithm can improve the calculation efficiency.With the computational theory of hexahedral element FEM, the method of hexahedral meshgeneration is carried out. A mesh deformation algorithm driven by hexahedral grid model is putforward. The hexahedral grid model of deformable model is constructed by subdividing the boundingbox of surface model. The mapping between mesh vertex and hexahedral grid model is established.Through imposing external loads on the node of hexahedral element, the deformation of hexahedral grid model is computed by deformation acculation method. The mesh deforms with hexahedral gridmodel simultaneously. This algorithm is able to realize the freedom design under load.The appearance of complex products is described by many free-form surfaces. For the shapemodification of surface connected by multi B-spline surfaces, a deformation algorithm based on thedeformation principle of rigid frame under force is presented. A uniform rigid frame model is createdthrough merger of control mesh topology among the surfaces. Smooth connection relationship amongdifferent surfaces and geometric constraint (point constraint, point and normal constraint) areextracted as constraint equations. Shape deformation of multi-surfaces under geometric constraints isachieved by finite element method. The deformed surfaces can not only subject to specified geometricconstraints, but also keep their smooth connectivity relationship.