Research And Application On Constrained Curve Surface Geometric Deformation Based On Metaball

The Metaball based technique is a newly developing important technique in computer aided geometry design and computer graphics field. The study of this thesis concerns the problems of the technique. The shape control factors in Metaball based deformation model are investigated. The flexibility of the model in geometry deformation and implicit surface is extended. We study and compare the attributes of existing field functions, and establish new field functions. The blending methods and tension control method for Metaball influence overlap area are proposed to obtain more smooth surfaces. A Metaball based deformation technique in parameter space is presented to create surfaces and curve with more abundant shapes and natural modality.To overcome the defects in existing curve surface deformation models, multiple skeletons are introduce into the Metaball based deformation model. And, the model is extended in several aspects, such as distance calculate, kernel attribute, influence scope, anisotropy. Established a joint method between potential fields to represent the implicit surface of a complex shape. Then the implicit surface is displayed after polygonization. The joint method is similar to CSG (Constructive Solid Geometry).When a curve surface is deformed by metaball based method, the field function embodies the deformation constraint and plays a crucial role. The primitive shape of the constraint is defined by the field function. So, we studied the forms, characters and signification of several existing field function formulae, as well as the features, the maximal and minimum values, continuity of their differential coefficient. By comparison and analysis of these properties, we ameliorated these field functions, and established several new field functions, such as basic spherical function, general exponent function, ellipsoid and super ellipsoid function. The new field functions proved to be a clever generalization over the old ones. They can adapt to various application background. Consequently, the applicable scope of metaball based curve surface deformation is extended, and the expressive force is enriched. In order to use several kinds of field function simultaneously, a hierarchical control method is advanced by assign the function type, group, and quality attribute to the keys.While implicit surface or surface deformation is represented by multiple metaballs, bulge, crease and tearing frequently appear in overlap area. The former researchers tried to tackle the defect by means of adjusting parameters of metaball, simple superposition and direct union. But the satisfied result with expectant effect and efficiency was not found. On the foundation of single metaball influence, and multiple metaball influence overlap area study, several blending methods are presented for point, line segment and curve segment skeleton respectively. The multiple metaball influence overlap blending methods include linear weight blend, algebraic blend, and exponent average blend. These blending methods are independent of expression of curve surface and the field function formula. The result value is smooth on boundary.Metaball-based constraint deformation technique is used after changing the definition of r, the straight-line distance from a space point to a constraint center in the original calculation of the potential function. By replacing the parameter of the parameterized curve t with the straight-line...