Research On Deformable Methods In Curve And Surface Modeling And Their Applications

Curve and surface modeling is an important topic in Computer Aided Geometric Design and Computer Graphics, whose major components are the representation, design, display and analysis of curves and surfaces using computer. In the past fifty years, traditional curve and surface modeling techniques have been developed deeply. However, with the enhancement of the demands for reality and real-timeliness in graphics display, and with the trends of variety and complexity of geometrical objects, curve and surface modeling faces many new problems and challenges, such as the description of soft objects. So the researchers began to study deformable modeling methods. In this dissertation, energy based deformation methods for curves and surfaces are studied first, and the proposed methods are applied to parametric modeling of human body and shrinkage predication of knitted fabrics. Then a novel physically-based modeling methods is presented for point-sampled surfaces. The main work and contributions are as follows:1. A new deformation method for polylines is first presented based on the intrinsic representation of the polylines. Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.2. Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.3. Deformation methods for point-sampled surfaces are studied in Chapter 5. A new physically-based method, mass-spring based simulation, is proposed for point-sampled surfaces. A tangent plane projection and Delaunay triangulation based simplification algorithm is applied to the original point-sampled surface to produce the simulation points, and then the mass-spring system for the simulation points is also constructed based on the Delaunay triangulation, which overcomes the lack of connectivity information. Deformation of the original point-sampled surface can be obtained from the deformed simulation surface by fitting. Experiments on some typical point-sampled surfaces indicate the feasibility and effectiveness.