Study And Realize On Surface Subdivision Based On Loop Scheme

The computer graphics has played important roles in many fields since it appeared. Drawing three dimensions image is one of the important parts of computer graphics. It generates the realistic images which likes the colorful photos in computer graphic equipment. It utilizes the knowledge on math, physics, computer science and other sciences to draw the image. With the development of the theories of computer graphics, great accomplishments have been achieved in this field. We have made considerable progress in the technology of surface modeling, illumination modeling, visibility, and texture mapping, etc. And now we are able to generate better and more realistic images. Surface modeling is one of the most active and important subject in computer graphics. It studies on the representing, designing, showing and analyzing of surface in a computer imaging system. The geometry representing on three dimensions object has been applied widely. The surface modeling is needed from the industrial model design of home electric appliances and light industrial products to three dimension model and design of cloth. There are several techniques for surface modeling, such as parameter surface modeling, implicit surface modeling, subdivision surface modeling, deformable surface modeling and surface modeling based on sharp hybrid.Form the early days of three dimensions graphics, the geometry model based on the polygonal meshes has been used. The traditional three surface modeling uses the polynomial function as describing tools. But it is difficult to describe the complex and real subjects. The polygonal mesh is a set which is composed of points on polyhedron and polygons. It is suitable to model any geometry subject for its simple connection and flexibility. The polygonal meshes are the basic unit for computer drawing. If a geometry model represented by a polynomial function will be showed in a computer screen, it needs to be sampled and dispersed as polygonal meshes. The transformation will not be performed if the geometry model is presented by polygonal meshes. The polygonal meshes has been developed and become a standard three dimension modeling tools for its efficiency.In the process of drawing the graph, the effect of image is influenced for the incompact polygonal meshes. A subdivision surface modeling method is presented and developed. The subdivision process is operated on initial polygonal meshes. The new subdivision meshes is obtained by inserting new points and connecting with the existed meshes. The position of the new points is calculated from the existed meshes. After subdivision, a compact polygonal mesh is obtained and the quality of drawing image is improved. The method of subdivision is a discrete modeling. It provides an algorithm instead of a expression to describe the procedure of generating new points. The subdivision method processes the polygonal meshes and it is not limited to the control meshes. So, it is applied widely in the fields of computer graphics and has become a hot topic in the theory and application field in the world. With the development of subdivision surface modeling, some modes appeared, such as Catmull-Clark scheme, Loop scheme, and 3 scheme et, al. The Loop scheme, presented by Loop in his master dissertation in 1987, is a subdivision method based on triangle meshes. It is studied in this paper in detail. In Loop scheme, it needs to calculate the new coordinates of a point, the new edge and the new face that the new point belongs to after subdivision. A edge is divided into two edges and a new point after subdivision. Calculate the beginning point and ending point of the new edge and the face that the new edge belongs to. Calculate the new coordinates of points after subdivide edge and calculate the edge and face that the new point belongs to. A face is divided into four faces. Three edges are produced. Calculate the points of new faces and the beginning point and ending point of the new edge. Calculate the face that the new edge belongs to.This paper studies the process of drawing image based on points. That is, store the polygonal meshes which represent the polygonal splitting of the subject surface. This is the step of real subject modeling. Secondly, transmit the three dimension information of a viewer form world coordinate to viewer coordinate. Generate the two dimension perspective graph by perspective projecting and window viewer transmitting. The implementation is as follows: calculate the pixel coordinates in screen for the points in point-table. Transform the world coordinate of points to the viewer coordinate. Calculate the position on screen through perspective projecting and window viewer transmitting. Further more, the drawing algorithm based on polygon meshes is given. In the process of drawing a graph, the effect is influenced for the un-compacted mesh. So, it needs to subdivide the polygon mesh to improve the effect of drawing image. The subdivision method is studied in this paper. The advantages of Loop scheme based on triangle mesh are discussed and the surface modeling based on Loop scheme is realized. The implement processing is as follows: Firstly, read the original mesh data from file. And then subdivide the surface by Loop scheme to get the mesh data of different consistency. Finally, give the numbers of points, edges and face and show the effect graph that obtained before and after subdivision. There are some shortages and defects in this paper. We only draw the points that can be seen from the viewer and the scene is simple. In order to improve the quality of the drawing graph some factors should be considered such as illumination, disappearing and texture mapping. Some works should be done in the future.