Research On Realizing Of Several Algorithms Of Computer Graphics

The development of newer and more powerful CG (Computer Graphics) devices and expansion of CG applications have significantly enriched the field of Computer Graphics, which now encompasses 2-D and 3-D geometry, visualization, rendering and animation. In this paper, we provide a set of useful CG algorithms which emphasize the real-world applications; our work includes line clipping algorithm, polygon Boolean operation, curved-edge polygon partition algorithm, distance computing algorithm in high-dimensional data space and Principal Component Regression (PCR) analysis algorithm. The followings are the highlights of those algorithms.Layer-based representation of plane polygons, which associates the edges of a polygon with a set of layered triangles, has very broad application in geometric modeling. In this paper, we expand the basic presentation model to cover curved-edge plane polygons (mainly conic edge) and design a full mathematic model for the representation; additionally, we introduce two new construction algorithms. In many cases when layer-based representation is impossible to represent complex curved-edge polygons, we provide several partitioning algorithms to divide the curved-edge into representable sections. Those partitioning algorithms include finding tangent point of conic section, cubic Bezier intersection detection and finding tangent point of different types of cubic Bezier curvesIn addition, we also provide several useful algorithms to calculate the area of curved-edge polygon. To simplify the discussion, in this paper, we assume all the edges of curved-edge polygon are either conic or cubic BezierFurthermore, we introduce the algorithms to calculate distance in high-dimensional data space, which is usually a type of hyper-sphere range query problem. We use linear combination of city block norm to approximate the Euclidean norm distance in the high dimensional data space. Such algorithms can significantly increase the efficiency by reducing complexity. However, the coefficients of the linear combination need to be carefully selected to minimize the error introduced by the approximationFinally, we examine the general applications of Multiple Regression Model in Computer Graphics and provide several new model reduction algorithms. This paper combines Bayesian network to propose a novel approach Bayesian Regression Tree (BRT). This multi-regression model need to choose variable. Based on Principal Component Regression (PCR) analysis and orthogonal rotation transformation to eliminate relevancy and redundancy of original data, BRT use variance contribution rate to choose character attributes and get a mapping of attribute space from high dimension to low dimension.