OpenGLChapter3.ppt

CIE OF NWSUAF Polygon Fill Areas (9) ---Polygon Tables Edge table can be expanded to include forward pointers into the surface-facet table so that a common edge between polygons could be identified more quickly(fig3-51) Similarly vertex table can be expanded to include forward pointers into Edge table The more information included in the data tables, the easier it is to check for errors. Therefore, error checking is easier when three data tables (vertex, edge, and surface facet) are used. Some of the tests that could be performed by a graphics package are:(1) that every vertex is listed as an endpoint for at least two edges, (2) that every edge is part of at least one polygon,(3) that every polygon is closed, (4) that each polygon has at least one shared edge, (5) that if the edge table contains pointers to polygons, every edge referenced by a polygon pointer has a reciprocal(相应的) pointer back to the polygon. CIE OF NWSUAF Plane properties (1) General equation of a plane we can select three successive convex-polygon vertices, (xl, yl, zl),(x2, y2, z2), and (x3, y3, z3), in a counterclockwise order and solve the following linear plane equations for the ratios A/D, B/D, and C/D: (A/D)xk + (B/D)yk + (C/D)zk = -1, k = 1, 2, 3 (3-60) Use Cramer’s rule to compute polygon facets parameter CIE OF NWSUAF Plane properties (2) Front and back polygon faces Back face, side of polygon faces into the object interior Front face, the visible or outward side Identify a point behind or in front of a polygon surface Put the point into the plane equation if Ax + By + Cz +D 0, the point (x,y,z) is behind the plane if Ax + By + Cz +D 0, the point (x,y,z) is in front of the plane Orientation of a polygon surface in space, described bynormal vector:from inside to outside(fig3-53) N(A,B,C)orN=(V2-V1) ×(V3-V1) CIE OF NWSUAF homework 3.17：分别描述奇偶测试和非零环绕规则测试，并比较。 3.18：如何判断一个顶点在一个面的前面还是后面 3.22 建立一个如图3-50所示的单位立方体的几何数据表。 CIE OF NWSUAF Overview 3-1 Coordinate reference frames 3-2~