图形学简单总结.docx

DAA算法：（直线）条件是：1、端点坐标：P0（x0，y0）P1(x1,y1)2、斜率：m=y/x,x=x1-x0y=y1-y03、直线方程：y=mx+B,0m1 交换x和y的位置2、m0 步长dx或dy取-1不足：取证操作和浮点运算仍十分耗时Bresenham画线算法：（圆和曲线）基本原理：从给定线段的左端点开始，逐步处理每个后继列，并在其扫描线y值最接近线段的像素上绘出一点。算法分析：在取样位置xk+1,使用dlower,dupper来表示两个像素与数学路径上的垂直偏移。y=m(xk+1)+b, dlower=y-yk=m(xk+1)+b-yk,dupper=(yk+1)-y=yk+1-m(xk+1)-b决策函数：pk=x(dlower-dupper)=2yxk-2xyk+c,pk+1-pk=2y(xk+1-xk)-2x(yk+1-yk)pk+1=pk+2y-2x(yk+1-yk)yk+1-yk=0或1p0=2y-x|m|1时的算法流程：1、输入线段的两个端点，将左端点存储在(x0,y0)中2、将(x0,y0)装入帧缓存,画出第一个点3、计算常量x、y、2y、2y-2x，并得到决策函数的第一个值4、从k=0开始，在沿线路径的每个 xk 处，进行决策函数检测5、重复步骤4，共x 1 次中点画圆：算法分析：采用圆函数决策函数：fcirc(x,y)=x2+y2-r2pk=fcirc(xk+1,yk-12),两个候选像素的中点，pk0时取yk，反之取yk-1pk+1=pk+2(xk+1)+(yk+12-yk2)-(yk+1-yk)+1,yk+1是yk(pk=yBezier曲线：N次Bezier曲线：Rt=i=0nRiBi,nt，0t1Bernstein基函数Bi,n(t)为：Bi,n（t）=Cni(1-t)n-iti，Cni=n!i!n-i!曲线性质：1、端点插值：R0=R0 , R1=Rn2、端点切向：R0=n(R1-R0), R1=n(Rn-Rn-1)3、对称性：iRn-iBi,nt=iRiBi,nt, 曲线的控制顶点的几何地位是对称的4、凸包性：Bezier曲线位于控制多边形的凸包内5、几何不变性：Bezier曲线的形状仅与控制多边形有关，与坐标系无关不足：1、整体性质：当移动曲线的一个控制定点时，整条曲线的形状都会发生改变2、表示复杂形状时，需要将更多条Bezier曲线光滑的拼接起来Cohen-Sutherland算法：通过初试测试来减少求交计算，从而提高效率特点：对显然不可见的线段快速判别，可直接推广到三维区域编码：用窗口四边所在的直线将整个平面分成9个区域，每个区域赋于一个四位的编码CtCbCrClCt=10 当yymaxelse ，Cb=10 当yxmaxelse，Cl=10 当xMaxDepth) *color=Black;else if(RayHit(start,direction,&hitPoint,&hitObject)=Nothing)*color=BackGround;else Shade(hitObject,hitPoint,&localColor); CalculateReflection(hitObject,hitPoint,direction,&rDirection);CalculateTransmmission(hitObject,hitPoint,direction,&tDirection);TraceRay(hitPoint,rDirection,depth+1,&rColor);TraceRay(hitPoint,tDirection,depth+1,&tColor); CombineColor(localColor,rColor,hitObject.ks,tColor, hitObject.kt,color);Photon Mapping:1、Photon tracinga)Emissionb)Scatteringc)Storing: only on diffuse surface2、Renderinga)Direct lightingb)Specular reflectionc)Causticsd)Indirect lightingZ-Buffering:Z buffering works by holding a depth value for each pixel in the image. Before rendering, the depth value for each pixel is set to the maximum value possible (very deep into the screen). The image is then rendered, polygon by polygon, and instead of just setting a pixel to a certain colour, we perform the following:Is the z screen value(depth) for this point on the polygon smaller(nearer to the viewer)than the depth value in the z buffer for this pixel?Yes:This point is nearer to the viewer than any points that have been written to this pixel previously. Calculate the shade of the pixel and write it to the screen. Write the depth of this point into the z buffer for this pixel.No:Another point has been written to this pixel which is nearer to the viewer.Do not write the pixel. Do not write into the z buffer.Advantages:1、It is easy to implement, and can easily be implemented in hardware. 2、Z buffering can be easily combined with many forms of rendering, polygon, CSG, parametric - the only constraint on the rendering method is the need to calculate the depth of points on an object.3、 Z buffer data can also be retained after rendering, allowing separate 3D images to be easily combined into one.Disadvantages：1、The Z buffer requires a large amount of memory, often more than the display. 2、Pixels are often shaded many times, implying