图形学期末实验报告

图形学期末实验报告161210318苏幸点第一题1、实验代码//改进的中点bresenham算法#include<gl/glut.h>#include<math.h>#include<stdio.h>voidInitial(void){ glClearColor(1.0f,1.0f,1.0f,1.0f);//设置窗口背景颜色为白色 glMatrixMode(GL_PROJECTION);//设置投影参数 gluOrtho2D(-1000.0,1000.0,-1000.0,1000.0);//调整一个窗口中含有的像素点的数量}voidLineMidPointBre(GLintx0,GLinty0,GLintx1,GLinty1){ GLintdx,dy,d,UpIncre,DownIncre,x,y; if(x0>x1) { x=x1;x1=x0;x0=x; y=y0;y1=y0;y0=y; } x=x0; y=y0; dx=x1-x0; dy=y1-y0; if(dy>0&&dy<=dx)//0<k<=1中点Bresenham算法的代码 { d=dx-2*dy; UpIncre=2*dx-2*dy; DownIncre=-2*dy; while(x<=x1) { glPointSize(3); glBegin(GL_POINTS); glVertex2i(x,y); glEnd(); x++; if(d<0) { y++; d+=UpIncre; } elsed+=DownIncre; } } elseif((dy>(-dx))&&dy<0)//斜率-1<=k<=0的中点Bresenham算法 { d=dx-2*dy; UpIncre=-2*dy; DownIncre=-2*dx-2*dy; while(x<=x1) { glPointSize(3); glBegin(GL_POINTS); glVertex2i(x,y); glEnd(); x++; if(d>0) { y--; d+=DownIncre; } elsed+=UpIncre; } } elseif(dy<(-dx))//斜率k<-1中点Bresenham算法 { d=-dy-2*dx; UpIncre=2*dx+2*dy; DownIncre=2*dx; while(y>=y1) { glPointSize(3); glBegin(GL_POINTS); glVertex2i(x,y); glEnd(); y--; if(d<0) { x++; d-=UpIncre; } elsed-=DownIncre; } } else//斜率k>1和k不存在时的的中点Bresenham算法 { d=dy-2*dx; UpIncre=2*dy-2*dx; DownIncre=-2*dx; while(y<=y1) { glPointSize(3); glBegin(GL_POINTS); glVertex2i(x,y); glEnd(); y++; if(d<0) { x++; d+=UpIncre; } elsed+=DownIncre; } }}voidDisplay(void){ glClear(GL_COLOR_BUFFER_BIT);//用当前背景色填充窗口 glColor3f(1.0f,0.0f,0.0f);//设置当前的绘图颜色为红色 LineMidPointBre(0,0,1000,1000);//调用中点Bresenham算法实现直线的扫描转换 glFlush();//处理所有的OpenGL程序}intmain(intargc,char*argv[])//目标是绘制出一条直线{ glutInit(&argc,argv); glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);//初始化窗口的显示模式 glutInitWindowSize(3600,3600);//设置窗口的尺寸 glutInitWindowPosition(270,270);//设置窗口的位置 glutCreateWindow("中点Bresenham算法绘制任意斜率直线");//设置标题 glutDisplayFunc(Display);//设置当前窗口的显示回调函数 Initial();//完成窗口初始化 glutMainLoop();//启动主GLUT事件处理循环 return0;}2、实验环境Windows10下的vs，按照网上的方法加入了opengl所需求的头文件，编程语言为c语言3、实验结果截图4、算法分析 Bresenham直线算法描绘的直线。假设我们需要由(x0,y0)这一点，绘画一直线至右下角的另一点(x1,y1)，x,y分别代表其水平及垂直坐标，并且x1-x0>y1-y0。在此我们使用电脑系统常用的坐标系，即x坐标值沿x轴向右增长，y坐标值沿y轴向下增长。因此x及y之值分别向右及向下增加，而两点之水平距离为x1−x0且垂直距离为y1-y0。由此得之，该线的斜率必定介乎于1至0之间。而此算法之目的，就是找出在x0与x1之间，第x行相对应的第y列，从而得出一像素点，使得该像素点的位置最接近原本的线。改进之后的算法加入了对斜率变化的应对第二题实验代码#include<graphics.h>#include<stdio.h>#include<conio.h>voidBresenhemCircle(intcenterx,intcentery,intradius,intcolor,inttype);voidcirclepoint(intx,inty,intcolor,intr){ putpixel(x+r,y+r,color);putpixel(y+r,x+r,color); putpixel(-x+r,y+r,color);putpixel(-y+r,x+r,color); putpixel(-x+r,-y+r,color);putpixel(-y+r,-x+r,color); putpixel(y+r,-x+r,color);putpixel(x,-y+r,color);}voidmidbrecir(intr,intcolor){ intx,y,d; x=0,y=r,d=1-r; while(x<=y) { circlepoint(x,y,color); if(d<0)d+=2*x+3; else { d+=2*(x-y)+5; y--; } x++; }}voidmain(){ intdrive=DETECT,mode; inti,j; i=0; initgraph(640,640); midbrecir(200,RED); scanf("%d",i);}2、实验环境 Windows10下的vc，按照网上的方法加入了opengl所需求的头文件，加入了graphics.h，编程语言为c语言3、实验结果图示4、算法说明由于圆具有对称性，所以我们只要考虑1/8个圆即可，我们选择y轴正方向到延其顺时针旋转45°的这个区间为例。我们先假设要画的圆的圆心在坐标原点，最后再平移到其应该存在的位置。设要画的圆的圆心在原点(0，0)，半径为R，起点在(0，R)处，终点在(，)处，顺时针生成八分之一圆，利用对称性画出全部的圆。第三题实验代码#include<GL/glut.h>#include<math.h>#include<stdlib.h>classPt3D{ public: GLfloatx,y,z;};voidGetCnk(GLintn,GLint*c){ GLinti,k; for(k=0;k<=n;k++){ c[k]=1; for(i=n;i>=k+1;i--)c[k]=c[k]*i; for(i=n-k;i>=2;i--)c[k]=c[k]/i; }}voidGetPointPr(GLint*c,GLfloatt,Pt3D*Pt,intControlN,Pt3D*ControlP){ GLintk,n=ControlN-1; GLfloatBernstein; Pt->x=0.0;Pt->y=0.0;Pt->z=0.0; for(k=0;k<ControlN;k++){ Bernstein=c[k]*pow(t,k)*pow(1-t,n-k); Pt->x+=ControlP[k].x*Bernstein; Pt->y+=ControlP[k].y*Bernstein; Pt->z+=ControlP[k].z*Bernstein; }}voidBezierCurve(GLintm,GLintControlN,Pt3D*ControlP){ GLint*C,i; Pt3DCurvePt; C=newGLint[ControlN]; GetCnk(ControlN-1,C); glBegin(GL_POINTS); for(i=0;i<=m;i++){ GetPointPr(C,(GLfloat)i/(GLfloat)m,&CurvePt,ControlN,ControlP); glVertex2f(CurvePt.x,CurvePt.y); } glEnd(); delete[]C;}voidinitial(void){ glClearColor(1.0,1.0,1.0,0.0);}voidDisplay(void){ glClear(GL_COLOR_BUFFER_BIT); GLintControlN=4,m=500; Pt3DControlP[4]={{-80.0,-20.0,0.0},{-70.0,-50.0,0.0},{-50.0,-50.0,0.0},{0.0,0.0,0.0}}; Pt3DControlP1[4]={{0.0,0.0,0.0},{50.0,50.0,0.0},{70.0,50.0,0.0},{80.0,20.0,0.0}}; glPointSize(2); glColor3f(0.0,0.0,0.0); BezierCurve(m,ControlN,ControlP); glColor3f(1.0,0.0,0.0); BezierCurve(m,ControlN,ControlP1); glColor3f(0.0,0.0,0.0); glBegin(GL_LINE_STRIP); for(GLinti=0;i<4;i++) glVertex3f(ControlP[i].x,ControlP[i].y,ControlP[i].z); glEnd(); glColor3f(1.0,0.0,0.0); glBegin(GL_LINE_STRIP); for(GLintj=0;j<4;j++) glVertex3f(ControlP1[j].x,ControlP1[j].y,ControlP1[j].z); glEnd(); glFlush();}voidReshape(GLintnewWidth,GLintnewHeight){ glViewport(0,0,newWidth,newHeight); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(-100.0,100.0,-100.0,100.0);}voidmain(void){ glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB); glutInitWindowPosition(100,100); glutInitWindowSize(400,400); glutCreateWindow("Bezier曲线"); initial(); glutDisplayFunc(Display); glutReshapeFunc(Reshape); glutMainLoop();}实验环境Windows10下的vc，按照网上的方法加入了opengl所需求的头文件，加入了graphics.h，编程语言为c语言实验结果算法说明一阶贝赛尔曲线上的由两个点确定

P0和P1,当t在0--->1区间上递增时，根据式（1）会得到多个点的坐标，其实这些的点就是一条直线上的点。

B(t)=(1-t)P0+tP1--------------------------------------（1）

即：

B(t).x=(1-t)P0.x+tP1.x

B(t).y=(1-t)P0.y+tP1.y

二阶贝赛尔曲线由3个点确定，它可以理解成是这样的一阶贝赛尔曲线：确定该一阶贝赛尔曲线的两个点是变化的。这两个点（设分别为Pm,Pn）是怎样变化的呢，这两个点又分别是(P0,P1)确定的一阶贝赛尔曲线和(P1,P2)确定的一阶贝赛尔曲线上的点。

于是有了2阶贝赛尔曲线的公式

Pm(t)=(1-t)P0+tP1

Pn(t)

=(1-t)P1+tP2

B(t)

=(1-t)Pm(t)+tPn(t)=(1-t)^2P0+2(1-t)tP1+t^2P2第四题实验代码#include<graphics.h>//#include<conio.h>#include<iostream.h>intencode(floatx,floaty,floatxl,floatyt,floatxr,floatyb)//编码函数{ intcode=0; code=x<xl?code|1:code; code=x>xr?code|2:code; code=y>yb?code|4:code; code=y<yt?code|8:code; returncode;}voidCohen_Sutherland(floatx1,floaty1,floatx2,floaty2,floatxl,floatyt,floatxr,floatyb){ intcode1,code2; floatx,y,k,temp,x10=x1,y10=y1,x20=x2,y20=y2; k=(y2-y1)/(x2-x1); code1=encode(x1,y1,xl,yt,xr,yb);//对p1，p2进行编码 code2=encode(x2,y2,xl,yt,xr,yb); while(code1!=0||code2!=0) { if(code1&code2)//code1&code2简弃 return; if(code1==0)//确保p1在窗口的外部 { code1=code2; temp=x1;x1=x2;x2=temp; temp=y1;y1=y2;y2=temp; code2=0; } if((code1&1)!=0)//左侧相交 { x=xl; y=y1+k*(x-x1); x1=x;y1=y; code1=encode(x1,y1,xl,yt,xr,yb); } if((code1&2)!=0)//右侧相交 { x=xr; y=y1+k*(x-x1); x1=x;y1=y; code1=encode(x1,y1,xl,yt,xr,yb); } if((code1&4)!=0)//下侧相交 { y=yb; x=x1+(y-y1)/k; x1=x;y1=y; code1=encode(x1,y1,xl,yt,xr,yb); } if((code1&8)!=0)//与上侧相交 { y=yt; x=x1+(y-y1)/k; x1=x;y1=y; code1=encode(x1,y1,xl,yt,xr,yb); } } if(x1>x2)//判断x1，x2的大小来画简弃的线段 { temp=x1;x1=x2;