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实验四 hermite bezier 样条三种曲线的绘制1、 实验目的 了解和学习hermite、bezier、样条三种曲线算法 掌握基于 win32、visual c+环境mfc绘制图形配置过程制过程 编程实现hermite、bezier、样条三种曲线的绘制2、 实验原理 三次参数曲线1. 曲线段可以用端点、切向量和曲线段之间的连续性等约束条件来定义 2. 两个端点和两端点处的切向量定义hermite曲线； 3. 两个端点和另外两个控制端点切向量的点定义的bezier曲线；4. 由四个控制顶点定义的样条曲线。3、 实验关键代码void cdrawytqxview:hermite()/绘制hermite三次插值样条int a44 =2,-2,1,1,-3,3,-2,-1,0,0,1,0,1,0,0,0;/mh矩阵系数int b42;/边界点 for(int i=0;i4;i+)b00=p1i0;b01=p1i1;/起点的坐标b10=p1i+10;b11=p1i+11;/终点的坐标b20=p2i0;b21=p2i1;/起点的导数b30=p2i+10;b31=p2i+11;/终点的导数caculate(a,b);cclientdc dc(this);cpen mypen,*poldpen;mypen.createpen(ps_solid,1,rgb(0,0,255);poldpen=dc.selectobject(&mypen);dc.moveto(p1i0,p1i1);for(double t=0.0;t=1;t+=1.0/400)int x=round(pow(t,3)*result00+pow(t,2)*result10+ t*result20+result30);int y=round(pow(t,3)*result01+pow(t,2)*result11+ t*result21+result31);dc.lineto(x,y);dc.selectobject(poldpen);mypen.deleteobject();void cdrawytqxview:caculate(int a44,int b42)/矩阵相乘int i,j,k;for(i=0;i4;i+)for(j=0;j2;j+)resultij=0;/矩阵清零for(i=0;i2;i+)for(j=0;j4;j+)for(k=0;k4;k+)resultji+=ajk*bki; void cdrawytqxview:drawbezier()/绘制bezier曲线cclientdc dc(this);double x,y;int rate=400,n;n=ctrlpoint-1;for(double t=0;t=1;t+=1.0/rate)x=0;y=0;for(int i=0;i=n;i+)x+=pti.x*cnk(n,i)*pow(t,i)*pow(1-t,n-i);y+=pti.y*cnk(n,i)*pow(t,i)*pow(1-t,n-i);dc.setpixel(round(x),round(y),rgb(0,0,255);/曲线颜色double cdrawytqxview:cnk(const int &n, const int &i)/bernstein第一项return double(factorial(n)/(factorial(i)*factorial(n-i);int cdrawytqxview:factorial(int m)/阶乘函数int f=1;for(int i=1;i=m;i+)f*=i;return f;void cdrawytqxview:drawb3_curves()/绘制b样条曲线cclientdc dc(this);int i,rate=10,m;long lx,ly;m=ctrlpoint-(3+1);double f03,f13,f23,f33;lx=round(pt0.x+4.0*pt1.x+pt2.x)/6.0);/t0的起点x坐标ly=round(pt0.y+4.0*pt1.y+pt2.y)/6.0);/t0的起点y坐标dc.moveto(lx,ly);cpen mypen2,*poldpen2;mypen2.createpen(ps_solid,2,rgb(0,0,255);/颜色设置poldpen2=dc.selectobject(&mypen2);for(i=1;im+2;i+)/m+1段三次样条曲线for(double t=0;t=1;t+=1.0/rate)f03=(-t*t*t+3*t*t-3*t+1)/6;/计算f0,3(t)f13=(3*t*t*t-6*t*t+4)/6;/计算f1,3(t)f23=(-3*t*t*t+3*t*t+3*t+1)/6;/计算f2,3(t)f33=t*t*t/6;/计算b3,3(t)lx=round(pti-1.x*f03+pti.x*f13+pti+1.x*f23+pti+2.x*f33);ly=round(pti-1.y*f03+pti.y*f13+pti+1.y*f23+pti+2.y*f33);dc.lineto(lx,ly);dc.selectobject(poldpen2);mypen2.deleteobject();void cdrawytqxview:drawcharpolygon()/绘制控制多边形cclientdc dc(this);cpen mypen,*poldpen;mypen.createpen(ps_solid,2,rgb(0,0,0);/控制多边形poldpen=dc.selectobject(&mypen);for(int i=0;ictrlpoint;i+)if(i=0)dc.moveto(pti);dc.ellipse(pti.x-2,pti.y-2,pti.x+2,pti.y+2);elsedc.lineto(pti);dc.ellipse(pti.x-2,pti.y-2,pti.x+2,pti.y+2);dc.selectobject(poldpen);mypen.deleteobject();void cdrawytqxview:onlbuttondown(uint nflags, cpoint point)/获得屏幕控制点坐标 / todo: add your message handler code here and/or call defaultcview:onlbuttondown(nflags, point);if(flag)ptctrlpoint.x=point.x;ptctrlpoint.y=point.y;if(ctrlpointn_max_point)ctrlpoint+;elseflag=false;drawcharpolygon();else drawcharpolygon1();void cdrawytqxview:onrbuttondown(uint nflags, cpoint point)/调用绘制函数 / todo: add your message handler code here and/or call defaultflag=false;if(sign=0)hermite();if(sign=1)drawbezier();if(sign=2)drawb3_curves();cview:onrbuttondown(nflags, point);4、 实验结果1、 绘制hermite曲线2、 绘制bezier曲线3. 绘制b样条曲线5、 心得体会通过实验进一步学习和了解mfc的菜单的实现及其响应函数的实现，并设置鼠标的左键激活绘制多边形，右键激活绘制hermite、bezier、b样条三种曲线。掌握了三个齐次坐标矩阵以及它们各自点的平移，旋转，缩放，错切变换的坐标矩阵。再做实验的同时又很好的复习了考试的内容，一举两得！ 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