计算机图形学第二次实验报告

姓名所使用的语言MATLAB学号完成日期2016/5/9一、绘制FERGUSON曲线1，改变各点处的一阶导数数值，绘制FERGUSON曲线进行对比分析A=100,300;120,200;220,200;270,100;370,100;420,200;420,300;220,280;100,300;B=10,-10;30,-30;30,-30;30,-10;20,20;20,20;-20,20;-20,10;20,-20;Q=2,-2,1,1;-3,3,-2,-1;0,0,1,0;1,0,0,0;plot(A(:,1),A(:,2);m,n=size(A);hold onfor i=1:m-1 for t=0:0.001:1 T=t3,t2,t,1; Px=A(i,1),A(i+1,1),B(i,1),B(i+1,1); Py=A(i,2),A(i+1,2),B(i,2),B(i+1,2); x=T*Q*Px; y=T*Q*Py plot(x,y,r); end end截图部分B=10,-10;30,-30;30,-30;30,-10;20,20;20,20;-20,20;-20,10;20,-20;B=210,-210;230,-230;230,-230;230,-210;220,240;250,250;-210,230;-220,210;220,-200;2，FERGUSON曲线丰满度实验A=100,300;120,200;220,200;270,100;370,100;420,200;420,300;220,280;100,300;B=10,-10;30,-30;30,-30;30,-10;20,20;20,20;-20,20;-20,10;20,-20;C=20,-20;60,-60;60,-60;60,-20;40,40;40,40;-40,40;-40,40;40,-40;D=40,-40;120,-120;120,-120;120,-40;80,80;80,80;-80,80;-80,80;80,-80;Q=2,-2,1,1;-3,3,-2,-1;0,0,1,0;1,0,0,0;plot(A(:,1),A(:,2);m,n=size(A);hold onfor i=1:m-1 for t=0:0.001:1 T=t3,t2,t,1; Px=A(i,1),A(i+1,1),B(i,1),B(i+1,1); Py=A(i,2),A(i+1,2),B(i,2),B(i+1,2); x=T*Q*Px; y=T*Q*Py; Px1=A(i,1),A(i+1,1),C(i,1),C(i+1,1); Py1=A(i,2),A(i+1,2),C(i,2),C(i+1,2); x1=T*Q*Px1; y1=T*Q*Py1; Px2=A(i,1),A(i+1,1),D(i,1),D(i+1,1); Py2=A(i,2),A(i+1,2),D(i,2),D(i+1,2); x2=T*Q*Px2; y2=T*Q*Py2;plot(x,y,r);plot(x1,y1,r);plot(x2,y2,r); endend二、绘制Bezier曲线1、二次Bernstein基函数性质分析 三次Bernstein基函数性质分析2、绘制任意二次三点Bezier曲线x=100 150 200 ;y=100 50 100 ;plot(x,y,k,LineWidth,1); k=length(x);for i=1:k-2 for t=0:0.005:1 Bx=(t2-2*t+1)*x(1)+(-2*t2+2*t)*x(2)+. (t2)*x(3); By=(t2-2*t+1)*y(1)+(-2*t2+2*t)*y(2)+. (t2)*y(3); hold on plot(Bx,By,r,LineWidth,2); endend3、绘制三次七点Bezier曲线clear allhold on B1=100,300;120,200;220,200;270,100; B2=270,100;370,100;420,200;420,300 plot(B1(:,1),B1(:,2),-b); plot(B2(:,1),B2(:,2),-b); for t=0:0.001:1 P=t*t*t t*t t 1; Q=-1,3,-3,1;3,-6,3,0;-3,3,0,0;1,0,0,0; P1=P*Q*B1; plot(P1(:,1),P1(:,2),.b,markersize,10); P1=P*Q*B2; plot(P1(:,1),P1(:,2),.b,markersize,10); end三、绘制B样条曲线 1、绘制均匀二次三点B样条曲线 x=100 150 200 250 300 350 400 450 500;y=100 50 100 50 150 50 100 50 100;plot(x,y,k,LineWidth,1); k=length(x);B=1/2;for i=1:k-2 for t=0:0.005:1 Bx=B*(t2-2*t+1)*x(i)+B*(-2*t2+2*t+1)*x(i+1)+. B*(t2)*x(i+2); By=B*(t2-2*t+1)*y(i)+B*(-2*t2+2*t+1)*y(i+1)+. B*(t2)*y(i+2); hold on plot(Bx,By,r,LineWidth,2); endend2、绘制三次B样条曲线x=100 120 220 270 370 420 420 ;y=300 200 200 100 100 200 300 ;plot(x,y,k,LineWidth,1); k=length(x);B=1/6;for i=1:k-3 for t=0:0.005:1 Bx=B*(-t3+3*t2-3*t+1)*x(i)+B*(3*t3-6*t2-0*t+4)*x(i+1)+. B*(-3*t3+3*t2+3*t+1)*x(i+2)+B*(1*t3-0*t2-0*t+0)*x(i+3); By=B*(-t3+3*t2-3*t+1)*y(i)+B*(3*t3-6*t2-0*t+4)*y(i+1)+. B*(-3*t3+3*t2+3*t+1)*y(i+2)+B*(1*t3-0*t2-0*t+0)*y(i+3); hold on plot(Bx,By,r,LineWidth,2); endend3、在同一控制顶点下(四个控制定点)绘制三次Bezier曲线和三次B样条曲线hold onx=220 270 300 320 340 360 370 420 ;y=200 100 150 150 150 150 100 200 ;plot(x,y,-b,LineWidth,2); plot(x,y,*r,LineWidth,3);k=length(x); B=1/6;for i=1:k-3 for t=0:0.001:1 Bx=B*(-t3+3*t2-3*t+1)*x(i)+B*(3*t3-6*t2-0*t+4)*x(i+1)+. B*(-3*t3+3*t2+3*t+1)*x(i+2)+B*(1*t3-0*t2-0*t+0)*x(i+3); By=B*(-t3+3*t2-3*t+1)*y(i)+B*(3*t3-6*t2-0*t+4)*y(i+1)+. B*(-3*t3+3*t2+3*t+1)*y(i+2)+B*(1*t3-0*t2-0*t+0)*y(i+3); plot(Bx,By,r,LineWidth,2); endend四、 有理曲线绘制绘制有理二次Bezier曲线x=100 150 200 250 300 350 400 450 500;y=100 50 100 50 150 50 100 50 100;plot(x,y,k,LineWidth,1); k=length(x);B=1/2;for i=1:k-2 for t=0:0.005:1 Bx=(B*(t2-2*t+1)*x(i)+B*(-2*t2+2*t+1)*x(i+1)+. B*(t2)*x(i+2)/(B*(t2-2*t+1)+B*(-2*t2+2*t+1)+. B*(t2); By=(B*(t2-2*t+1)*y(i)+B*(-2*t2+2*t+1)*y(i+1)+. B*(t2)*y(i+2)/(B*(t2-2*t+1)+B*(-2*t2+2*t+1)+. B*(t2); hold on plot(Bx,By,r,LineWidth,2); endend各种参数图形均匀有理B样条曲线绘制有理三次B样条曲线hold onx=220 270 300 320 340 370 420 ;y=200 100 140 150 130 100 200 ;plot(x,y,-b,LineWidth,2); k=length(x); B=1/6;for i=1:k-3 for t=0:0.001:1 Bx=(B*(-t3+3*t2-3*t+1)*x(i)+B*(3*t3-6*t2-0*t+4)*x(i+1)+. B*(-3*t3+3*t2+3*t+1)*x(i+2)+B*(1*t3-0*t2-0*t+0)*x(i+3)/(B*(-t3+3*t2-3*t+1)+B*(3*t3-6*t2-0*t+4)+. B*(-3*t3+3*t2+3*t+1)+B*(1*t3-0*t2-0*t+0); By=(B*(-t3+3*t2-3*t+1)*y(i)+B*(3*t