[终稿]Matlab 画二次及三次Bezier曲线,8控制点的B样条曲线

[终稿]Matlab 画二次及三次Bezier曲线,8控制点的B样条曲线 二次Bezier曲线代码: m-文件函数: function bezier2(p0,p1,p2) t=0:0.001:1; x=(p2(1)-2*p1(1)+p0(1))*t.^2+2*(p1(1)-p0(1))*t+p0(1); y=(p2(2)-2*p1(2)+p0(2))*t.^2+2*(p1(2)-p0(2))*t+p0(2); plot([p0(1) p1(1) p2(1)],[p0(2) p1(2) p2(2)],'b'),hold on plot(x,y,'r'); 执行: >> bezier2([1,3],[4,18],[7,6]) 18 16 14 12 10 8 6 4 21234567 三次Bezier曲线代码: function bezier3(p0,p1,p2,p3) t=0:0.001:1; x=(1-t).^3*p0(1)+3*t.*(1-t).^2*p1(1)+3*t.^2.*(1-t)*p2(1)+t.^3*p3(1); y=(1-t).^3*p0(2)+3*t.*(1-t).^2*p1(2)+3*t.^2.*(1-t)*p2(2)+t.^3*p3(2); plot([p0(1) p1(1) p2(1) p3(1)],[p0(2) p1(2) p2(2) p3(2)],'b'); hold on; plot(x,y,'r'); 执行: >> bezier3([0,3],[5,20],[7,2],[9,1]) 20 18 16 14 12 10 8 6 4 2 00123456789 B样条曲线代码(方法一): function Byangtiao8(p) t=0:0.005:1; hold on for i=1:5 x=p(1,i)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p(1,i+1)*(1/6)*(3*t.^3-6*t.^2+4)... +p(1,i+2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p(1,i+3)*(1/6)*t.^3; y=p(2,i)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p(2,i+1)*(1/6)*(3*t.^3-6*t.^2+4)... +p(2,i+2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p(2,i+3)*(1/6)*t.^3; plot(x,y,'k'); end plot([p(1,1) p(1,2) p(1,3) p(1,4) p(1,5) p(1,6) p(1,7) p(1,8)],[p(2,1) p(2,2) p(2,3) p(2,4) p(2,5) p(2,6) p(2,7) p(2,8)]); 执行: >> Byangtiao8([4,6,3,1,7,9,15,11;0,9,11,15,15,7,6,12]) 15 10 5 0051015 B样条曲线代码(方法二): function Byt8(p0,p1,p2,p3,p4,p5,p6,p7) t=0:0.001:1; %m=[-1 3 -3 1;3 -6 3 0;-3 0 3 0;1 4 1 0]; x=p0(1)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p1(1)*(1/6)*(3*t.^3-6*t.^2+4)... +p2(1)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p3(1)*(1/6)*t.^3; y=p0(2)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p1(2)*(1/6)*(3*t.^3-6*t.^2+4)... +p2(2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p3(2)*(1/6)*t.^3; %plot([p0(1) p1(1) p2(1) p3(1)],[p0(2) p1(2) p2(2) p3(2)]); hold on; plot(x,y,'r'); x=p1(1)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p2(1)*(1/6)*(3*t.^3-6*t.^2+4)... +p3(1)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p4(1)*(1/6)*t.^3; y=p1(2)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p2(2)*(1/6)*(3*t.^3-6*t.^2+4)... +p3(2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p4(2)*(1/6)*t.^3; %plot([p0(1) p1(1) p2(1) p3(1)],[p0(2) p1(2) p2(2) p3(2)]); hold on; plot(x,y,'r'); x=p2(1)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p3(1)*(1/6)*(3*t.^3-6*t.^2+4)... +p4(1)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p5(1)*(1/6)*t.^3; y=p2(2)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p3(2)*(1/6)*(3*t.^3-6*t.^2+4)... +p4(2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p5(2)*(1/6)*t.^3; %plot([p0(1) p1(1) p2(1) p3(1)],[p0(2) p1(2) p2(2) p3(2)]); hold on; plot(x,y,'r'); x=p3(1)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p4(1)*(1/6)*(3*t.^3-6*t.^2+4)... +p5(1)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p6(1)*(1/6)*t.^3; y=p3(2)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p4(2)*(1/6)*(3*t.^3-6*t.^2+4)... +p5(2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p6(2)*(1/6)*t.^3; %plot([p0(1) p1(1) p2(1) p3(1)],[p0(2) p1(2) p2(2) p3(2)]); hold on; plot(x,y,'r'); x=p4(1)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p5(1)*(1/6)*(3*t.^3-6*t.^2+4)... +p6(1)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p7(1)*(1/6)*t.^3; y=p4(2)*(1/6)*(-t.^3+3*t.^2-3*t+1)+p5(2)*(1/6)*(3*t.^3-6*t.^2+4)... +p6(2)*(1/6)*(-3*t.^3+3*t.^2+3*t+1)+p7(2)*(1/6)*t.^3; %plot([p0(1) p1(1) p2(1) p3(1)],[p0(2) p1(2) p2(2) p3(2)]); hold on; plot(x,y,'r'); plot([p0(1) p1(1) p2(1) p3(1) p4(1) p5(1) p6(1) p7(1)],[p0(2) p1(2) p2(2) p3(2) p4(2) p5(2) p6(2) p7(2)]); 执行: >> Byt8([0,0],[1,4],[3,9],[5,7],[6,2],[7,6],[9,5],[11,3]) 9 8 7 6 5 4 3 2 1 0024681012