写出用matlab绘制四叶玫瑰线P=sin2Θ（Θ∈(0，2π））的程序

theta=linspace(0,2*pi,400)rou=4*sin(2*theta)polar(theta,rou)

^>>x = -2:0.1:2

>>y = exp(-(x.^bai2))

>>theta = linspace(0, 2*pi)

>>rho = sin(2*theta)

>>t1 = linspace(0,30,1000)

>>x3 = 3*t1./(1+t1.^3)

>>y3 = 3*t1.^2./(1+t1.^3)

>>t2 = linspace(0,2*pi)

>>档颂 x4 = t2 - sin(t2)

>>y4 = 1 - cos(t2)

>>subplot(2,2,1)plot(x,y)title('概率曲线 y = exp(-x^2)')

>>subplot(2,2,2)polar(theta,rho),title('四叶玫瑰线 p = sin(2*t)')

>>subplot(2,2,3)plot(x3,y3)title('叶形线')

>>subplot(2,2,4)plot(x4,y4)title('摆线')

扩展资料：

四叶玫瑰线(four-leaved的一拆蠢棚种.定长线段AB =2a，它的两个端点在垂直两直线上滑动，从两直线的交点O向线段AB作垂线OM，垂足M的轨迹称一’为四叶玫瑰线(见旅则图).其极坐标方程为P=a sin 2B。

^clcclear

subplot(2,2,1)

ezplot('exp(-x^bai2)')

subplot(2,2,2)

ezpolar('sin(2*t)')

subplot(2,2,3)

t=0:pi/100:2*pi

x=3*t./(1+t.^3)

y=3*t.^2./(1+t.^3)

参考资料来源：百度百科-四叶玫瑰线

function plot_rose

draw_main(450,90)

function draw_main(x,y)

%粉红色玫瑰

arcdata{1}=[65 -60 150 350 8

66 -54 300 470 8

65 -56 30 230 10

64 -57 300 49017]

ellipsedata{1}=[73 -30 250 450 27 40

59 -30 100 290 2740

65 -40140 270 20 30]

arcdata{2}=[0 0 150 350 12

1 8 280 470 12

0 2 30 230 16

0 3 80 240 28

2 8 180 330 22

-2 2 310 460 25]

ellipsedata{2}=[-12 30 120 300 30 40

10 28 250 423 3042

-4 10290 393 30 40]

ellipsedata{3}=[120 5 0 360 15 25]

ellipsedata{4}=[-70 10 0 360 14 20]

rose_e{2}=[x+16 y+32 235 355 26 35

x-15 y+32 190 310 3035

x+0 y+35 190 350 4350]

rose_e{1}=[x+80 y-48 220 350 22 50

x+50 y-48 190 320 2250

x+65 y-28 180 360 3650]

rose_e{3}=[x+120 y-6 200 340 17 25

x+120 y+7 160 380 1727]

rose_e{4}=[x-70 y+15 140 390 17 20

x-75 y-10 205 340 1030

x-60 y-10 195 340 530]

arcdata{3}=[0 82 190 350 6]

ss={'m','r','b','y'}

s0={'k','k','g'}

figure('menubar','none','numbertitle','off','name','rose')

% figure('numbertitle','off'耐颂坦皮,'name','rose'昌信郑)

hold on

for j=1:length(ellipsedata)

fori=1:size(ellipsedata{j},1)

rectangle('Position',[x+ellipsedata{j}(i,1)-ellipsedata{j}(i,5),y+ellipsedata{j}(i,2)-ellipsedata{j}(i,6),2*ellipsedata{j}(i,5),2*ellipsedata{j}(i,6)],'Curvature',[1,1],...

'FaceColor',ss{j})

end

ifj<4

for i=1:size(arcdata{j},1)

draw_arc(x+arcdata{j}(i,1),y+arcdata{j}(i,2),arcdata{j}(i,3),arcdata{j}(i,4),arcdata{j}(i,5),s0{j})

end

end

fori=1:size(rose_e{j},1)

plot_rose_e(rose_e{j},j)

end

end

for j=1:3

zhuzhi=[x-98,y+100+j,255,371,100,80

x-20,y+30+j,260,358,140,140

x+224,y+20+j,180,218,160,140]

draw_branch(zhuzhi)

end

ce_branch=[x+70,y+34,180,233,140,140

x,y+40,205,255,100,120

x+135,y-30,209,249,72,120

x,y+20,263,301,100,120

x+85,y-10,278,305,100,120

x+100,y-62,282,308,90,120

x-50,y-10,277,314,30,120

x+70,y+80,222,266,52,120

x-60,y-45,229,266,52,120

x+79,y-45,229,266,52,120

x+84,y,224,273,52,120

x+110,y+40,240,282,100,120]

draw_branch(ce_branch)

t_leaf=[x+168,y+282,10,20,-40

x+160,y+252,8,16,260

x+145,y+270,8,16,-15

x+156,y+224,10,20,-45

x+150,y+200,8,16,270

x+135,y+220,8,16,-10

x+146,y+144,8,16,-80

x+130,y+130,6,12,235

x+125,y+154,7,14,-10

x+78,y+98,6,12,-90

x+60,y+90,5,10,180

x+70,y+109,5,10,-45

x-125,y+270,12,24,60

x-95,y+270,10,20,10

x-110,y+245,10,20,90

x-105,y+220,10,20,45

x-100,y+190,8,16,135

x-75,y+210,8,16,-45

x+65,y+190,10,20,-45

x+40,y+185,8,16,0

x+55,y+165,8,16,90]

for j=1:size(t_leaf,1)

draw_elli(t_leaf(j,1),t_leaf(j,2),t_leaf(j,3),t_leaf(j,4),t_leaf(j,5))

end

axis ij

axis off

set(gcf,'color','k')

daspect([1,1,1])

% 画旋转椭圆

function draw_elli(x0,y0,a,b,theta)

theta=-theta

t = 0:0.01:2*pi

x = a*cos(t)

y = b*sin(t)

xy = zeros(2,length(t))

for i = 1:length(t)

xy(:,i) =expm([0,-pi/180*thetapi/180*theta,0])*[x(i)y(i)]

end

plot(x0 +xy(1,:),480-y0 + xy(2,:),'g')

% 画弧线

function draw_arc(x0,y0,st_a,en_a,r,c_c)

t = (pi/180*st_a:0.01:pi/180*en_a)-pi

x = x0 + r*cos(t)

y = y0 + r*sin(t)

plot(x,y,c_c)

% 花萼

function plot_rose_e(matr,ch)

x=[]y=[]n=size(matr,1)

for i=1:size(matr,1)

t=(matr(i,3):matr(i,4))*pi/180-pi

x1=matr(i,1)+matr(i,5)*cos(t)

y1=matr(i,2)+matr(i,6)*sin(t)

ifi<3

x1=2*matr(i,1)-x1

end

x1=fliplr(x1)

y1=fliplr(y1)

if n<3&&i<2

x1=fliplr(x1)

y1=fliplr(y1)

end

if ch==4&&i==2

x1=fliplr(x1)

y1=fliplr(y1)

end

x=[x,x1]

y=[y,y1]

end

fill(x,y,'g')

% 画树枝

function draw_branch(zhuzhi)

for k=1:size(zhuzhi,1)

t=(zhuzhi(k,3):zhuzhi(k,4))*pi/180-pi

x1=zhuzhi(k,1)+zhuzhi(k,5)*cos(t)

y1=zhuzhi(k,2)+zhuzhi(k,6)*sin(t)

x1=2*zhuzhi(k,1)-x1

plot(x1,y1,'g','linewidth',2)

end

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