Question

用MATLAB在同一坐标轴中绘制下列两条曲线交叉点:(1)y=2x-0.5;(2)0<=t<=pi,x=sin(3t)*cost,y=sin(3t)*sint.

我已经把两条曲线画出来了，但是不知道怎么绘制两条曲线的交点。还请指教！
a=find(abs(y1-y2)<1e-3); 这句话写进去不对啊.还是无法画出来,能不能把运行后的图传上来啊?

Answer 1

在同一坐标轴中绘制下列两条曲线交叉点，可以用solve()函数命令求得其各个交叉点（x,y）的精确值,然后用plot()函数命令标记出各个交叉点的位置。如用find()函数命令寻找满足abs(y1-y2)<1e-3条件，需要取比较多的点（t>10000），然后去筛选出各个交叉点（x,y）的值也是近似值。

Answer 2

function zfsolve
clc;clear
t=0:0.001:pi;
x2=sin(3*t).*cos(t);
y2=sin(3*t).*sin(t);

x1=cos(t);
y1=2*x1-0.5;

plot(x2,y2,x1,y1),grid
axis([-1 1 -1 1])
axis square

%解析法
[t,x,y]=solve('x=sin(3*t)*cos(t)','y=sin(3*t)*sin(t)','y=2*x-0.5')

%数值法
t=fsolve(@fun,[0:0.8:pi])
x=sin(3*t).*cos(t)
y=sin(3*t).*sin(t)
function Y=fun(t)
Y=2*sin(3*t).*cos(t)-0.5-sin(3*t).*sin(t)

%以上做图，可以看到有4个交点。图形见：
http://hi.baidu.com/chemical%5Fengineering/album/item/990515ce15be2533b700c803.html

结果：
t =

-2.3561944901923449288469825374596
.78539816339744830961566084581988
-3.0530039379653160512523791543580
1.9970966965040862114921990286944
-1.7639348577319212053010586432573
1.3776577958578720331615847400222
-1.1444959570857070269704443545851
.88588715624477187210264228921518e-1

x =

.50000000000000000000000000000000
.50000000000000000000000000000000
.26161863976285227756382570648005
.11899345502089812629285088101918
-.16061209478375040385667658749922
-.16061209478375040385667658749922
.11899345502089812629285088101918
.26161863976285227756382570648005

y =

.50000000000000000000000000000000
.50000000000000000000000000000000
.23237279525704555127651412960095e-1
-.26201308995820374741429823796165
-.82122418956750080771335317499845
-.82122418956750080771335317499845
-.26201308995820374741429823796165
.23237279525704555127651412960095e-1

t =

0.0886 0.7854 1.3777 1.9971

x =

0.2616 0.5000 -0.1606 0.1190

y =

0.0232 0.5000 -0.8212 -0.2620

Answer 3

楼上的可能误解了吧,LZ是要画出两曲线的交点