Plotting ellipses with parametric curves

Question

Szabolcs Simon-Guth 2021-11-9

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582474-plotting-ellipses-with-parametric-curves

评论： Szabolcs Simon-Guth 2021-11-9

采纳的回答： Chunru

在 MATLAB Online 中打开

Hi all!

I need to plot the following ellipses on the same plot:

Ellips 1:

Ellipse 2:

I have substituted the formula for the second ellipse by u and v:

u =

v =

Ellipse 2:

I have used the following parametrisation:

For an ellipse with the general fomula

the parametrization:

and

So, I have rearranged the equation of both ellipses to fit the general formula and then calculated a and b according the get the parametrization above. I was supposed to get the following plot:

Instead I have got this:

I have written the following code:

% First ellipse
t = linspace(0,2*pi,200);
a = sqrt(2);
b = sqrt(2/3);
x = a.*cos(t);
y = b.*sin(t);
plot(((1/2)*(x.^2)), ((3/2).*(y.^2)), '-k', 'LineWidth', 1.5)
axis equal
hold on
% Second ellipse
t = linspace(0,2*pi,200);
a = 2;
b = 1;
x = (-a/3).*(cos(t)+((-2*b/3).*sin(t)));
y = (((2*a/3).*cos(t))+((7*b/3).*sin(t)));
u = x-(2.*y);
v = (2.*x)+y;
plot(((1/4).*(u.^2)), ((v.^2)), '-k', 'LineWidth', 1.5)
axis equal
hold off

What is it that I'm doing wrong? I am very thankful for all the help in advance!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Chunru 2021-11-9

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582474-plotting-ellipses-with-parametric-curves#answer_827369

在 MATLAB Online 中打开

% First ellipse

t = linspace(0,2*pi,200);

a = sqrt(2);

b = sqrt(2/3);

x = a.*cos(t);

y = b.*sin(t);

%plot(((1/2)*(x.^2)), ((3/2).*(y.^2)), '-k', 'LineWidth', 1.5)

plot(x, y, '-k', 'LineWidth', 1.5)

axis equal

hold on

% Second ellipse

t = linspace(0,2*pi,200);

a = 2;

b = 1;

u = a.*cos(t);

v = b.*sin(t);

xy= ([1 -2; 2 1])\[u; v]; % since [u; v] = [1 -2; 2 1][x; y]

xy = 2×200

0.4000 0.4124 0.4244 0.4360 0.4472 0.4579 0.4682 0.4780 0.4873 0.4961 0.5044 0.5123 0.5196 0.5264 0.5327 0.5384 0.5436 0.5483 0.5524 0.5560 0.5590 0.5615 0.5634 0.5647 0.5655 0.5657 0.5653 0.5644 0.5629 0.5609 -0.8000 -0.7933 -0.7858 -0.7775 -0.7684 -0.7586 -0.7480 -0.7367 -0.7246 -0.7118 -0.6984 -0.6842 -0.6693 -0.6537 -0.6376 -0.6207 -0.6033 -0.5852 -0.5666 -0.5474 -0.5277 -0.5074 -0.4866 -0.4654 -0.4436 -0.4215 -0.3989 -0.3759 -0.3525 -0.3288

x = xy(1, :);

y = xy(2, :);

%plot(((1/4).*(u.^2)), ((v.^2)), '-g', 'LineWidth', 1.5)

plot(x, y, '-g', 'LineWidth', 1.5)

axis equal

hold off