I want to draw an ellipsoide with one cercle and one ellipse inside it and have the axis of the cercle and the ellipse drawn too

I want to draw an ellipsoide with one cercle and one ellipse inside it and have the axis of the cercle and the ellipse drawn too,

i would like the ellipsoide be transparaent (grey light color ).

attached the figure in 2D, i want to make it in 3D.

please if anyone could help me on this issue

thank you very much for your help

Answer 1

[Kevin Holly]

Here is the ellipsoid and the circle. Did you want the ellipse to be at a particular angle?

% Parameters
% Center
xc = 0;
yc = 0;
zc = 0;
% Radius
xr = 0.5;
yr = 0.5;
zr = 1;

% Minor Axes Length
minor_length = min([xr,yr,zr]);

% Plot
figure
% Ellipsoid
ellipsoid(xc,yc,zc,xr,yr,zr)
axis equal
handle = gca; % get axes handle
handle.Children.EdgeColor = [.8 .8 .8];
handle.Children.FaceColor = [.8 .8 .8];
handle.Children.FaceAlpha = .5;

% Circle
viscircles([xc,yc], minor_length,'Color','r');
hold on
% Circle Axes
line([xc,xc],[-yr,yr],'Color','r')
line([-xr,xr],[yc,yc],'Color','r')

[Kevin Holly]

% Parameters
% Center
xc = 0;
yc = 0;
zc = 0;
% Radius
xr = 0.5;
yr = 0.5;
zr = 1;
% Rotation Angle
angle = 25;
% Minor Axes Length
minor_length = min([xr,yr,zr]);

% Plot
figure
% Ellipsoid
[x, y, z] = ellipsoid(xc,yc,zc,xr,yr,zr);
h = surf(x, y, z); 
axis equal
hold on
set(h, 'FaceColor',[.8 .8 .8], 'FaceAlpha', 0.2,'EdgeAlpha', 0.2)

% Circle
hc = viscircles([xc,yc], minor_length,'Color','r','LineWidth', 5);
hc.Children(2).Color = 'r';
hold on
lc1 = line([xc,xc],[-0.5 0.5],'Color','r','LineWidth',5);
lc2 = line([-0.5 0.5],[yc,yc],'Color','r','LineWidth',5);

% Rotate Ellipsoid and Circle with its Axes
rotate(h,[1 0 0],angle)
rotate(hc.Children(1),[1 0 0],angle)
rotate(hc.Children(2),[1 0 0],angle)
rotate(lc1,[1 0 0],angle)
rotate(lc2,[1 0 0],angle)

Used code from Image Analyst found in the link below to draw ellipse in the following section.

https://www.mathworks.com/matlabcentral/answers/86615-how-to-plot-an-ellipse

% Define parameters.
fontSize = 15;
x1 = 0;
x2 = 0;
y1 = -.8; % value based on angle of 25 degrees
y2 = .8; % value based on angle of 25 degrees
eccentricity = y2;
numPoints = 300; % Less for a coarser ellipse, more for a finer resolution.
% Make equations:
a = (1/2) * sqrt((x2 - x1) ^ 2 + (y2 - y1) ^ 2);
b = a * sqrt(1-eccentricity^2);
t = linspace(0, 2 * pi, numPoints); % Absolute angle parameter
X = a * cos(t);
Y = b * sin(t);
% Compute angles relative to (x1, y1).
angles = atan2(y2 - y1, x2 - x1);
x = (x1 + x2) / 2 + X * cos(angles) - Y * sin(angles);
y = (y1 + y2) / 2 + X * sin(angles) + Y * cos(angles);

hold on
plot3(x,zeros(size(y)),y,'-','Color','b', 'LineWidth', 5);	
plot3(x,zeros(size(y)),zeros(size(y)),'b-', 'LineWidth', 5);
plot3(zeros(size(x)),zeros(size(y)),y,'b-', 'LineWidth', 5);
view(-75,20)

[walid albugami]

wooow

thank you very much Kevin

this is excately what i want but do you could please tell me

Q1: how can i make the lines (blue) and (red) less thick (just to be more nice to see).

and

Q2: with the same angle of view, i want to make the blue ellipse perpeniculare to the red ellipse ?

[walid albugami]

Kevin

for the question 2: i would keep the two ellipses as they are, and just add a third one perpendiculare to the red ellipse (with a green color).

appreciate your wonderful answers.

[Kevin Holly]

I made variables linethickness_red,linethickness_green, and linethickness_blue that you can adjust.

If you have an equation to calculate the major axis length and eccentricity value of the ellipse when rotated, you can automate the procress. You can easily make an App with a slider bar. If you need it for such purposes.

% Parameters
% Center
xc = 0;
yc = 0;
zc = 0;
% Radius
xr = 0.5;
yr = 0.5;
zr = 1;
% Rotation Angle
angle = 25;
% Minor Axes Length
minor_length = min([xr,yr,zr]);
linethickness_red = 2;

% Plot
figure
% Ellipsoid
[x, y, z] = ellipsoid(xc,yc,zc,xr,yr,zr);
h = surf(x, y, z); 
axis equal
hold on
set(h, 'FaceColor',[.8 .8 .8], 'FaceAlpha', 0.2,'EdgeAlpha', 0.2)
% Circle
hc = viscircles([xc,yc], minor_length,'Color','r','LineWidth',linethickness_red);
hc.Children(2).Color = 'r';
hold on
lc1 = line([xc,xc],[-0.5 0.5],'Color','r','LineWidth',linethickness_red);
lc2 = line([-0.5 0.5],[yc,yc],'Color','r','LineWidth',linethickness_red);
% Rotate Ellipsoid and Circle with its Axes
rotate(h,[1 0 0],angle)
rotate(hc.Children(1),[1 0 0],angle)
rotate(hc.Children(2),[1 0 0],angle)
rotate(lc1,[1 0 0],angle)
rotate(lc2,[1 0 0],angle)

% Define parameters for blue ellipse
linethickness_blue = 2;
x1 = 0;
x2 = 0;
y1 = -.8; % value based on angle of 25 degrees
y2 = .8; % value based on angle of 25 degrees
eccentricity = .78;
numPoints = 300; % Less for a coarser ellipse, more for a finer resolution.
% Make equations:
a = (1/2) * sqrt((x2 - x1) ^ 2 + (y2 - y1) ^ 2);
b = a * sqrt(1-eccentricity^2);
t = linspace(0, 2 * pi, numPoints); % Absolute angle parameter
X = a * cos(t);
Y = b * sin(t);
% Compute angles relative to (x1, y1).
angles = atan2(y2 - y1, x2 - x1);
x = (x1 + x2) / 2 + X * cos(angles) - Y * sin(angles);
y = (y1 + y2) / 2 + X * sin(angles) + Y * cos(angles);
hold on
plot3(x,zeros(size(y)),y,'-','Color','b', 'LineWidth', linethickness_blue);	
plot3(x,zeros(size(y)),zeros(size(y)),'b-', 'LineWidth', linethickness_blue);
plot3(zeros(size(x)),zeros(size(y)),y,'b-', 'LineWidth', linethickness_blue);
view(-75,20)

% Define parameters of green ellipse
linethickness_green = 2;
x1 = 0;
x2 = 0;
y1 = -1;
y2 = 1;
eccentricity = .866;
numPoints = 300; % Less for a coarser ellipse, more for a finer resolution.
% Make equations:
a = (1/2) * sqrt((x2 - x1) ^ 2 + (y2 - y1) ^ 2);
b = a * sqrt(1-eccentricity^2);
t = linspace(0, 2 * pi, numPoints); % Absolute angle parameter
X = a * cos(t);
Y = b * sin(t);
% Compute angles relative to (x1, y1).
angles = atan2(y2 - y1, x2 - x1);
x = (x1 + x2) / 2 + X * cos(angles) - Y * sin(angles);
y = (y1 + y2) / 2 + X * sin(angles) + Y * cos(angles);
hold on
green_ellipse_handle.ellipse = plot3(x,zeros(size(y)),y,'-','Color','g', 'LineWidth', linethickness_blue);	
green_ellipse_handle.axis1 = plot3(x,zeros(size(y)),zeros(size(y)),'g-', 'LineWidth', linethickness_blue);
green_ellipse_handle.axis2 = plot3(zeros(size(x)),zeros(size(y)),y,'g-', 'LineWidth', linethickness_blue);

% Rotate Green Ellipse with its Axes

rotate(green_ellipse_handle.ellipse,[1 0 0],angle)
rotate(green_ellipse_handle.axis1,[1 0 0],angle)
rotate(green_ellipse_handle.axis2,[1 0 0],angle)