EDITED : Generate sphere whose center is not at origin

Question

Tanmayee Pathre 2024-7-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2141151-edited-generate-sphere-whose-center-is-not-at-origin

评论： Star Strider 2024-7-30

How do I generate a sphere with center at [x = 4.26, y = 1.76, z = 1.62] with a radius of 0.25 units? The sphere needs to have 101 points. Please see the attached Sphere_101.fig for reference. The output should look like the figure produced by figure 'Sphere_101.png. Below this figure, is my code. When I run the code, the points are randomly arranged on the sphere instead of being neatly spaced. Can anyone please help?

I = imread('Sphere_101.png');
imshow(I);
%Center of sphere 
recPosition = [4.26 1.76 1.62];
rng(0,'twister');
radius = 0.25;
%Number of points
nPoints = 100;
%Create array 
test_xyz = zeros(101,3);
test_xyz(1,1) = recPosition(1);
test_xyz(1,2) = recPosition(2);
test_xyz(1,3) = recPosition(3);
radius  = zeros(nPoints,1)+radius  ;           
azimuth  = rand(size(radius)) * 2*pi;      
elevation = (rand(size(radius)) .* pi)-pi/2;
[x,y,z] = sph2cart(azimuth,elevation,radius);
test_xyz(2:end,1) = test_xyz(1,1)+x;
test_xyz(2:end,2) = test_xyz(1,2)+y;
test_xyz(2:end,3) = test_xyz(1,3)+z;
figure
scatter3(test_xyz(:,1),test_xyz(:,2),test_xyz(:,3));

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Steven Lord 2024-7-29

在 MATLAB Online 中打开

How exactly do you want to select the 101 points? I'd personally scale and translate the output from the sphere function if you want them "nicely arranged".

[x, y, z] = sphere;

% Scale -- I'll let you determine the correct scaling factor for your

% application.

x2 = 0.5*x;

y2 = 0.5*y;

z2 = 0.5*z;

% translate

x3 = x2 + 1;

y3 = y2 - 2;

z3 = z2 + 4;

figure

surf(x, y, z);

title('Unscaled, untranslated')

figure

surf(x2, y2, z2);

title('Scaled')

figure

surf(x3, y3, z3)

title('Scaled and translated')

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Answer 1

Star Strider 2024-7-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2141151-edited-generate-sphere-whose-center-is-not-at-origin#answer_1491991

在 MATLAB Online 中打开

I made a few adjustments to your original code, adding (or changing) only these:

p1 = 1:51;

p2 = 52:101;

figure

scatter3(test_xyz(p1,1),test_xyz(p1,2),test_xyz(p1,3), 10, 'b', 'filled');

hold on

scatter3(test_xyz(p2,1),test_xyz(p2,2),test_xyz(p2,3), 10, 'r', 'filled');

hold off

axis('equal')

Try this —

I = imread('Sphere.png');

imshow(I);

%Center of sphere

recPosition = [4.26 1.76 1.62];

rng(0,'twister');

radius = 0.25;

%Number of points

nPoints = 100;

%Create array

test_xyz = zeros(101,3);

test_xyz(1,1) = recPosition(1);

test_xyz(1,2) = recPosition(2);

test_xyz(1,3) = recPosition(3);

radius = zeros(nPoints,1)+radius ;

azimuth = rand(size(radius)) * 2*pi;

elevation = (rand(size(radius)) .* pi)-pi/2;

[x,y,z] = sph2cart(azimuth,elevation,radius);

test_xyz(2:end,1) = test_xyz(1,1)+x;

test_xyz(2:end,2) = test_xyz(1,2)+y;

test_xyz(2:end,3) = test_xyz(1,3)+z;

p1 = 1:51;

p2 = 52:101;

figure

scatter3(test_xyz(p1,1),test_xyz(p1,2),test_xyz(p1,3), 10, 'b', 'filled');

hold on

scatter3(test_xyz(p2,1),test_xyz(p2,2),test_xyz(p2,3), 10, 'r', 'filled');

hold off

axis('equal')

I am not certain what you intend by ‘first 51’ and ‘last 50’, so I interpreted those literally to create ‘p1’ and ‘p2’.

.

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Tanmayee Pathre 2024-7-29

Thanks for your answer. But I have edited my question. I have updated the figure. The blue and red markers made my question unclear.

Star Strider 2024-7-30

在 MATLAB Online 中打开

If you want them regularly-spaced rather than random, just use the speere function and be done with it —

I = imread('Sphere_101.png');

imshow(I);

%Center of sphere

recPosition = [4.26 1.76 1.62];

% rng(0,'twister');

% radius = 0.25;

%

% %Number of points

% nPoints = 100;

%

% %Create array

% test_xyz = zeros(101,3);

%

% test_xyz(1,1) = recPosition(1);

% test_xyz(1,2) = recPosition(2);

% test_xyz(1,3) = recPosition(3);

%

% radius = zeros(nPoints,1)+radius ;

% % azimuth = rand(size(radius)) * 2*pi;

% % elevation = (rand(size(radius)) .* pi)-pi/2;

% azimuth = linspace(1E-4, 2*pi, numel(radius)).';

% elevation = linspace(pi/2, 1E-4, numel(radius)).';

%

% [x,y,z] = sph2cart(azimuth,elevation,radius);

%

% test_xyz(2:end,1) = test_xyz(1,1)+x;

% test_xyz(2:end,2) = test_xyz(1,2)+y;

% test_xyz(2:end,3) = test_xyz(1,3)+z;

[X,Y,Z] = sphere(100);

X = X + recPosition(1);

Y = Y + recPosition(2);

Z = Z + recPosition(3);

p1 = 1:51;

p2 = 52:101;

figure

scatter3(X(p1,:), Y(p1,:), Z(p1,:), 10, 'b', 'filled');

hold on

scatter3(X(p2,:), Y(p2,:), Z(p2,:), 10, 'r', 'filled');

hold off

axis('equal')

.

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EDITED : Generate sphere whose center is not at origin

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