3D Sphere projection in Matlab

Hi to all,

I have a problem making sphere projection in Matlab. I have a lot of horizontal (i = 1:360) and vertical (j = 1:180) values that represents a distance between the geometric center of an object and the outher limit of the bubble. I am using the mesh function and it shows perfect results but only in 2D projection. Also, I am using formula (see below) to transform the spherical coordinates to Cartesien coordinates. After this tranformation, the result is half-sphere design that is not suitable for my presentation and also it is much harder to understand the results. The result should be presented as irregular bubble around the object (center of the coordinate system, position 0-0-0).

Is there any possible way to make full sphere using my values (mentioned "i" and "j")?

sph2cart formula

n=1;
for i=1:360
    for j=1:180
        [x(n), y(n), z(n)] = sph2cart(deg2rad(i),deg2rad(j),final_results(j,i));
        n=n+1;
    end
end

x_int = linspace(min(x),max(x));
y_int = linspace(min(y),max(y));

[X, Y] = meshgrid(x_int,y_int);
Z = griddata(x,y,z, X,Y, 'cubic');
surf(X,Y,Z)

Answer 1

[darova]

interpolate in spherical coordinates

i = rand(20,1);
j = rand(20,1);
r = 1 + 0.1*rand(20,1);
i1 = linspace(min(i),max(i),30);
j1 = linspace(min(j),max(j),30);
[I,J] = meshgrid(i1,j1);            % fine mesh
R = griddata(i,j,r,I,J);            % interpolate in spherical system
[x,y,z] = sph2cart(I,J,R);          % convert to cartesian
[x1,y1,z1] = sph2cart(i,j,r);
[xs,ys,zs] = sphere(30);
plot3(x1,y1,z1,'.r')
surface(x,y,z)
surface(xs,ys,zs,'facecolor','none','edgecolor',ones(1,3)*0.3)
view(45,45)
axis equal

[Dominik Jerinic]

Thank you for your effort but maybe I don't understand this code you sent that good that I can use it in my case. Other solution below seems much easier so I will try use that if possible.

Answer 2

[Star Strider]

I worked on this for a while yesterday, without success. Today, I used a relatively straightforward approach that simply flips ‘Z’ by subtracting it from the minimum of the existing ‘Z’, and then plotting it on the same axes.

See if this does what you want with your ‘final_results’ matrix —

final_results = 1 + rand(180,360)/10;

n=1;
for i=1:360
    for j=1:180
        [x(n), y(n), z(n)] = sph2cart(deg2rad(i),deg2rad(j),final_results(j,i));
        n=n+1;
    end
end

x_int = linspace(min(x),max(x));
y_int = linspace(min(y),max(y));

[X, Y] = meshgrid(x_int,y_int);
Z = griddata(x,y,z, X,Y, 'cubic');

Warning: Duplicate x-y data points detected: using average values for duplicate points.

figure
surf(X,Y,Z)
hold on
surf(X,Y,min(Z(:))-Z)
hold off
view(30,30)
axis('equal')
title('Original View')

figure
surf(X,Y,Z)
hold on
surf(X,Y,min(Z(:))-Z)
hold off
view(45,90)
axis('equal')
title('Oblique Top View')

figure
surf(X,Y,Z)
hold on
surf(X,Y,min(Z(:))-Z)
hold off
view(45,0)
axis('equal')
title('Oblique Side View')

Experiment to get different results.

.

[Star Strider]

I still have no idea what you want.

Try this —

x_bl = 2; 
y_bl = 1; 
z_bl = 0.5; 
V_bl = -5; 
V_bl_v = 0; 
mi = 0; 
URE_sop_h = 0.715;
URE_sop_v = 0.5; 
O_poz = 10; 

 
%% 1. layer

gs_bl = zeros (180, 360); 
xy_bl_max = max (x_bl, y_bl);  
d_first_layer = max (xy_bl_max, z_bl) / 2; 
first_layer = gs_bl + d_first_layer;
 

%% 2. layer

if V_bl == 0
    V_bl_h = 0; 
elseif V_bl > 0
    V_bl_h = (V_bl^2 - V_bl_v^2)^0.5; 
elseif V_bl < 0
    V_bl_h = - (V_bl^2 - V_bl_v^2)^0.5;
end


Vjer_p_h = (URE_sop_h / 2 * 6) + mi; 
G_p_h_max = abs(V_bl_h) / O_poz; 


Vjer_p_v = (URE_sop_v / 2 * 6) + mi; 
G_p_v_max = abs(V_bl_v) / O_poz; 


if V_bl >= 0
    for i = 1:360  
        for j = 1:180 
            if i >= 270 || i <= 90
                if j <= 90 && V_bl_v >= 0
                    G_p_h (i) = Vjer_p_h + cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v + cosd (j) * G_p_v_max;
                elseif j < 90 && V_bl_v < 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j > 90 && V_bl_v > 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j >= 90 && V_bl_v <= 0
                    G_p_h (i) = Vjer_p_h + cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v - cosd(j) * G_p_v_max;
                end
            else G_p_h (i) = Vjer_p_h;
                G_p_v (j) = Vjer_p_v;
            end
            G_p_hv (j,i) = (G_p_h (i)^2 + G_p_v (j)^2)^0.5; 
            second_layer (j,i) = first_layer (j,i) + G_p_hv (j,i);
        end
    end
else 
    for i = 1:360
        for j = 1:180
            if i <= 270 && i >= 90
                if j <= 90 && V_bl_v >= 0
                    G_p_h (i) = Vjer_p_h - cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v + cosd (j) * G_p_v_max;
                elseif j < 90 && V_bl_v < 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j > 90 && V_bl_v > 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j >= 90 && V_bl_v <= 0
                    G_p_h (i) = Vjer_p_h - cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v - cosd (j) * G_p_v_max;
                end
            else G_p_h (i) = Vjer_p_h;
                G_p_v (j) = Vjer_p_v;
            end
            G_p_hv (j,i) = (G_p_h (i)^2 + G_p_v (j)^2)^0.5;
            second_layer (j,i) = first_layer (j,i) + G_p_hv (j,i);
        end
    end
end


% 2D graphics
mesh (1:360, 1:180, second_layer)
title ('final\_results')

% 3D graphics
n=1;
for i=1:360
    for j=1:180
        [x(n), y(n), z(n)] = sph2cart(deg2rad(i),deg2rad(j),second_layer(j,i));
        n=n+1;
    end
    
end

x_int = linspace(min(x),max(x), 1000);
y_int = linspace(min(y),max(y), 1000);

[X, Y] = meshgrid(x_int,y_int);
Z = griddata(x,y,z, X,Y, 'cubic');

Warning: Duplicate x-y data points detected: using average values for duplicate points.

surf(X,Y,Z, 'EdgeColor','none')
axis('equal')

% THIS 2D FORMULA MAKES PERFECT RESULTS. WHEN YOU CHANGE "V_bl" FROM 5 TO
% -5 RESULT IS AS EXPECTED.

% THIS 3D GRAPHICS FORMULA MAKE HALF-SPHERE BUBBLE AND I NEED FULL-SPHERE
% IRREGULAR BUBBLE ACCORDING TO GIVEN VALUES. WHEN YOU CHANGE "V_bl" FROM 5 TO
% -5 RESULT IS INCORRECT BECAUSE I GET THE SAME SHAPE.

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y, min(Z(:))-Z+0.5, 'EdgeColor','none')
hold off
view(30,30)
axis('equal')
title('Original View')

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y,min(Z(:))-Z+0.5, 'EdgeColor','none')
hold off
view(45,90)
axis('equal')
title('Oblique Top View')

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y,min(Z(:))-Z+0.5, 'EdgeColor','none')
hold off
view(45,0)
axis('equal')
title('Oblique Side View')

.

[Dominik Jerinic]

I am looking to present my results with BUBBLECHART3 if possible. I don't know how to explain you with more detail but if you have time we can arrange Teams meeting if possible?

[Star Strider]

I have never used bubblechart3, however looking at the documentation, it appears to be a version of scatter3. If you have more of these spheres and want to put them in different locations, the only requirement is to translate the coordinates by adding constant values to them.

Example —

x_bl = 2; 
y_bl = 1; 
z_bl = 0.5; 
V_bl = -5; 
V_bl_v = 0; 
mi = 0; 
URE_sop_h = 0.715;
URE_sop_v = 0.5; 
O_poz = 10; 

 
%% 1. layer

gs_bl = zeros (180, 360); 
xy_bl_max = max (x_bl, y_bl);  
d_first_layer = max (xy_bl_max, z_bl) / 2; 
first_layer = gs_bl + d_first_layer;
 

%% 2. layer

if V_bl == 0
    V_bl_h = 0; 
elseif V_bl > 0
    V_bl_h = (V_bl^2 - V_bl_v^2)^0.5; 
elseif V_bl < 0
    V_bl_h = - (V_bl^2 - V_bl_v^2)^0.5;
end


Vjer_p_h = (URE_sop_h / 2 * 6) + mi; 
G_p_h_max = abs(V_bl_h) / O_poz; 


Vjer_p_v = (URE_sop_v / 2 * 6) + mi; 
G_p_v_max = abs(V_bl_v) / O_poz; 


if V_bl >= 0
    for i = 1:360  
        for j = 1:180 
            if i >= 270 || i <= 90
                if j <= 90 && V_bl_v >= 0
                    G_p_h (i) = Vjer_p_h + cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v + cosd (j) * G_p_v_max;
                elseif j < 90 && V_bl_v < 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j > 90 && V_bl_v > 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j >= 90 && V_bl_v <= 0
                    G_p_h (i) = Vjer_p_h + cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v - cosd(j) * G_p_v_max;
                end
            else G_p_h (i) = Vjer_p_h;
                G_p_v (j) = Vjer_p_v;
            end
            G_p_hv (j,i) = (G_p_h (i)^2 + G_p_v (j)^2)^0.5; 
            second_layer (j,i) = first_layer (j,i) + G_p_hv (j,i);
        end
    end
else 
    for i = 1:360
        for j = 1:180
            if i <= 270 && i >= 90
                if j <= 90 && V_bl_v >= 0
                    G_p_h (i) = Vjer_p_h - cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v + cosd (j) * G_p_v_max;
                elseif j < 90 && V_bl_v < 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j > 90 && V_bl_v > 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j >= 90 && V_bl_v <= 0
                    G_p_h (i) = Vjer_p_h - cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v - cosd (j) * G_p_v_max;
                end
            else G_p_h (i) = Vjer_p_h;
                G_p_v (j) = Vjer_p_v;
            end
            G_p_hv (j,i) = (G_p_h (i)^2 + G_p_v (j)^2)^0.5;
            second_layer (j,i) = first_layer (j,i) + G_p_hv (j,i);
        end
    end
end


% 2D graphics
mesh (1:360, 1:180, second_layer)
title ('final\_results')

% 3D graphics
n=1;
for i=1:360
    for j=1:180
        [x(n), y(n), z(n)] = sph2cart(deg2rad(i),deg2rad(j),second_layer(j,i));
        n=n+1;
    end
    
end

x_int = linspace(min(x),max(x), 1000);
y_int = linspace(min(y),max(y), 1000);

[X, Y] = meshgrid(x_int,y_int);
Z = griddata(x,y,z, X,Y, 'cubic');

Warning: Duplicate x-y data points detected: using average values for duplicate points.

surf(X,Y,Z, 'EdgeColor','none')
axis('equal')

% THIS 2D FORMULA MAKES PERFECT RESULTS. WHEN YOU CHANGE "V_bl" FROM 5 TO
% -5 RESULT IS AS EXPECTED.

% THIS 3D GRAPHICS FORMULA MAKE HALF-SPHERE BUBBLE AND I NEED FULL-SPHERE
% IRREGULAR BUBBLE ACCORDING TO GIVEN VALUES. WHEN YOU CHANGE "V_bl" FROM 5 TO
% -5 RESULT IS INCORRECT BECAUSE I GET THE SAME SHAPE.

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y, min(Z(:))-Z+0.5, 'EdgeColor','none')
surf(X+5,Y+5,Z+5, 'EdgeColor','none')
surf(X+5,Y+5, (min(Z(:))-Z+0.5)+5, 'EdgeColor','none')
hold off
view(30,30)
axis('equal')
title('Original View With Two Spheres')

% figure
% surf(X,Y,Z, 'EdgeColor','none')
% hold on
% surf(X,Y,min(Z(:))-Z+0.5, 'EdgeColor','none')
% hold off
% view(45,90)
% axis('equal')
% title('Oblique Top View')
% 
% figure
% surf(X,Y,Z, 'EdgeColor','none')
% hold on
% surf(X,Y,min(Z(:))-Z+0.5, 'EdgeColor','none')
% hold off
% view(45,0)
% axis('equal')
% title('Oblique Side View')

.

[Dominik Jerinic]

I have only one bubble (sphere) but according to results, I should have flat and smooth outher edge of the sphere in backward direction and irregular shape in front side (from 0° vertical position up and down 90°, and also 90° left and right from the 0° horizontal position). If you use mesh function for the code I sent you, you will be able to see which are should be irregular or at more distance from the center. I hope I am explaining this correct because the sphere is really complex.

[Star Strider]

I am completely lost.

I have done th best I can, and I am stopping here.

.

[Dominik Jerinic]

I will thank you again for your effort. You did a great job and now I have some more codes to think about. Unfortunately, those codes are not satisfied for my project but I will try to figure out something. If you get to some new idea please share with me, I will be very thankful. Best regards.

[Star Strider]

My pleasure!

One final attempt —

x_bl = 2; 
y_bl = 1; 
z_bl = 0.5; 
V_bl = -5; 
V_bl_v = 0; 
mi = 0; 
URE_sop_h = 0.715;
URE_sop_v = 0.5; 
O_poz = 10; 

 
%% 1. layer

gs_bl = zeros (180, 360); 
xy_bl_max = max (x_bl, y_bl);  
d_first_layer = max (xy_bl_max, z_bl) / 2; 
first_layer = gs_bl + d_first_layer;
 

%% 2. layer

if V_bl == 0
    V_bl_h = 0; 
elseif V_bl > 0
    V_bl_h = (V_bl^2 - V_bl_v^2)^0.5; 
elseif V_bl < 0
    V_bl_h = - (V_bl^2 - V_bl_v^2)^0.5;
end


Vjer_p_h = (URE_sop_h / 2 * 6) + mi; 
G_p_h_max = abs(V_bl_h) / O_poz; 


Vjer_p_v = (URE_sop_v / 2 * 6) + mi; 
G_p_v_max = abs(V_bl_v) / O_poz; 


if V_bl >= 0
    for i = 1:360  
        for j = 1:180 
            if i >= 270 || i <= 90
                if j <= 90 && V_bl_v >= 0
                    G_p_h (i) = Vjer_p_h + cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v + cosd (j) * G_p_v_max;
                elseif j < 90 && V_bl_v < 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j > 90 && V_bl_v > 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j >= 90 && V_bl_v <= 0
                    G_p_h (i) = Vjer_p_h + cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v - cosd(j) * G_p_v_max;
                end
            else G_p_h (i) = Vjer_p_h;
                G_p_v (j) = Vjer_p_v;
            end
            G_p_hv (j,i) = (G_p_h (i)^2 + G_p_v (j)^2)^0.5; 
            second_layer (j,i) = first_layer (j,i) + G_p_hv (j,i);
        end
    end
else 
    for i = 1:360
        for j = 1:180
            if i <= 270 && i >= 90
                if j <= 90 && V_bl_v >= 0
                    G_p_h (i) = Vjer_p_h - cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v + cosd (j) * G_p_v_max;
                elseif j < 90 && V_bl_v < 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j > 90 && V_bl_v > 0
                    G_p_h (i) = Vjer_p_h;
                    G_p_v (j) = Vjer_p_v;
                elseif j >= 90 && V_bl_v <= 0
                    G_p_h (i) = Vjer_p_h - cosd (i) * G_p_h_max;
                    G_p_v (j) = Vjer_p_v - cosd (j) * G_p_v_max;
                end
            else G_p_h (i) = Vjer_p_h;
                G_p_v (j) = Vjer_p_v;
            end
            G_p_hv (j,i) = (G_p_h (i)^2 + G_p_v (j)^2)^0.5;
            second_layer (j,i) = first_layer (j,i) + G_p_hv (j,i);
        end
    end
end


% 2D graphics
mesh (1:360, 1:180, second_layer)
title ('final\_results')

% 3D graphics
n=1;
for i=1:360
    for j=1:180
        [x(n), y(n), z(n)] = sph2cart(deg2rad(i),deg2rad(j),second_layer(j,i));
        n=n+1;
    end
    
end

x_int = linspace(min(x),max(x), 1000);
y_int = linspace(min(y),max(y), 1000);

[X, Y] = meshgrid(x_int,y_int);
Z = griddata(x,y,z, X,Y, 'cubic');

Warning: Duplicate x-y data points detected: using average values for duplicate points.

surf(X,Y,Z, 'EdgeColor','none')
axis('equal')

% THIS 2D FORMULA MAKES PERFECT RESULTS. WHEN YOU CHANGE "V_bl" FROM 5 TO
% -5 RESULT IS AS EXPECTED.

% THIS 3D GRAPHICS FORMULA MAKE HALF-SPHERE BUBBLE AND I NEED FULL-SPHERE
% IRREGULAR BUBBLE ACCORDING TO GIVEN VALUES. WHEN YOU CHANGE "V_bl" FROM 5 TO
% -5 RESULT IS INCORRECT BECAUSE I GET THE SAME SHAPE.

lower_half = 4.25*ones(180,360);

n=1;
for i=1:360
    for j=1:180
        [x(n), y(n), z2(n)] = sph2cart(deg2rad(i),deg2rad(j),lower_half(j,i));
        n=n+1;
    end
end

x_int = linspace(min(x),max(x), 1000);
y_int = linspace(min(y),max(y), 1000);

[X, Y] = meshgrid(x_int,y_int);
Z2 = griddata(x,y,z2, X,Y, 'cubic');

Warning: Duplicate x-y data points detected: using average values for duplicate points.

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y, min(Z(:))-Z2+0.6, 'EdgeColor','none')
hold off
view(30,30)
axis('equal')
title('Original View')

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y,min(Z(:))-Z2+0.6, 'EdgeColor','none')
hold off
view(45,90)
axis('equal')
title('Oblique Top View')

figure
surf(X,Y,Z, 'EdgeColor','none')
hold on
surf(X,Y,min(Z(:))-Z2+0.6, 'EdgeColor','none')
hold off
view(45,0)
axis('equal')
title('Oblique Side View')

This provides a smooth lower half, however the circumferences do not exactly match, so I leave that for you to resolve, since I have never been able to figure out how your code works.

This is the best I can do, and my final effort.

.

Answer 3

[Dominik Jerinic]

Thank you for your effort but the upper and lower half-sphere shows the same results even my values are not the same. Maybe there is an errot in the code you sent me or there are some adjustments needed inside the code to show the correct picture. Also, I don't know how to solve the problem of the blank space in the horizontal line 0 (see picture above you posted). In the code, I put i = 1:360 and j = 1:180 values so the i = 0 and j = 0 are blank spots. :( Or maybe it is something in my code but when I am using "mesh" function, everything is great.

[Star Strider]

I do not have your ‘final_results’ matrix (that I assume is (180x360), since that is how you are addressing it), so I cannot determine what the problem is.

My impression is that your matrix depicts half a sphere, and that you want to plot the whole sphere. I assume that you want a mirror image of the data you have, reflected so that it becomes two symmetric hemispheres, and my code does exactly that.

I need to have the ‘final results’ matrix to work with if you want me to help you with it.

.

[Dominik Jerinic]

My final_results matrix is 180x360 as you said. If we are looking the "i" values, 0 and 360 represents to position right in front of the object (0° or 360°), 90 represents the position exacly to the right side (90° to the right), 180 represents position on the back (backside) and 270 represents position exacly to the left side (90° to the left). If we are looking the "j" values, 0 represents vertical position overhead (+90° pitch), 90 represents the horizontal position (0° pitch) and 180 represents vertical position underground (-90° pitch). So that means that I covered every single degree in horizotal and vertical axis so I should have enough values to make irregular bubble. As you asked, I am sending you the final_result matrix in attachment. It will help me a lot to proceed with my work so I thank you in advance.