Plot area with equation
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Alex Lee
on 17 Jul 2020
Commented: Alex Lee
on 18 Jul 2020
Hello everyone,
I want to plot an area on a sphere, which is defined with the following equations:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/333243/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/333645/image.png)
R = 50
could somebody help?
Best regards
Alex
0 Comments
Accepted Answer
Abdolkarim Mohammadi
on 17 Jul 2020
Edited: Abdolkarim Mohammadi
on 18 Jul 2020
r = 50;
NumPoints = 500;
[UnitX,UnitY,UnitZ] = sphere (NumPoints);
RealX = r * UnitX;
RealY = r * UnitY;
RealZ = r * UnitZ;
x = RealX(:);
y = RealY(:);
z = RealZ(:);
Mask = 2.*y .* (sqrt(r.^2-x.^2-y.^2)./(r.^2)).* sind(15) ...
+ ((r.^2-2*x.^2-2*y.^2)./(r.^2)) .* cosd(15) ...
>= cosd(5.8);
% ----------------
figure ('Position', [62,182,1172,338]);
MaskPatchPositive = all ([Mask,z>0], 2);
MaskPatchNegative = all ([Mask,z<0], 2);
% ----------------
subplot (1,3, 1);
hold on
surf (RealX,RealY,RealZ, ...
'EdgeAlpha', 0.05, ...
'FaceAlpha', 0.05);
scatter3 (x(Mask),y(Mask),z(Mask),9, ...
'MarkerEdgeColor', 'none', ...
'MarkerFaceColor', 'r');
hold off
view ([-35,45]);
grid ('on');
box ('on');
daspect ('auto');
ax = gca;
ax.BoxStyle = 'full';
title ('All points');
% ----------------
subplot (1,3, 2);
hold on
surf (RealX,RealY,RealZ, ...
'EdgeAlpha', 0.1, ...
'FaceAlpha', 0.1);
scatter3 (x(MaskPatchPositive),y(MaskPatchPositive),z(MaskPatchPositive),9, ...
'MarkerEdgeColor', 'none', ...
'MarkerFaceColor', 'r');
hold off
xlim ([-5,5]);
ylim ([0,15]);
zlim ([45,50]);
grid ('on');
box ('on');
daspect ([1,1,1]);
view ([-60,30]);
ax = gca;
ax.BoxStyle = 'full';
title ('Upper part');
% ----------------
subplot (1,3, 3);
hold on
surf (RealX,RealY,RealZ, ...
'EdgeAlpha', 0.1, ...
'FaceAlpha', 0.1);
scatter3 (x(MaskPatchNegative),y(MaskPatchNegative),z(MaskPatchNegative),9, ...
'MarkerEdgeColor', 'none', ...
'MarkerFaceColor', 'r');
hold off
xlim ([-5,5]);
ylim ([0,15]);
zlim ([-50,-45]);
grid ('on');
box ('on');
daspect ([1,1,1]);
view ([-60,30]);
ax = gca;
ax.BoxStyle = 'full';
title ('Lower part');
3 Comments
Abdolkarim Mohammadi
on 18 Jul 2020
Edited: Abdolkarim Mohammadi
on 18 Jul 2020
You are right. I read the post again and realized that I wrote the condition for = cos(5.8) mistakenly, instead of >= cos(5.8). I revised the code and plots and there is no need for Epsilon anymore. You can increase NumPoints to get better accuracy. If the new code is correct, please mark it as the accepted answer. Thanks.
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