MATLAB Answers

Rescale multiple spheres on the same 3d plot

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James Peach
James Peach on 5 Oct 2020
Commented: James Peach on 15 Oct 2020
I am trying to plot multipe spheres of different sizes on the same 3D plot. I'd like the spheres placed closest to the origin to be the largest and the smallest ones furtherest away. I've tried sending a vector into the function function to control how many faces the sphere will have, but I get this error. The line numebrs in the error code don't match up exaclty because I have commented out my previous attempts at fixing the problem that don't apply.
Error in sphere (line 29)
cosphi = cos(phi); cosphi(1) = 0; cosphi(n+1) = 0;
Error in BioM3D_SphereTest>createspheres (line 83)
[x, y, z] = sphere(n);
Error in BioM3D_SphereTest (line 71)
[x_loc,y_loc,z_loc, spheresXYZ{i}] = createspheres(FNA_x(i),FNA_y(i),FNA_z(i), n(i,1));
Below is my code. Any help or ideas would be appreciated.
clear
close
clc
A = [0,0,0;0.00977495601952172,0.0129188554738323,0.999868768093125;-0.566794094824837,-0.823750570492204,0.0133959578031223;0.0279587435128966,0.0380588867245362,1.99938731654588;0.830388266617646,0.583999369869120,0.978401571089338;-1.07826433834531,-1.64452537544960,0.267810795303313;0.168715496407312,0.263085998125572,2.96351922435162;-0.791458202545459,0.611268411797120,0.998070417818667;-1.41124221175034,-0.289407593850698,0.0506110237693017;1.69942938355116,1.04462646221878,1.15892918358242;-1.55216375501531,-2.44987966243271,0.623934110066297;0.188310075544404,0.501770043093754,3.93441879647330;-1.44603145623221,1.35107113546187,1.15371676572365;-2.35391403973316,0.0183196401577155,0.179737992978120;2.59879677816763,1.38804628951095,1.42948622326796;-1.92629974765512,-3.28302931738291,1.03122259685150;0.190461468181228,0.731318108759712,4.90771374511875;-2.01837467713375,2.14014570650778,1.37684130228734;-3.30531517848174,0.217844651708771,0.414313445558867;3.50709118523837,1.65551615551852,1.75113998255253;-2.23204460424917,-4.13488361866807,1.45650407075820;0.193343935566412,0.934427321909631,5.88686559182864;-2.51244231909718,2.97180232130260,1.63030617210704;-4.25650570961388,0.357419056329789,0.689550723301627;4.41845060685608,1.87363023778730,2.10021053665969];
x = A(:, 1);
y = A(:, 2);
z = A(:, 3);
% Create Hemisphere Domain
[x_dom,y_dom,z_dom] = sphere(80); %Create Sphere
x_dom = x_dom(41:end,:); % Keep top 41 x points
y_dom = y_dom(41:end,:); % Keep top 41 y points
z_dom = z_dom(41:end,:); % Keep top 41 z points
hemisphere_radius = 80;
figure();
Hemi_sf = surf(hemisphere_radius.*x_dom,hemisphere_radius.*y_dom,hemisphere_radius.*z_dom, 'FaceColor','#4DBEEE','EdgeColor', 'none');
alpha 0.2 %Sets transparency of boundary hemisphere
axis equal
x_ax_lab = xlabel('x axis', 'Color', '#4DBEEE');
y_ax_lab = ylabel('y axis', 'Color', '#4DBEEE');
z_ax_lab = zlabel('z axis', 'Color', '#4DBEEE');
% Plot Outerboundary Circular Plane
x_c = 0;
y_c = 0;
z_c = 0;
radii_plane = 80;
radii_vein = 1;
center_plane = [x_c, y_c]; % center point of circular plane
viscircles(center_plane, radii_plane, 'color', '#77AC30');
hold on
SizeofA = size(A,1);
FNA_x = A(:, 1);
FNA_y = A(:, 2);
FNA_z = A(:, 3);
n = [6.96370042788934;5.96370042788934;5.96370042788934;4.96375547570639;5.55378214243664;4.97904924545806;3.98374650974911;5.55083110747708;5.52220023318542;4.65666303595053;3.99715084015465;2.99294670513842;4.67296636191766;4.60286314806927;3.68897172789716;3.02005588750933;1.99814346506139;3.71566225784534;3.62540440258680;2.70847851108481;2.04428077071202;1;2.74447376195869;2.63691531214705;1.72499063143428];
% Create Spheres
for i = 1:SizeofA
[x_loc,y_loc,z_loc, spheresXYZ{i}] = createspheres(FNA_x(i),FNA_y(i),FNA_z(i), n(i,1));
h(i) = surf(x_loc, y_loc, z_loc,'FaceColor', 'k');
end
function [X,Y,Z,spheresXYZ] = createspheres(spherex, spherey, spherez, n)
[x, y, z] = sphere(n);
X = (x+spherex);
Y = (y+spherey);
Z = (z+spherez);
spheresXYZ = [X,Y,Z];
end

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Accepted Answer

Adam Danz
Adam Danz on 5 Oct 2020
Edited: Adam Danz on 5 Oct 2020
On the first iteration of the i-loop, n equals 6.9637.... This value is passed to sphere(n) and, as the error message indicates,
Array indices must be positive integers or logical values.
n is not an integer. In the function sphere(n), n determines the size of the outpus which can be understood as the resolution of the sphere. Matrix sizes must be positive integers.
Demo 1
To scale the size of the unit-spheres produced by sphere(n), simply multiply the x,y,z outputs by a scaling factor.
[x,y,z] = sphere(20);
clf()
hold on
surf(x,y,z,'FaceColor','b','FaceAlpha',.5)
surf(x*2,y*2,z*2,'FaceColor','r','FaceAlpha',.2)
view(3)
axis equal
grid on
Demo 2
Scale the size of n randomly placed spheres based on their distance from (0,0,0), marked by a black +.
rng(999) % for reproducibility purposes
nSpheres = 10; % Number of spheres
maxEccentricity = 100; % max distance of sphere center from (0,0)
[x,y,z] = sphere(20);
clf()
colors = jet(nSpheres);
hold on
view(3)
grid on
box on
plot3(x,y,z,'k+')
for i = 1:nSpheres
az = rand(1)*2*pi;
el = rand(1)*pi - (pi/2);
radius = randi(maxEccentricity+1)-1;
[sx,sy,sz] = sph2cart(az,el,radius);
surf(x*radius/3+sx, y*radius/3+sy, z*radius/3+sz, 'FaceColor', 'interp', 'FaceAlpha', .6, 'EdgeAlpha',.3);
end
axis equal
view([-46.943, 11.247])

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James Peach
James Peach on 15 Oct 2020
Hey Adam so I was able generate resized spheres but I am having trouble getting them to their actual locations instead of centered at 0,0,0. Here is what I have.
Edit: I think i fixed it by adding the points again to offset them in the surface command call, but is there any way to clean the spheres up so that they are more distinct?
Edit 2: I solved my clarity problem by rescaling the vector i used to resize them by dividing by the max value in the rescaling vector. So that all the other scaling values are a fraction of the largest value. Thanks again for all your help!
clear
close
clc
% A = 25 pts
%A = [0,0,0;0.00977495601952172,0.0129188554738323,0.999868768093125;-0.566794094824837,-0.823750570492204,0.0133959578031223;0.0279587435128966,0.0380588867245362,1.99938731654588;0.830388266617646,0.583999369869120,0.978401571089338;-1.07826433834531,-1.64452537544960,0.267810795303313;0.168715496407312,0.263085998125572,2.96351922435162;-0.791458202545459,0.611268411797120,0.998070417818667;-1.41124221175034,-0.289407593850698,0.0506110237693017;1.69942938355116,1.04462646221878,1.15892918358242;-1.55216375501531,-2.44987966243271,0.623934110066297;0.188310075544404,0.501770043093754,3.93441879647330;-1.44603145623221,1.35107113546187,1.15371676572365;-2.35391403973316,0.0183196401577155,0.179737992978120;2.59879677816763,1.38804628951095,1.42948622326796;-1.92629974765512,-3.28302931738291,1.03122259685150;0.190461468181228,0.731318108759712,4.90771374511875;-2.01837467713375,2.14014570650778,1.37684130228734;-3.30531517848174,0.217844651708771,0.414313445558867;3.50709118523837,1.65551615551852,1.75113998255253;-2.23204460424917,-4.13488361866807,1.45650407075820;0.193343935566412,0.934427321909631,5.88686559182864;-2.51244231909718,2.97180232130260,1.63030617210704;-4.25650570961388,0.357419056329789,0.689550723301627;4.41845060685608,1.87363023778730,2.10021053665969];
% A = 100 pts
A = [0,0,0;0.00977495601952172,0.0129188554738323,0.999868768093125;-0.566794094824837,-0.823750570492204,0.0133959578031223;0.0279587435128966,0.0380588867245362,1.99938731654588;0.830388266617646,0.583999369869120,0.978401571089338;-1.07826433834531,-1.64452537544960,0.267810795303313;0.168715496407312,0.263085998125572,2.96351922435162;-0.791458202545459,0.611268411797120,0.998070417818667;-1.41124221175034,-0.289407593850698,0.0506110237693017;1.69942938355116,1.04462646221878,1.15892918358242;-1.55216375501531,-2.44987966243271,0.623934110066297;0.188310075544404,0.501770043093754,3.93441879647330;-1.44603145623221,1.35107113546187,1.15371676572365;-2.35391403973316,0.0183196401577155,0.179737992978120;2.59879677816763,1.38804628951095,1.42948622326796;-1.92629974765512,-3.28302931738291,1.03122259685150;0.190461468181228,0.731318108759712,4.90771374511875;-2.01837467713375,2.14014570650778,1.37684130228734;-3.30531517848174,0.217844651708771,0.414313445558867;3.50709118523837,1.65551615551852,1.75113998255253;-2.23204460424917,-4.13488361866807,1.45650407075820;0.193343935566412,0.934427321909631,5.88686559182864;-2.51244231909718,2.97180232130260,1.63030617210704;-4.25650570961388,0.357419056329789,0.689550723301627;4.41845060685608,1.87363023778730,2.10021053665969;-2.47842156351806,-4.99324597672323,1.90651791078471;0.204283419234320,1.13357858075284,6.86677329350173;0.617793464714887,0.0559247730198438,6.10612769252045;-2.96417360323821,3.81704174520463,1.91580426879081;-5.20242439373799,0.476408999682868,0.991344090368801;5.32672360772571,2.06445068867013,2.47253796167180;-2.69346338350278,-5.85030685131976,2.37470982965291;0.218591936197924,1.32878562119851,7.84743096960627;-3.26247612265381,-4.91985596911837,1.29018005288354;1.20197539596291,-0.580347098756520,6.61000225666269;-3.37592827171665,4.67443410026770,2.22457026832058;-6.14584567995603,0.584770610127789,1.30473528056482;6.23299868743130,2.22581272192086,2.86321400922248;-2.89467385558292,-6.70726873056154,2.84918921113506;0.209717491582492,1.53184472980862,8.82655723451965;5.28440710514136,1.17097130314088,2.91964410258613;0.576278852478300,2.24513662818586,7.66753960818188;-4.04653068178957,-4.84646596151352,0.673842194982372;1.72465217643194,-1.18852390077965,7.20743841278270;-3.76500316313530,5.53715317053961,2.54758193166533;-7.08499357301506,0.666849489054822,1.63829830698843;7.13773556686645,2.38268963160310,3.25924533904186;-3.08850223839479,-7.56458389242937,3.32609724340970;0.176682672356017,1.77636612069925,9.79563823738556;5.70892694024996,0.283366758099107,3.09836478191717;0.834848920291403,3.20098548783449,7.80716223363894;2.23645813228566,-1.80307906039568,7.80775218019269;-4.13663420978661,6.40608142770811,2.87446730769027;-8.01389420090031,0.739303774953617,2.00147044244114;8.04005085003118,2.54735749010561,3.65763161659614;-3.28567882346993,-8.41947317913047,3.80597816799600;0.151573909742903,2.03767830086445,10.7605659520551;-6.82918401328041,0.278600280775844,2.52363667248442;-3.41363523840503,-7.08870431609608,4.14330417016278;6.35396040499232,-0.474663609164808,3.19491420795479;1.06216210967955,4.10256481833496,8.17524296492560;2.75275937858220,-2.40442829800382,8.41751616527277;-4.49887555491066,7.27474744137621,3.21240304800297;-8.93747200633802,0.809847032829654,2.37833604988111;8.93679366464217,2.75035659507643,4.05087923302196;-3.49679202503365,-9.27121011623096,4.28553567873291;0.120474891403918,2.30220475044321,11.7244428158357;-6.57337445354577,-0.109648927503134,3.40897503798041;-3.90131441220521,-6.94494653825290,5.00440969491056;7.05097560070378,-1.18529470189817,3.29069138158143;1.32262284552297,4.97356081042056,8.59180771001900;3.28964279764057,-2.99261263184027,9.02232637002263;-4.85227421135047,8.14355948795292,3.55920993569369;-9.85594939518955,0.878289437178573,2.76784204913582;9.82550611659926,2.98592839011066,4.44419349302377;-3.72248319429006,-10.1171476702764,4.76870557719025;0.0788524583019931,2.54046289454804,12.6947523694476;2.70499218347696,-3.21391766868317,7.83232794441650;-2.84203085926377,-9.70887276953909,3.66930583711619;-6.31756489381112,-0.497898135782113,4.29431340347640;-4.51675110863053,-6.94038338635526,5.79258280428302;7.75826716048403,-1.87839080959415,3.42981878707837;1.60739083428736,5.83327554833172,9.01583337197052;3.81380630124427,-3.57090289370221,9.64749274349896;-5.21110077179350,9.00941019096056,3.90784450027642;-10.7701023523524,0.936847376158581,3.16895966118096;10.7111773842992,3.23085322898537,4.83865290649108;-3.95158917741763,-10.9629681728992,5.25047121091495;0.0248941422755761,2.76290060345524,13.6682049701363;-3.96468559986903,8.59207273742804,3.45422268973630;-4.53038653298116,-10.2195319906366,4.18835254129213;-0.734431529015096,3.08504028776024,12.4898020857790;-2.18726969349390,-10.1465354228472,3.05307599549947;-5.19378789303215,-7.06258274529947,6.51831588830272;8.48339326062922,-2.55215288868641,3.57207489297718;1.87742850700644,6.69346716517060,9.44844178339196;4.34166392226097,-4.13247115672692,10.2846798572246;-5.56586475306079,9.87609452074379,4.25855918503254;-11.6790955983398,1.00013474235130,3.58093780141378;11.5912722790929,3.48104407126623,5.24218421704439];
x = A(:, 1);
y = A(:, 2);
z = A(:, 3);
x_c = 0;
y_c = 0;
z_c = 0;
Center_Root = [x_c, y_c, z_c];
[x_dom,y_dom,z_dom] = sphere(80); % Create Sphere
x_dom = x_dom(41:end,:); % Keep top 41 x points
y_dom = y_dom(41:end,:); % Keep top 41 y points
z_dom = z_dom(41:end,:); % Keep top 41 z points
hemisphere_radius = 80;
figure();
Hemi_sf = surf(hemisphere_radius.*x_dom,hemisphere_radius.*y_dom,hemisphere_radius.*z_dom, 'FaceColor','#4DBEEE','EdgeColor', 'none');
alpha 0.2
hold on
radii_plane = 80;
center_plane = [x_c, y_c]; % center point of circular plane
viscircles(center_plane, radii_plane, 'color', '#77AC30');
dist1a = pdist2(A,Center_Root);
s = (max(dist1a) - dist1a + 1);
s = s./max(dist1a);
SizeofA = size(A,1);
% Create Spheres
axis equal
x_ax_lab = xlabel('x axis', 'Color', '#4DBEEE');
y_ax_lab = ylabel('y axis', 'Color', '#4DBEEE');
z_ax_lab = zlabel('z axis', 'Color', '#4DBEEE');
for i = 1:SizeofA
[x_loc,y_loc,z_loc, spheresXYZ{i}] = createspheres(x(i),y(i),z(i), s(i));
h(i) = surf(x_loc+x(i), y_loc+y(i), z_loc+z(i), 'FaceColor', 'interp', 'FaceAlpha', .5);
end
%view([-46.943, 11.247]);
%%
for i = 1:SizeofA
Bx{i}= h(i).XData;
By{i} = h(i).YData;
Bz{i} = h(i).ZData;
end
Bx = cell2mat(Bx);
By = cell2mat(By);
Bz = cell2mat(Bz);
%%
% Call Surf2stl
%surf2stl('extracttest.stl',Bx,By,Bz);
%%
function [X,Y,Z,spheresXYZ] = createspheres(spherex, spherey, spherez, s)
[x, y, z] = sphere(11);
X = (s*x)+spherex;
Y = (s*y)+spherey;
Z = (s*z)+spherez;
spheresXYZ = [X,Y,Z];
end
Adam Danz
Adam Danz on 15 Oct 2020
" is there any way to clean the spheres up so that they are more distinct?"
You could use color
% Define colormap
cmap = jet(SizeofA);
for i = 1:SizeofA
[x_loc,y_loc,z_loc, spheresXYZ{i}] = createspheres(x(i),y(i),z(i), s(i));
h(i) = surf(x_loc+x(i), y_loc+y(i), z_loc+z(i), 'FaceColor', cmap(i,:), ...
'FaceAlpha', .5, 'EdgeColor', 'k', 'EdgeAlpha', .5);
end
And you could zoom into the spheres
xlim([min(Bx(:)),max(Bx(:))])
ylim([min(By(:)),max(By(:))])
zlim([min(Bz(:)),max(Bz(:))])
view([-43,38])
James Peach
James Peach on 15 Oct 2020
Thank you the color map enhances the image immensely!

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