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fcnuniformsphere.m
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fcnuniformsphere.m
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function [cc, az1, el1, naz, nel, elazCells, elvec, azvec] = fcnuniformsphere(nel,naz,plotflag)
%cc = x y z unit vectors that make up a uniform sphere
if nargin==2
plotflag = false;
elseif nargin==0
nel = 11;
naz = 23;
plotflag = false;
end
if mod(naz,2)==0
naz = naz+1;
end
if mod(nel,2)==0
nel = nel+1;
end
elvec = linspace(-pi/2,pi/2,nel);
azvec = linspace(-pi,pi,naz);
azvec(ceil(naz/2)) = 0;
elvec(ceil(nel/2)) = 0;
[azu, elu] = meshgrid(azvec,elvec);
np = size(azu,2)*size(elu,1);
az0 = reshape(azu,np,1);
el0 = reshape(elu,np,1);
leftlim = -pi*cos(el0);
rightlim = pi*cos(el0);
v1 = find(az0>=leftlim & az0<=rightlim);
el1 = el0(v1);
az1 = az0(v1);
az1 = az1./cos(el1);
cc = fcnSC2CC(1,el1,az1);
%az per el row
elazCells = cell(1,nel);
for i = 1:nel
el = elvec(i);
saz = azvec./cos(el);
v1 = saz>=-pi & saz<pi;
elazCells{i} = azvec(v1)/cos(elvec(i));
end
if plotflag
fig(2,2,3,1.5);
subplot(221);
plot(az0,el0,'m.'); hold on
y1 = (-pi/2):pi/20:(pi/2);
x1 = -pi*cos(y1);
plot(x1,y1,'g','LineWidth',3)
y2 = (-pi/2):pi/20:(pi/2);
x2 = pi*cos(y2);
plot(x2,y2,'r','LineWidth',3)
axis equal tight;
v1 = find(az0>=leftlim & az0<=rightlim);
el1 = [el0(v1); -pi/2; pi/2];
az1 = [az0(v1); 0; 0];
plot(az1,el1,'.b','MarkerSize',20)
xlabel('Az*cos(El) (rad)'); ylabel('El (rad)'); title('Sinusoidal Projection')
set(gca,'XTick',-4*pi:pi:4*pi,'XTickLabel',{'-4pi','-3pi','-2pi','-pi','0','pi','2pi','3pi','4pi'})
set(gca,'YTick',-pi/2:pi/4:pi/2,'YTickLabel',{'-pi/2','-pi/4','0','pi/4','pi/2'})
subplot(212);
az1 = az1./cos(el1);
az0 = az0./cos(el0);
v1 = find(abs(az0)<(6*pi));
plot(az0(v1),el0(v1),'.m'); hold on
plot(az1,el1,'.b','MarkerSize',20);
plot(x2./cos(y2),y2,'r','LineWidth',5)
plot(x1./cos(y1),y1,'g','LineWidth',5)
axis equal tight;
xlabel('Az (rad)'); ylabel('El (rad)'); title('Mercator Projection')
set(gca,'XTick',-4*pi:pi:4*pi,'XTickLabel',{'-4pi','-3pi','-2pi','-pi','0','pi','2pi','3pi','4pi'})
set(gca,'YTick',-pi/2:pi/4:pi/2,'YTickLabel',{'-pi/2','-pi/4','0','pi/4','pi/2'})
subplot(222);
[x,y,z] = sphere(30); surf(x,y,z,'EdgeColor','w','FaceColor',[.7 .7 .7]); hold on
cc3 = fcnSC2CC([ones(numel(v1),1) el0(v1) az0(v1)]);
plot3(cc3(:,1),cc3(:,2),cc3(:,3),'m.','MarkerSize',10); axis tight equal vis3d; grid off; box on
plot3(cc(:,1),cc(:,2),cc(:,3),'b.','MarkerSize',20);
cc1 = fcnSC2CC([ones(numel(y1),1)*1.02 y1' (x1./cos(y1))'+.03]);
cc2 = fcnSC2CC([ones(numel(y2),1)*1.02 y2' (x2./cos(y2))'-.03]);
plot3(cc1(:,1),cc1(:,2),cc1(:,3),'g','LineWidth',5)
plot3(cc2(:,1),cc2(:,2),cc2(:,3),'r','LineWidth',5)
xlabel('X'); ylabel('Y'); zlabel('Z'); set(gca,'YDir','reverse','ZDir','reverse'); title('3D Sphere')
end
% cc = [ -0.747652890184928 -0.321586967393372 -0.581030961482139
% 0.313090254120263 -0.840625615359261 0.441953693928191
% -0.902919734077452 -0.392255513187521 0.175703062544449
% -0.445057852355085 -0.877254384661835 -0.179856199917226
% 0.0191648378856287 -0.478187525660449 0.878048631507137
% 0.729805093994244 -0.0150100959550102 -0.683490469428415
% 0.318485158269486 0.202798610459204 -0.925980522234608
% -0.933471505851571 0.264331910846754 0.242403771982418
% 0.366283766697754 -0.88325889419163 -0.292728420357649
% -0.504083568272385 0.830941138339376 0.235449741586273
% -0.422134990469078 -0.473629027206033 -0.772966748579483
% 0.562122376389526 0.342971801034031 -0.75258805309257
% 0.47488670832709 -0.0440884468022111 -0.878941876982107
% -0.316503181926798 0.824206835710962 -0.469583674969154
% -0.851012783302676 -0.227403528224722 0.47335491758973
% -0.201505059887582 0.960918311025049 0.189820205395708
% 0.134946638458873 0.99035188966013 0.0315045935580923
% 0.956463939949156 -0.0172333109503254 -0.291341285386447
% 0.153634967997045 -0.812976248914578 -0.561663524994573
% -0.045116422233054 -0.998512785714592 0.0306059668916889
% -0.851158728687144 0.318701805244035 -0.417082699130372
% -0.64292364111967 -0.155491800804942 0.749980994140427
% 0.040027769326845 -0.781222928464844 0.622967506153836
% 0.57151139162512 0.817770040488456 0.0680212475791796
% -0.971118251972848 -0.0129809866388241 -0.238245324552412
% 0.0323659781466574 0.622499622994987 0.781950550117914
% 0.939826349692285 -0.311045842208315 -0.141339720068332
% -0.699855468794036 -0.532820179093236 0.47571522947046
% 0.884582439150109 0.417684693614843 0.207493144626801
% -0.107696877907393 -0.625660797430301 -0.772625361380196
% 0.363222628527568 0.474154172814948 0.802026896386709
% 0.551762851974431 -0.834000144142603 -0.00123075227426574
% 0.27960636753143 -0.957537236287372 0.0703044832071291
% 0.363881413036082 0.708661541363741 -0.604474264993002
% -0.522709698368653 -0.441760688569855 0.729124176848937
% -0.312284938916817 0.58820851768192 -0.745981807185777
% -0.0128329111799609 0.779532704937268 -0.626230052236263
% -0.779718558233148 0.586454163718457 0.219341021708448
% 0.578451311054925 -0.745640759268962 0.330777778660606
% 0.99315012315382 0.0865462962729932 0.0785020476228455
% -0.987890830135373 -0.0930487208242668 0.124151694661858
% 0.788628509471027 0.609585501908488 -0.0804399770790797
% -0.0784996629834994 0.376122478822591 -0.923238692774424
% -0.384884756311282 -0.915763911488638 0.115065993126704
% -0.313066647875459 0.517145832803742 0.796586129430928
% -0.554806509075221 -0.143692417802117 -0.819476800497701
% 0.65876932530018 0.671967917752027 0.338352026084595
% -0.254459300309275 -0.676496600754889 0.691088137398692
% -0.402379046598918 -0.796846871477315 0.450695203297042
% -0.911921204272241 -0.335869454901685 -0.235778341801596
% 0.74581589590743 -0.628285591530498 -0.221395268438532
% 0.343388654882662 0.718252032209972 0.605143164816493
% -0.604829957280966 0.620809175765224 -0.498775189901431
% -0.227144421869287 -0.266247376452159 -0.936759171903862
% 0.813080183948139 0.257581369317655 -0.522065563556246
% 0.569112449239518 -0.369089264521919 -0.734768082414625
% 0.246066903817843 -0.560988943200037 -0.790406531129903
% -0.284839653090177 -0.813300409571453 -0.507354723855386
% 0.815092574733733 -0.566794371384457 0.119867573516913
% -0.622586701434447 0.328624653435316 -0.710205348016679
% -0.0733078266960112 0.332881994506803 0.940114642093335
% 0.884013881761852 0.149745110832594 0.442827120481659
% 0.840431358597636 -0.199677067461463 0.503789837348593
% 0.190260750853732 -0.275806772752388 -0.9421950280003
% -0.20085419577021 0.967185759121349 -0.155593378375697
% 0.933727761326556 0.314658230439894 -0.170712230799476
% 0.650921103688794 -0.520418850096799 0.552689729628196
% 0.0305873117972021 0.884132504791687 0.466233986671712
% -0.50543776999959 0.855690731805726 -0.111022665071695
% 0.532829355615869 -0.675578483373161 -0.509594535486005
% 0.823831850597751 -0.301991467935533 -0.479689728089758
% 0.110743175640674 0.940094201833908 -0.322426488873487
% 0.666791937825853 0.582104277076188 -0.465341941221778
% 0.329417540082174 0.899426569509102 0.287255862163502
% -0.0439468377733134 -0.939627008368994 0.339366705192571
% 0.948814651096306 -0.236388980960605 0.209454070252649
% 0.310035380581945 -0.612759065549374 0.7269142936925
% -0.396601385487369 0.0949805932480039 0.913064087529324
% -0.954550001085586 0.292376909645775 -0.0578795139362359
% -0.645445184601952 0.562533971108522 0.516677892911076
% 0.63002695382143 0.128406643103572 0.765883654000633
% -0.61668440961551 0.259526556183791 0.743200044115009
% -0.823654849167562 -0.00106346347191296 -0.567090432372302
% 0.194857699669509 0.534368241656557 -0.822484686294151
% 0.275044521357146 -0.260105542586792 0.925578531507213
% 0.313567027234433 0.154224719893331 0.936958086151768
% 0.584712672669503 -0.244117581199286 0.773639255059551
% 0.68142388750756 0.441899259748013 0.583426541878446
% 0.466285115842187 0.847572412435529 -0.253375603447246
% -0.298200316746928 0.785843911675329 0.541780322247725
% -0.849628081653607 0.114230384678788 0.514862643898105
% -0.745037813621811 -0.641914244076033 -0.181286401933311
% -0.70546243568549 -0.69042213253881 0.160125047188933
% -0.259344936509856 -0.291422993713237 0.920767529098368
% -0.766592229687691 0.623586220822615 -0.153220685883546
% -0.587183394609228 -0.628643391709435 -0.50992464850725
% -0.0315702938628221 -0.956129296010598 -0.291238881085088
% -0.367915383869698 0.154640371163042 -0.916910369621027
% 0 0 1
% 0 0 -1];
%PLOT SPHERE POINTS
% figure;
% [x,y,z] = sphere(100);
% surf(x,y,z,'EdgeColor','none','FaceColor',[.7 .7 .7]); hold on
% plot3(cc(:,1),cc(:,2),cc(:,3),'r.','MarkerSize',20);
% camlight; view(30,30); material dull; axis equal vis3d
%CREATE NEW SPHERE POINTS
% clc
% close all
% clear all
%
% np = 100;
% cc = randn(np,3);
% cc = fcnVec2uVec(cc)*1; %unit vectors around the sphere
% cc(99,1:3) = [0 0 1];
% cc(100,1:3) = [0 0 -1];
%
% figure;
% [x,y,z] = sphere(100); xlabel('X'); ylabel('Y'); zlabel('Z'); set(gca,'YDir','reverse','ZDir','reverse');
% surf(x,y,z,'EdgeColor','none','FaceColor',[.7 .7 .7]); hold on
% h = plot3(cc(:,1),cc(:,2),cc(:,3),'r.','MarkerSize',20);
% camlight; view(30,30); material dull; axis equal vis3d
%
% pause(.5)
%
% vi = [1:np]';
% for j = 1:10000
% for i = 1:np
% p1 = cc(i,1:3);
% rv = ones(np,1)*p1 - cc;
% r = sqrt(rv(:,1).^2+rv(:,2).^2+rv(:,3).^2);
%
% v1 = find(r<1 & r~=0);
% if numel(v1)~=0
% for k = (v1')
% if k<(np-2) %don't move 2 polar ones
% minr = r(k);
% p2 = cc(k,1:3); %to be moved
%
% vec = (p2-p1)/minr*.0015/minr^2*2;
% p2 = p2+vec;
% p2 = p2/norm(p2); %normalize back to the surface
% cc(k,1:3) = p2;
% end
% end
% end
% end
% delete(h)
% h = plot3(cc(:,1),cc(:,2),cc(:,3),'r.','MarkerSize',20);
% drawnow
% end