Why the contours does not appear in the empty region?

1 view (last 30 days)
Shreen El-Sapa
Shreen El-Sapa on 19 Aug 2023
Commented: Shreen El-Sapa on 19 Aug 2023
Ran in:
A =[ 0.506207
-1.175631
3.791971
-8.367277
15.218631
-24.775942
37.354122
-53.596046
73.775154
-98.864357
128.993118
-165.690033
208.780502
-260.760254
320.860199
-393.309998
476.185974
-576.973877
691.446899
-833.655273
994.502441
-1202.786865
1438.045410
-1768.520142
2142.382813
-2773.383545
3490.939697
-5789.086914
8474.064453
-4602.666992];
B=[ -1.898113
1.420040
-2.795280
4.554918
-6.620665
9.012413
-11.705348
14.778024
-18.184662
22.053255
-26.295725
31.114862
-36.357929
42.347446
-48.827950
56.320488
-64.398186
73.929947
-84.185623
96.693771
-110.143478
127.466537
-146.105637
172.564941
-201.088440
250.779495
-304.517883
487.777771
-690.493896
363.089630];
C=[ -4.395421
7.855587
-14.091352
13.265227
-8.180313
3.734594
-1.344997
0.401312
-0.101679
0.022491
-0.004390
0.000771
-0.000122
0.000018
-0.000002
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000];
AA=[ 0.239048
0.007455
-0.001080
0.000172
-0.000024
0.000003
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000];
BB=[ -0.000673
-0.000037
0.000007
-0.000001
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000];
CC=[ 0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
-0.000001
0.000003
-0.000010
0.000012];
a = 1 ; %RADIUS
%L=.5;
eta=0.1;alpha1=1./sqrt(eta);
dd=.99;
%c =-a/L;
%b =a/L;
m =a*200; % NUMBER OF INTERVALS
[x,y]=meshgrid((-3:.1:3),(0:.1:3)');
%[x,y]=meshgrid((c:(b-c)/m:b),(0:(b-c)/m:b)');
[I, J]=find(sqrt(x.^2+y.^2)<(a-0.1));
if ~isempty(I)
x(I,J) = 0; y(I,J) = 0;
end
r=sqrt(x.^2+y.^2);
t=atan2(y,x);
r2=sqrt(r.^2+dd.^2+2.*r.*dd.*cos(t));
zet=(-r.^2+r2.^2+dd.^2)./(2.*r2.*dd);
warning on
psi1=0;
for i=2:10
Ai=A(i-1);Bi=B(i-1);Ci=C(i-1);AAi=AA(i-1);BBi=BB(i-1);CCi=CC(i-1);
%psi1=-psi1-(Ai.*r.^(-i-1)+r.^(-3./2).*besselk(i-1./2,r.*alpha1).*Bi+r.^(-3./2).*besselk(i-1./2,r.*alpha2).*Ci).*legendreP(i-1,cos(t))-(AAi.*r2.^(-i-1)+r2.^(-3./2).*besselk(i-1./2,r2.*alpha1).*BBi+r2.^(1./2).*besselk(i-1./2,r2.*alpha2).*CCi).*legendreP(i-1,zet);
psi1=psi1+(Ai.*r.^(-i+1)+r.^(-i+3).*Bi+r.^(1./2).*besselk(i-1./2,r.*alpha1).*Ci).*gegenbauerC(i,-1./2, cos(t))+(AAi.*r2.^(i)+r2.^(i+2)*BBi+r2.^(1./2).*besseli(i-1./2,r2.*alpha1).*CCi).*gegenbauerC(i,-1./2,zet);
end
hold on
%[DH1,h1]=contour(x,y,psi1,50,'--k','LineWidth',1.1); %,psi2,'--k',psi2,':k'
%[DH1,h1]=contour(x,y,psi1);
[DH1,h1]=contour(x,y,psi1,'--k','LineWidth',1.1,'ShowText','on');
%p1=contour(x,y,psi1,'--k','LineWidth',1.1,'ShowText','on'); %,'ShowText','on'
%p2=contour(x,y,psi1,[5 5],'r','LineWidth',1.1);
%%%%%%%%%%%%%%% $\frac{\textstyle a_1+a_2}{\textstyle h}=6.0,\;
hold on
t3 = linspace(0,pi,1000);
h2=0;
k2=0;
rr2=3;
x2 = rr2*cos(t3)+h2;
y2 = rr2*sin(t3)+k2;
set(plot(x2,y2,'-k'),'LineWidth',1.1);
% fill(x2,y2,'w')
hold on
t2 = linspace(0,pi,1000);
h=dd;
k=0;
rr=1;
x1 = rr*cos(t2)+h;
y1 = rr*sin(t2)+k;
set(plot(x1,y1,'-k'),'LineWidth',1.1);
fill(x1,y1,'w')
axis square;
axis('equal')
box on
%set(gca,'XTick',[], 'YTick', [])
axis on
patch([x2 flip(x2)], [y2 ones(size(y2))*max(ylim)], 'w')
% xticklabels([])
% yticklabels([])
%legend('0.01','0.05','0.1','0.4','0.6','0.8','Location','northwest')
% figure
% surfc(x,y,psi1) %,'--r','LineWidth',1.1); %,psi2,'--k',psi2,':k'

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Accepted Answer

Voss
Voss on 19 Aug 2023
Edited: Voss on 19 Aug 2023
Ran in:
I assume the empty region you mean is the roughly square region with corners (0,0) and (-1,1).
openfig('untitled.fig');
That region is empty because the psi1 values there are NaNs.
disp(psi1)
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-1.5383 -1.5462 -1.1919 -1.2204 -1.2490 -1.2775 -1.3057 -1.3336 -1.3609 -1.3874 -1.4131 -1.4376 -1.4609 -1.4827 -1.5029 -1.5214 -1.5378 -1.5523 -1.5645 -1.5746 -1.5823 -1.2330 -1.2613 -1.2896 -1.3178 -1.3457 -1.3731 -1.3999 -1.4260 -1.4512 -1.4752 -1.4979 -1.5192 -1.5389 -1.5569 -1.5729 -1.5870 -1.5989 -1.6087 -1.6162 -1.2721 -1.3002 -1.3282 -1.3560 -1.3835 -1.4105 -1.4369 -1.4625 -1.4871 -1.5106 -1.5328 -1.5536 -1.5728 -1.5903 -1.6059 -1.6196 -1.6312 -1.6407 -1.6480 -1.3094 -1.3371 -1.3648 -1.3923 -1.4193 -1.4459 -1.4718 -1.4968 -1.5209 -1.5439 -1.5656 -1.5858 -1.6045 -1.6215 -1.6367 -1.6500 -1.6613 -1.6705 -1.6775 Columns 20 through 38 0 -0.0000 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.0440 -0.0727 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.1491 -0.2269 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.2625 -0.3540 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.3508 -0.4150 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.4131 -0.4399 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.4641 -0.4661 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.5157 -0.5085 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.5726 -0.5652 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN -0.6344 -0.6296 -0.6206 -0.6134 -0.6158 -0.6286 -0.6325 -0.5887 -0.4900 -0.4258 -0.4989 -0.6262 -0.6240 -0.5018 -0.4079 -0.3915 -0.4027 -0.4018 -0.3849 -0.6988 -0.6967 -0.6920 -0.6878 -0.6861 -0.6836 -0.6700 -0.6352 -0.5884 -0.5646 -0.5870 -0.6228 -0.6165 -0.5645 -0.5096 -0.4791 -0.4661 -0.4551 -0.4388 -0.7640 -0.7637 -0.7608 -0.7568 -0.7515 -0.7423 -0.7253 -0.6992 -0.6719 -0.6568 -0.6592 -0.6649 -0.6539 -0.6228 -0.5856 -0.5553 -0.5336 -0.5156 -0.4968 -0.8287 -0.8294 -0.8272 -0.8227 -0.8154 -0.8040 -0.7875 -0.7670 -0.7472 -0.7337 -0.7272 -0.7211 -0.7071 -0.6828 -0.6534 -0.6251 -0.6006 -0.5786 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disp(isnan(psi1))
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