-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathdsdiagram.m
251 lines (226 loc) · 7.13 KB
/
dsdiagram.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
function dsdiagram
% Geometry
%
% Simons & Dahlen (2007), Figure 1
%
% Last modified by fjsimons-at-alum.mit.edu, 03/28/2007
% Which vector to plot
ang=40;
% Down to this z level for the projection
lz=-0.2;
% Rotation of the geodesic
rotg=-30;
% Rotation of the X-axis
rots=10;
clf
[ah,ha]=krijetem(subnum(1,4));
% FIRST FIGURE PANEL ------------------------------
axes(ah(1))
[h,cord]=circ(1,[-pi/2 pi/2]); delete(h)
eq(1)=plot3(cord(:,1),cord(:,2),zeros(size(cord(:,1))));
hold on
[h,cord]=circ(1,[0 3*pi/2]); delete(h)
eqd(2)=plot3(cord(:,1),cord(:,2),zeros(size(cord(:,1))),':');
[h,cord]=circ(1); delete(h)
ol(1)=plot3(zeros(size(cord(:,1))),cord(:,2),cord(:,1));
% Plot the X-axis
[axt(1),axh(1)]=plotx;
% Plot the Y-axis
[axt(2),axh(2)]=ploty;
% Plot the Z-axis
[axt(3),axh(3)]=plotz;
% Plot the random vector
ft=[1 1];
vax=arrow(0,0,0,0.85,'v',2,ang,ft);
xdv=get(vax,'Xdata'); ydv=get(vax,'Ydata'); delete(vax)
axt(4)=plot3(zeros(size(ydv{1})),xdv{1}-ft(1),ydv{1}-ft(2));
%axh(4)=plot3(zeros(size(ydv{2})),xdv{2}-ft(1),ydv{2}-ft(2));
ydv{2}(4)=ydv{2}(1);
xdv{2}(4)=xdv{2}(1);
axh(4)=fill3(zeros(size(ydv{2})),xdv{2}-ft(1),ydv{2}-ft(2),'k');
% Plot first arclength
[h,cord]=circ(0.5,[pi/2-ang/180*pi pi/2]); delete(h)
arcl(1)=plot3(zeros(size(cord(:,1))),cord(:,1),cord(:,2));
% Plot the arrow head
fudg=10; % Used to be 4
parh=plot3(0,cord(1+fudg,1),cord(1+fudg,2),'k^');
% Plot projections
proj(1)=plot3([0 0],repmat(max(xdv{1})-ft(1),1,2),...
[max(ydv{1})-ft(1) lz]);
proj(2)=plot3([0 0],[0 max(xdv{1})-ft(1)],[0 lz]);
% Plot second arclength
[h,cord]=circ(0.4,[-rots*pi/180 ang/180*pi]); delete(h)
arcl(2)=plot3(cord(:,1),cord(:,2),zeros(size(cord(:,1))));
% Plot the second arrow head
parh(2)=plot3(cord(end,1)+0.025,cord(end,2)-0.05,0,'kv');
set(parh,'markerf','k','markere','k','markers',3)
onax=axis; onax=onax.*1.1;
viewpars(onax)
% SECOND FIGURE PANEL
axes(ah(2))
% Plot Earth outline
[h,cord]=circ(1); delete(h)
ol(3)=plot3(zeros(size(cord(:,1))),cord(:,2),cord(:,1));
hold on
% First blob
[lo,la]=blob;
lo=scale(lo,(-60+[0 50])*pi/180);
la=scale(la,[40 70]*pi/180);
[X,Y,Z]=sph2cart(lo,la,1);
arcl(3)=fill3(X,Y,Z,grey);
% Second blob
[lo,la]=blob;
lo=scale(lo,(30+[-40 0])*pi/180);
la=scale(la,[20 -20]*pi/180);
[X,Y,Z]=sph2cart(lo,la,1);
arcl(6)=fill3(X,Y,Z,grey);
curs=0;
if curs==1
[phint,thp,php]=phicurve([pi/2-la(:) lo(:)],...
linspace(pi/2-max(la),pi/2-min(la),10));
% Now get the great circle coordinates
thp=thp'; php=php';
for index=1:size(php,1)
lola=grcircle(...
[php(index,1) pi/2-thp(index,1)],...
[php(index,2) pi/2-thp(index,2)],100);
[X,Y,Z]=sph2cart(lola(:,1),lola(:,2),1);
hasj(index)=plot3(X,Y,Z,'k');
end
end
viewpars(onax)
% THIRD FIGURE PANEL
axes(ah(3))
% Plot Earth outline
[h,cord]=circ(1); delete(h)
ol(4)=plot3(zeros(size(cord(:,1))),cord(:,2),cord(:,1));
hold on
% Plot polar cap
ang1=30;
[h,cord]=circ(cos(ang1*pi/180),[-pi/2 pi/2]); delete(h)
eq(4)=plot3(cord(:,1),cord(:,2),ones(size(cord(:,1)))*sin(ang1*pi/180));
[h,cord2]=circ(1,[ang1 180-ang1]*pi/180); delete(h)
eqx=fill3([cord(:,1) ; ; zeros(size(cord2(:,1)))]',...
[cord(:,2) ; ; cord2(:,1)]',...
[ones(size(cord(:,1)))*sin(ang1*pi/180) ; ...
; cord2(:,2)]',...
grey);
viewpars(onax)
% FOURTH FIGURE PANEL --------------------------------------------
axes(ah(4))
[h,cord]=circ(1); delete(h)
ol(4)=plot3(zeros(size(cord(:,1))),cord(:,2),cord(:,1));
hold on
viewpars(onax)
% Plot polar cap on TOP
ang2=20;
[h,cord]=circ(cos(ang2*pi/180),[-pi/2 pi/2]); delete(h)
eq(6)=plot3(cord(:,1),cord(:,2),ones(size(cord(:,1)))*sin(ang2*pi/180));
[h,cord2]=circ(1,[ang2 180-ang2]*pi/180); delete(h)
eqx=fill3([cord(:,1) ; ; zeros(size(cord2(:,1)))]',...
[cord(:,2) ; ; cord2(:,1)]',...
[ones(size(cord(:,1)))*sin(ang2*pi/180) ; ...
; cord2(:,2)]',...
grey);
% Plot bottom polar cap on TOP
ang2=-ang2;
% Make an equatorial half circle
[h,cord]=circ(cos(ang2*pi/180),[-pi/2 pi/2]); delete(h)
% But plot it at the right height
eq(3)=plot3(cord(:,1),cord(:,2),ones(size(cord(:,1)))*sin(ang2*pi/180));
% Define another boundary
[h,cord2]=circ(1,[-ang2 180+ang2]*pi/180); delete(h)
% Make this grey
eqx=fill3([cord(:,1) ; zeros(size(cord2(:,1)))]',...
[cord(:,2) ; cord2(:,1)]',...
[ones(size(cord(:,1)))*sin(ang2*pi/180) ; -cord2(:,2)]',...
grey);
viewpars(onax)
% Cosmetics & Annotations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
serre(ah(1:4),-1/3,'across')
%Next couple of lines for krijetem(subnum(2,2))
%serre(ah(1:2),1,'across')
%serre(ah(3:4),1,'across')
%serre(ha(1:2),0.6,'down')
%serre(ha(3:4),0.6,'down')
%set(ah,'camerav',5.5)
set(ah,'camerav',4.75)
% Next line not for 2,2
set(ah,'xlim',[-1.25 1.25],'ylim',[-1.25 1.25],'zlim',[-1.25 1.25])
set(findobj('Color','b'),'LineW',1,'Color','k')
set([eq(~~eq) proj(~~proj)],'LineS',':')
% Plot labels
axes(ah(1))
lpost=[1.9 -0.4 0 ;
0.5 1.2 0 ;
0 0.125 1.2;
0 0.5 0.7];
axpo=[1 1 1 1];
ltxt={'x','y','z','\bfr'};
for i=1:length(axpo)
axes(ah(axpo(i)))
l(i)=text(lpost(i,1),lpost(i,2),lpost(i,3),ltxt{i});
end
axes(ah(1))
l(8)=text(0,0.2,0.6,'\theta');
l(9)=text(0.65,0.2,0.02,'\phi');
l(7)=text(0,0.4,-0.7,'\Omega');
axes(ah(2))
l(11)=text(0,0.53,-0.45,'R_2');
l(13)=text(0,-0.05,0.6,'R_1');
axes(ah(3))
l(14)=text(0,0.93,0.55,sprintf('%s','\Theta'));
axes(ah(4))
l(15)=text(0,1.0,0.4,sprintf('%s','\Theta'));
l(16)=text(0,1.0,-0.4,sprintf('%s-%s','\pi','\Theta'));
fig2print(gcf,'portrait')
figdisp([],[],[],0)
keyboard
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function viewpars(onix)
defval('onix',[-2 2 -2 2])
% Set viewing parameters
% Really would need another rotation around x
view(90,17.5); axis equal
axis(onix); axis off
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t,h]=plotx
% Plots x-axis for the unit sphere
ft=[1 1]; % To get it on the right plane
% Rotation of the X-axis
rots=10;
xax=arrow(0,0,1.75,0,'h',2,rots,ft);
xdx=get(xax,'Xdata'); ydx=get(xax,'Ydata'); delete(xax)
t(1)=plot3(xdx{1}-ft(1),ydx{1}-ft(2),zeros(size(ydx{1})));
% Regular arrow head
% h(1)=plot3(xdx{2}-ft(1),ydx{2}-ft(2),zeros(size(ydx{2})));
% Filled arrow head, but unrotated
ydx{2}(4)=ydx{2}(1);
xdx{2}(4)=xdx{2}(1);
h(1)=fill3(xdx{2}-ft(1),ydx{2}-ft(2),zeros(size(ydx{2})),'k');
% Filled and properly rotated arrow head
% rots1=rotz(-rots*pi/180);
% rots2=rotx(pi/2);
% rots3=rotz(rots*pi/180);
% done=(rots3*rots2*rots1*[xdx{2}-ft(1),ydx{2}-ft(2),zeros(size(ydx{2}))]')';
% h(1)=fill3(done(:,1),done(:,2),done(:,3),'k');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t,h]=ploty
% Plots y-axis for the unit sphere
yax=arrow(0,0,0,1.4,'v',3);
xdy=get(yax,'Xdata'); ydy=get(yax,'Ydata'); delete(yax)
t(1)=plot3(xdy{1},ydy{1},zeros(size(ydy{1})));
% h(1)=plot3(zeros(size(ydy{2})),ydy{2},xdy{2});
ydy{2}(4)=ydy{2}(1);
xdy{2}(4)=xdy{2}(1);
h(1)=fill3(zeros(size(ydy{2})),ydy{2},xdy{2},'k');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t,h]=plotz
% Plots z-axis for the unit sphere
zax=arrow(0,0,0,1.4,'v',3);
xdz=get(zax,'Xdata'); ydz=get(zax,'Ydata'); delete(zax)
t(1)=plot3(zeros(size(ydz{1})),xdz{1},ydz{1});
% h(1)=plot3(zeros(size(ydz{2})),xdz{2},ydz{2});
ydz{2}(4)=ydz{2}(1);
xdz{2}(4)=xdz{2}(1);
h(1)=fill3(zeros(size(ydz{2})),xdz{2},ydz{2},'k');