-
Notifications
You must be signed in to change notification settings - Fork 0
/
PlotTessellations.m
139 lines (110 loc) · 2.99 KB
/
PlotTessellations.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
% Plots tessellations for various spectral diffeomorphisms
%
% AUTHOR: D Lantzberg, Nov. 2017
boxArea = 1/4;
xl = -8;
xr = 8;
yu = -4;
yo = 4;
FlowLines = 2*xl : sqrt(boxArea) : xr*2 ;
y = (yu : .01 : yo);
%% SIN / COS Symplecto
sigCos = @(x) 2*x + sin(x);
dSigCos = @(x) 2 + cos(x);
figure(1);
plot( FlowLines(:)*( dSigCos(y) ) , y ,'r' , 'LineWidth', .4 );
PlotPhaseSpaceTessellation( dSigCos , xl , xr , yu , yo , boxArea , 1.5);
axis([-4 4 -4 4]);
plotaxis(0,'k-',4); axis square;
box on;
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
axis square;
ax = gca;
xtl = ax.XTickLabel;
xtl(5) = {'Q'};
ytl = ax.YTickLabel;
ytl(5) = {'P'};
ax.XTickLabel = xtl;
ax.YTickLabel = ytl;
axis square;
%zoom(2);
plotTickLatex2D('xlabeldy',.0,'ylabeldx',.0,'fontsize',22);
pause(.1);
%% LOG2 Symplecto (Wavelet tesselation)
sigLog = @(x) log2(abs(x));
dSigLog = @(x) 1 ./ ( abs(x) );
figure(2);
plot( (xl*4 : sqrt(boxArea) : xr*4).'*( dSigLog(y) ) , y ,'r', 'LineWidth', 0.4 );
PlotPhaseSpaceTessellation( dSigLog , xl , xr , yu , yo , boxArea , 1.5);
axis([-4 4 -4 4]);
plotaxis(0,'k-',4); axis square;
box on;
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
axis square;
ax = gca;
xtl = ax.XTickLabel;
xtl(5) = {'Q'};
ytl = ax.YTickLabel;
ytl(5) = {'P'};
ax.XTickLabel = xtl;
ax.YTickLabel = ytl;
axis square;
plotTickLatex2D('xlabeldy',.0,'ylabeldx',.0,'fontsize',22);
%% IDENTICAL Symplecto (STFT tesselation)
sigId = @(x) x;
dSigId = @(x) ones(size(x));
figure(3);
plot( FlowLines(:)*( dSigId(y) ) , y ,'r-', 'LineWidth', 0.4 );
PlotPhaseSpaceTessellation( dSigId , xl , xr , yu , yo , boxArea , 1.5);
axis([-4 4 -4 4]);
plotaxis(0,'k-',4); axis square;
box on;
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
axis square;
ax = gca;
xtl = ax.XTickLabel;
xtl(5) = {'Q'};
ytl = ax.YTickLabel;
ytl(5) = {'P'};
ax.XTickLabel = xtl;
ax.YTickLabel = ytl;
axis square;
%zoom(2);
plotTickLatex2D('xlabeldy',.0,'ylabeldx',.0,'fontsize',22);
pause(.1);
%% SIN / COS Symplecto
sigCos = @(x) 1.25*x + cos(x);
dSigCos = @(x) 1.25 - sin(x);
figure(4);
plot( FlowLines(:)*( dSigCos(y) ) , y ,'r' , 'LineWidth', .4 );
PlotPhaseSpaceTessellation( dSigCos , xl , xr , yu , yo , boxArea , 1.5);
axis([-4 4 -4 4]);
plotaxis(0,'k-',4); axis square;
box on;
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
set(gca,'FontSize',16);
set(gca,'FontName','CMU Serif');
ax = gca;
xtl = ax.XTickLabel;
xtl(5) = {'Q'};
ytl = ax.YTickLabel;
ytl(5) = {'P'};
ax.XTickLabel = xtl;
ax.YTickLabel = ytl;
axis square;
plotTickLatex2D('xlabeldy',.0,'ylabeldx',.0,'fontsize',22);
pause;
SaveAsEps(1,'SinCosTessellation');
SaveAsEps(2,'Log2Tessellation');
SaveAsEps(3,'GaborTessellation');
SaveAsEps(4,'SinCosWideTessellation');