Limited line style for differentiating curves in the plot
Clash Royale CLAN TAG#URR8PPP
3
$begingroup$
Question 1
I have a plot which consists of six curves, and I wanted to differentiate these line without using any color. I the only option that I left with is to use different line style. After looking at the documentation I only come up with these three, but I have six curves? how to do this?
Question 2
Out of these six plots, bottom three curves I have to name as mode shapes, the upper three curves as non-dimensional frequency. And there is a no horizontal line crossing at y=0; how to fix this?
ClearAll["Global`*"];
s1 = 4.76592, 4.80264, 4.84021, 4.87866, 4.91803, 4.95834, 4.99961,
5.04189, 5.08519, 5.12956, 5.17503, 5.22163, 5.26941, 5.31839,
5.36862, 5.42013, 5.47298, 5.52719, 5.58282, 5.63992, 5.69852,
5.75867, 5.82042, 5.88383, 5.94893, 6.01577, 6.08441, 6.15488,
6.22724, 6.30151, 6.37773, 6.45593, 6.53613, 6.61831, 6.70246,
6.78854, 6.87645, 6.96606, 7.05715, 7.14942, 7.24241, 7.33546,
7.42764, 7.51761, 7.60347, 7.6826, 7.7515, 7.80584, 7.84099,
7.8532, 7.84099, 7.80584, 7.7515, 7.6826, 7.60347, 7.51761,
7.42764, 7.33546, 7.24241, 7.14942, 7.05715, 6.96606, 6.87645,
6.78854, 6.70246, 6.61831, 6.53613, 6.45593, 6.37773, 6.30151,
6.22724, 6.15488, 6.08441, 6.01577, 5.94893, 5.88383, 5.82042,
5.75867, 5.69852, 5.63992, 5.58282, 5.52719, 5.47298, 5.42013,
5.36862, 5.31839, 5.26941, 5.22163, 5.17503, 5.12956, 5.08519,
5.04189, 4.99961, 4.95834, 4.91803, 4.87866, 4.84021, 4.80264,
4.76592;
s2 = 7.91294, 7.97447, 8.03787, 8.10242, 8.17017, 8.23608, 8.30852,
8.38107, 8.45563, 8.53225, 8.61098, 8.69187, 8.77496, 8.8603,
8.94792, 9.03787, 9.13018, 9.22488, 9.32199, 9.42152, 9.52347,
9.62782, 9.7345, 9.84343, 9.95447, 10.0674, 10.1818, 10.2973,
10.4131, 10.528, 10.6403, 10.7472, 10.8444, 10.9251, 10.9794,
10.995, 10.9619, 10.8794, 10.7575, 10.6107, 10.4515, 10.2891,
10.1298, 9.97812, 9.83806, 9.71347, 9.60863, 9.52835, 9.47753,
9.46008, 9.47753, 9.52835, 9.60863, 9.71347, 9.83806, 9.97812,
10.1298, 10.2891, 10.4515, 10.6107, 10.7575, 10.8794, 10.9619,
10.995, 10.9794, 10.9251, 10.8444, 10.7472, 10.6403, 10.528,
10.4131, 10.2973, 10.1818, 10.0674, 9.95447, 9.84343, 9.7345,
9.62782, 9.52347, 9.42152, 9.32199, 9.22488, 9.13018, 9.03787,
8.94792, 8.8603, 8.77496, 8.69187, 8.61098, 8.53225, 8.45563,
8.38107, 8.30852, 8.23794, 8.17017, 8.10242, 8.03741, 7.97447,
7.91294;
s3 = 11.0794, 11.1662, 11.2555, 11.3489, 11.4432, 11.5415, 11.6428,
11.7471, 11.8545, 11.965, 12.0786, 12.1953, 12.3151, 12.4381,
12.5641, 12.6931, 12.825, 12.9595, 13.0965, 13.2354, 13.3757,
13.5164, 13.6558, 13.7914, 13.9186, 14.0295, 14.11, 14.1365,
14.0811, 13.9338, 13.7184, 13.4721, 13.2245, 12.9965, 12.8054,
12.6674, 12.5945, 12.5884, 12.6394, 12.7332, 12.8573, 13.0026,
13.1625, 13.3323, 13.5074, 13.6822, 13.8488, 13.9943, 14.0984,
14.1372, 14.0984, 13.9943, 13.8488, 13.6822, 13.5074, 13.3323,
13.1625, 13.0026, 12.8573, 12.7332, 12.6394, 12.5884, 12.5945,
12.6674, 12.8054, 12.9965, 13.2245, 13.4721, 13.7184, 13.9338,
14.0811, 14.1365, 14.11, 14.0295, 13.9186, 13.7914, 13.6558,
13.5164, 13.3757, 13.2354, 13.0965, 12.9595, 12.825, 12.6931,
12.5641, 12.4381, 12.3151, 12.1953, 12.0786, 11.965, 11.8545,
11.7471, 11.6428, 11.5415, 11.4432, 11.348, 11.2555, 11.1667,
11.0794;
z1 = Table[i, i, 0.01, 0.99, 0.01];
data1 = Transpose[z1, s1];
data2 = Transpose[z1, s2];
data3 = Transpose[z1, s3];
peaks1 = FindPeaks[s1];
peaks2 = FindPeaks[s2];
peaks3 = FindPeaks[s3];
mark1 = 0.50, 7.8532;
mark2 = 0.36, 10.995, 0.64, 10.995;
mark3 = 0.28, 14.1365, 0.50, 14.1372, 0.72, 14.1365;
mark4 = 0.50, 0;
mark5 = 0.36, 0, 0.64, 0;
mark6 = 0.28, 0, 0.50, 0, 0.72, 0;
p1 = ListPlot[data1, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p2 = ListPlot[data2, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p3 = ListPlot[data3, Joined -> True,
PlotStyle -> Black, Thickness[0.004], AxesStyle -> Black,
PlotRange -> All];
p4 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark1];
p5 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark2];
p6 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark3];
p7 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark4];
p8 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark5];
p9 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark6];
L = 1;
beta1 = 4.7300, 7.8532, 10.9956, 14.1372;
modefunction = ((Cos[b*x2] -
Cosh[b*x2]) - (((Cos[b*L] - Cosh[b*L])/(Sin[b*L] -
Sinh[b*L]))*(Sin[b*x2] - Sinh[b*x2])));
m3 = modefunction /. b -> beta1[[2]];
m4 = modefunction /. b -> beta1[[3]];
m5 = modefunction /. b -> beta1[[4]];
p10 = Plot[m3, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p11 = Plot[m4, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p12 = Plot[m5, x2, 0, L, PlotStyle -> Black, Thickness[0.004],
AxesStyle -> Black, PlotRange -> All];
fig = Show[p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12,
PlotRange -> All, AxesStyle -> Black,
Frame -> True, True, True, False,
FrameLabel -> "Beam Length", "Non-dimensional [Beta]", ,
"Mode Shapes", PlotLabel -> None,
LabelStyle -> FontFamily -> "Arial", 40, GrayLevel[0]];
fig = Style[fig, GraphicsBoxOptions -> ImageSize -> 1000]
plotting legending style
asked Feb 6 at 6:03
acousticsacoustics
44119
$endgroup$
add a comment |
3
$begingroup$
Question 1
I have a plot which consists of six curves, and I wanted to differentiate these line without using any color. I the only option that I left with is to use different line style. After looking at the documentation I only come up with these three, but I have six curves? how to do this?
Question 2
Out of these six plots, bottom three curves I have to name as mode shapes, the upper three curves as non-dimensional frequency. And there is a no horizontal line crossing at y=0; how to fix this?
ClearAll["Global`*"];
s1 = 4.76592, 4.80264, 4.84021, 4.87866, 4.91803, 4.95834, 4.99961,
5.04189, 5.08519, 5.12956, 5.17503, 5.22163, 5.26941, 5.31839,
5.36862, 5.42013, 5.47298, 5.52719, 5.58282, 5.63992, 5.69852,
5.75867, 5.82042, 5.88383, 5.94893, 6.01577, 6.08441, 6.15488,
6.22724, 6.30151, 6.37773, 6.45593, 6.53613, 6.61831, 6.70246,
6.78854, 6.87645, 6.96606, 7.05715, 7.14942, 7.24241, 7.33546,
7.42764, 7.51761, 7.60347, 7.6826, 7.7515, 7.80584, 7.84099,
7.8532, 7.84099, 7.80584, 7.7515, 7.6826, 7.60347, 7.51761,
7.42764, 7.33546, 7.24241, 7.14942, 7.05715, 6.96606, 6.87645,
6.78854, 6.70246, 6.61831, 6.53613, 6.45593, 6.37773, 6.30151,
6.22724, 6.15488, 6.08441, 6.01577, 5.94893, 5.88383, 5.82042,
5.75867, 5.69852, 5.63992, 5.58282, 5.52719, 5.47298, 5.42013,
5.36862, 5.31839, 5.26941, 5.22163, 5.17503, 5.12956, 5.08519,
5.04189, 4.99961, 4.95834, 4.91803, 4.87866, 4.84021, 4.80264,
4.76592;
s2 = 7.91294, 7.97447, 8.03787, 8.10242, 8.17017, 8.23608, 8.30852,
8.38107, 8.45563, 8.53225, 8.61098, 8.69187, 8.77496, 8.8603,
8.94792, 9.03787, 9.13018, 9.22488, 9.32199, 9.42152, 9.52347,
9.62782, 9.7345, 9.84343, 9.95447, 10.0674, 10.1818, 10.2973,
10.4131, 10.528, 10.6403, 10.7472, 10.8444, 10.9251, 10.9794,
10.995, 10.9619, 10.8794, 10.7575, 10.6107, 10.4515, 10.2891,
10.1298, 9.97812, 9.83806, 9.71347, 9.60863, 9.52835, 9.47753,
9.46008, 9.47753, 9.52835, 9.60863, 9.71347, 9.83806, 9.97812,
10.1298, 10.2891, 10.4515, 10.6107, 10.7575, 10.8794, 10.9619,
10.995, 10.9794, 10.9251, 10.8444, 10.7472, 10.6403, 10.528,
10.4131, 10.2973, 10.1818, 10.0674, 9.95447, 9.84343, 9.7345,
9.62782, 9.52347, 9.42152, 9.32199, 9.22488, 9.13018, 9.03787,
8.94792, 8.8603, 8.77496, 8.69187, 8.61098, 8.53225, 8.45563,
8.38107, 8.30852, 8.23794, 8.17017, 8.10242, 8.03741, 7.97447,
7.91294;
s3 = 11.0794, 11.1662, 11.2555, 11.3489, 11.4432, 11.5415, 11.6428,
11.7471, 11.8545, 11.965, 12.0786, 12.1953, 12.3151, 12.4381,
12.5641, 12.6931, 12.825, 12.9595, 13.0965, 13.2354, 13.3757,
13.5164, 13.6558, 13.7914, 13.9186, 14.0295, 14.11, 14.1365,
14.0811, 13.9338, 13.7184, 13.4721, 13.2245, 12.9965, 12.8054,
12.6674, 12.5945, 12.5884, 12.6394, 12.7332, 12.8573, 13.0026,
13.1625, 13.3323, 13.5074, 13.6822, 13.8488, 13.9943, 14.0984,
14.1372, 14.0984, 13.9943, 13.8488, 13.6822, 13.5074, 13.3323,
13.1625, 13.0026, 12.8573, 12.7332, 12.6394, 12.5884, 12.5945,
12.6674, 12.8054, 12.9965, 13.2245, 13.4721, 13.7184, 13.9338,
14.0811, 14.1365, 14.11, 14.0295, 13.9186, 13.7914, 13.6558,
13.5164, 13.3757, 13.2354, 13.0965, 12.9595, 12.825, 12.6931,
12.5641, 12.4381, 12.3151, 12.1953, 12.0786, 11.965, 11.8545,
11.7471, 11.6428, 11.5415, 11.4432, 11.348, 11.2555, 11.1667,
11.0794;
z1 = Table[i, i, 0.01, 0.99, 0.01];
data1 = Transpose[z1, s1];
data2 = Transpose[z1, s2];
data3 = Transpose[z1, s3];
peaks1 = FindPeaks[s1];
peaks2 = FindPeaks[s2];
peaks3 = FindPeaks[s3];
mark1 = 0.50, 7.8532;
mark2 = 0.36, 10.995, 0.64, 10.995;
mark3 = 0.28, 14.1365, 0.50, 14.1372, 0.72, 14.1365;
mark4 = 0.50, 0;
mark5 = 0.36, 0, 0.64, 0;
mark6 = 0.28, 0, 0.50, 0, 0.72, 0;
p1 = ListPlot[data1, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p2 = ListPlot[data2, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p3 = ListPlot[data3, Joined -> True,
PlotStyle -> Black, Thickness[0.004], AxesStyle -> Black,
PlotRange -> All];
p4 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark1];
p5 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark2];
p6 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark3];
p7 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark4];
p8 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark5];
p9 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark6];
L = 1;
beta1 = 4.7300, 7.8532, 10.9956, 14.1372;
modefunction = ((Cos[b*x2] -
Cosh[b*x2]) - (((Cos[b*L] - Cosh[b*L])/(Sin[b*L] -
Sinh[b*L]))*(Sin[b*x2] - Sinh[b*x2])));
m3 = modefunction /. b -> beta1[[2]];
m4 = modefunction /. b -> beta1[[3]];
m5 = modefunction /. b -> beta1[[4]];
p10 = Plot[m3, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p11 = Plot[m4, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p12 = Plot[m5, x2, 0, L, PlotStyle -> Black, Thickness[0.004],
AxesStyle -> Black, PlotRange -> All];
fig = Show[p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12,
PlotRange -> All, AxesStyle -> Black,
Frame -> True, True, True, False,
FrameLabel -> "Beam Length", "Non-dimensional [Beta]", ,
"Mode Shapes", PlotLabel -> None,
LabelStyle -> FontFamily -> "Arial", 40, GrayLevel[0]];
fig = Style[fig, GraphicsBoxOptions -> ImageSize -> 1000]
plotting legending style
asked Feb 6 at 6:03
acousticsacoustics
44119
$endgroup$
add a comment |
3
3
3
$begingroup$
Question 1
I have a plot which consists of six curves, and I wanted to differentiate these line without using any color. I the only option that I left with is to use different line style. After looking at the documentation I only come up with these three, but I have six curves? how to do this?
Question 2
Out of these six plots, bottom three curves I have to name as mode shapes, the upper three curves as non-dimensional frequency. And there is a no horizontal line crossing at y=0; how to fix this?
ClearAll["Global`*"];
s1 = 4.76592, 4.80264, 4.84021, 4.87866, 4.91803, 4.95834, 4.99961,
5.04189, 5.08519, 5.12956, 5.17503, 5.22163, 5.26941, 5.31839,
5.36862, 5.42013, 5.47298, 5.52719, 5.58282, 5.63992, 5.69852,
5.75867, 5.82042, 5.88383, 5.94893, 6.01577, 6.08441, 6.15488,
6.22724, 6.30151, 6.37773, 6.45593, 6.53613, 6.61831, 6.70246,
6.78854, 6.87645, 6.96606, 7.05715, 7.14942, 7.24241, 7.33546,
7.42764, 7.51761, 7.60347, 7.6826, 7.7515, 7.80584, 7.84099,
7.8532, 7.84099, 7.80584, 7.7515, 7.6826, 7.60347, 7.51761,
7.42764, 7.33546, 7.24241, 7.14942, 7.05715, 6.96606, 6.87645,
6.78854, 6.70246, 6.61831, 6.53613, 6.45593, 6.37773, 6.30151,
6.22724, 6.15488, 6.08441, 6.01577, 5.94893, 5.88383, 5.82042,
5.75867, 5.69852, 5.63992, 5.58282, 5.52719, 5.47298, 5.42013,
5.36862, 5.31839, 5.26941, 5.22163, 5.17503, 5.12956, 5.08519,
5.04189, 4.99961, 4.95834, 4.91803, 4.87866, 4.84021, 4.80264,
4.76592;
s2 = 7.91294, 7.97447, 8.03787, 8.10242, 8.17017, 8.23608, 8.30852,
8.38107, 8.45563, 8.53225, 8.61098, 8.69187, 8.77496, 8.8603,
8.94792, 9.03787, 9.13018, 9.22488, 9.32199, 9.42152, 9.52347,
9.62782, 9.7345, 9.84343, 9.95447, 10.0674, 10.1818, 10.2973,
10.4131, 10.528, 10.6403, 10.7472, 10.8444, 10.9251, 10.9794,
10.995, 10.9619, 10.8794, 10.7575, 10.6107, 10.4515, 10.2891,
10.1298, 9.97812, 9.83806, 9.71347, 9.60863, 9.52835, 9.47753,
9.46008, 9.47753, 9.52835, 9.60863, 9.71347, 9.83806, 9.97812,
10.1298, 10.2891, 10.4515, 10.6107, 10.7575, 10.8794, 10.9619,
10.995, 10.9794, 10.9251, 10.8444, 10.7472, 10.6403, 10.528,
10.4131, 10.2973, 10.1818, 10.0674, 9.95447, 9.84343, 9.7345,
9.62782, 9.52347, 9.42152, 9.32199, 9.22488, 9.13018, 9.03787,
8.94792, 8.8603, 8.77496, 8.69187, 8.61098, 8.53225, 8.45563,
8.38107, 8.30852, 8.23794, 8.17017, 8.10242, 8.03741, 7.97447,
7.91294;
s3 = 11.0794, 11.1662, 11.2555, 11.3489, 11.4432, 11.5415, 11.6428,
11.7471, 11.8545, 11.965, 12.0786, 12.1953, 12.3151, 12.4381,
12.5641, 12.6931, 12.825, 12.9595, 13.0965, 13.2354, 13.3757,
13.5164, 13.6558, 13.7914, 13.9186, 14.0295, 14.11, 14.1365,
14.0811, 13.9338, 13.7184, 13.4721, 13.2245, 12.9965, 12.8054,
12.6674, 12.5945, 12.5884, 12.6394, 12.7332, 12.8573, 13.0026,
13.1625, 13.3323, 13.5074, 13.6822, 13.8488, 13.9943, 14.0984,
14.1372, 14.0984, 13.9943, 13.8488, 13.6822, 13.5074, 13.3323,
13.1625, 13.0026, 12.8573, 12.7332, 12.6394, 12.5884, 12.5945,
12.6674, 12.8054, 12.9965, 13.2245, 13.4721, 13.7184, 13.9338,
14.0811, 14.1365, 14.11, 14.0295, 13.9186, 13.7914, 13.6558,
13.5164, 13.3757, 13.2354, 13.0965, 12.9595, 12.825, 12.6931,
12.5641, 12.4381, 12.3151, 12.1953, 12.0786, 11.965, 11.8545,
11.7471, 11.6428, 11.5415, 11.4432, 11.348, 11.2555, 11.1667,
11.0794;
z1 = Table[i, i, 0.01, 0.99, 0.01];
data1 = Transpose[z1, s1];
data2 = Transpose[z1, s2];
data3 = Transpose[z1, s3];
peaks1 = FindPeaks[s1];
peaks2 = FindPeaks[s2];
peaks3 = FindPeaks[s3];
mark1 = 0.50, 7.8532;
mark2 = 0.36, 10.995, 0.64, 10.995;
mark3 = 0.28, 14.1365, 0.50, 14.1372, 0.72, 14.1365;
mark4 = 0.50, 0;
mark5 = 0.36, 0, 0.64, 0;
mark6 = 0.28, 0, 0.50, 0, 0.72, 0;
p1 = ListPlot[data1, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p2 = ListPlot[data2, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p3 = ListPlot[data3, Joined -> True,
PlotStyle -> Black, Thickness[0.004], AxesStyle -> Black,
PlotRange -> All];
p4 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark1];
p5 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark2];
p6 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark3];
p7 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark4];
p8 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark5];
p9 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark6];
L = 1;
beta1 = 4.7300, 7.8532, 10.9956, 14.1372;
modefunction = ((Cos[b*x2] -
Cosh[b*x2]) - (((Cos[b*L] - Cosh[b*L])/(Sin[b*L] -
Sinh[b*L]))*(Sin[b*x2] - Sinh[b*x2])));
m3 = modefunction /. b -> beta1[[2]];
m4 = modefunction /. b -> beta1[[3]];
m5 = modefunction /. b -> beta1[[4]];
p10 = Plot[m3, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p11 = Plot[m4, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p12 = Plot[m5, x2, 0, L, PlotStyle -> Black, Thickness[0.004],
AxesStyle -> Black, PlotRange -> All];
fig = Show[p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12,
PlotRange -> All, AxesStyle -> Black,
Frame -> True, True, True, False,
FrameLabel -> "Beam Length", "Non-dimensional [Beta]", ,
"Mode Shapes", PlotLabel -> None,
LabelStyle -> FontFamily -> "Arial", 40, GrayLevel[0]];
fig = Style[fig, GraphicsBoxOptions -> ImageSize -> 1000]
plotting legending style
asked Feb 6 at 6:03
acousticsacoustics
44119
$endgroup$
Question 1
I have a plot which consists of six curves, and I wanted to differentiate these line without using any color. I the only option that I left with is to use different line style. After looking at the documentation I only come up with these three, but I have six curves? how to do this?
Question 2
Out of these six plots, bottom three curves I have to name as mode shapes, the upper three curves as non-dimensional frequency. And there is a no horizontal line crossing at y=0; how to fix this?
ClearAll["Global`*"];
s1 = 4.76592, 4.80264, 4.84021, 4.87866, 4.91803, 4.95834, 4.99961,
5.04189, 5.08519, 5.12956, 5.17503, 5.22163, 5.26941, 5.31839,
5.36862, 5.42013, 5.47298, 5.52719, 5.58282, 5.63992, 5.69852,
5.75867, 5.82042, 5.88383, 5.94893, 6.01577, 6.08441, 6.15488,
6.22724, 6.30151, 6.37773, 6.45593, 6.53613, 6.61831, 6.70246,
6.78854, 6.87645, 6.96606, 7.05715, 7.14942, 7.24241, 7.33546,
7.42764, 7.51761, 7.60347, 7.6826, 7.7515, 7.80584, 7.84099,
7.8532, 7.84099, 7.80584, 7.7515, 7.6826, 7.60347, 7.51761,
7.42764, 7.33546, 7.24241, 7.14942, 7.05715, 6.96606, 6.87645,
6.78854, 6.70246, 6.61831, 6.53613, 6.45593, 6.37773, 6.30151,
6.22724, 6.15488, 6.08441, 6.01577, 5.94893, 5.88383, 5.82042,
5.75867, 5.69852, 5.63992, 5.58282, 5.52719, 5.47298, 5.42013,
5.36862, 5.31839, 5.26941, 5.22163, 5.17503, 5.12956, 5.08519,
5.04189, 4.99961, 4.95834, 4.91803, 4.87866, 4.84021, 4.80264,
4.76592;
s2 = 7.91294, 7.97447, 8.03787, 8.10242, 8.17017, 8.23608, 8.30852,
8.38107, 8.45563, 8.53225, 8.61098, 8.69187, 8.77496, 8.8603,
8.94792, 9.03787, 9.13018, 9.22488, 9.32199, 9.42152, 9.52347,
9.62782, 9.7345, 9.84343, 9.95447, 10.0674, 10.1818, 10.2973,
10.4131, 10.528, 10.6403, 10.7472, 10.8444, 10.9251, 10.9794,
10.995, 10.9619, 10.8794, 10.7575, 10.6107, 10.4515, 10.2891,
10.1298, 9.97812, 9.83806, 9.71347, 9.60863, 9.52835, 9.47753,
9.46008, 9.47753, 9.52835, 9.60863, 9.71347, 9.83806, 9.97812,
10.1298, 10.2891, 10.4515, 10.6107, 10.7575, 10.8794, 10.9619,
10.995, 10.9794, 10.9251, 10.8444, 10.7472, 10.6403, 10.528,
10.4131, 10.2973, 10.1818, 10.0674, 9.95447, 9.84343, 9.7345,
9.62782, 9.52347, 9.42152, 9.32199, 9.22488, 9.13018, 9.03787,
8.94792, 8.8603, 8.77496, 8.69187, 8.61098, 8.53225, 8.45563,
8.38107, 8.30852, 8.23794, 8.17017, 8.10242, 8.03741, 7.97447,
7.91294;
s3 = 11.0794, 11.1662, 11.2555, 11.3489, 11.4432, 11.5415, 11.6428,
11.7471, 11.8545, 11.965, 12.0786, 12.1953, 12.3151, 12.4381,
12.5641, 12.6931, 12.825, 12.9595, 13.0965, 13.2354, 13.3757,
13.5164, 13.6558, 13.7914, 13.9186, 14.0295, 14.11, 14.1365,
14.0811, 13.9338, 13.7184, 13.4721, 13.2245, 12.9965, 12.8054,
12.6674, 12.5945, 12.5884, 12.6394, 12.7332, 12.8573, 13.0026,
13.1625, 13.3323, 13.5074, 13.6822, 13.8488, 13.9943, 14.0984,
14.1372, 14.0984, 13.9943, 13.8488, 13.6822, 13.5074, 13.3323,
13.1625, 13.0026, 12.8573, 12.7332, 12.6394, 12.5884, 12.5945,
12.6674, 12.8054, 12.9965, 13.2245, 13.4721, 13.7184, 13.9338,
14.0811, 14.1365, 14.11, 14.0295, 13.9186, 13.7914, 13.6558,
13.5164, 13.3757, 13.2354, 13.0965, 12.9595, 12.825, 12.6931,
12.5641, 12.4381, 12.3151, 12.1953, 12.0786, 11.965, 11.8545,
11.7471, 11.6428, 11.5415, 11.4432, 11.348, 11.2555, 11.1667,
11.0794;
z1 = Table[i, i, 0.01, 0.99, 0.01];
data1 = Transpose[z1, s1];
data2 = Transpose[z1, s2];
data3 = Transpose[z1, s3];
peaks1 = FindPeaks[s1];
peaks2 = FindPeaks[s2];
peaks3 = FindPeaks[s3];
mark1 = 0.50, 7.8532;
mark2 = 0.36, 10.995, 0.64, 10.995;
mark3 = 0.28, 14.1365, 0.50, 14.1372, 0.72, 14.1365;
mark4 = 0.50, 0;
mark5 = 0.36, 0, 0.64, 0;
mark6 = 0.28, 0, 0.50, 0, 0.72, 0;
p1 = ListPlot[data1, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p2 = ListPlot[data2, Joined -> True,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p3 = ListPlot[data3, Joined -> True,
PlotStyle -> Black, Thickness[0.004], AxesStyle -> Black,
PlotRange -> All];
p4 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark1];
p5 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark2];
p6 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark3];
p7 = Graphics[Text[Style["[EmptyUpTriangle]", 25], #] & /@ mark4];
p8 = Graphics[Text[Style["[EmptyCircle]", 25], #] & /@ mark5];
p9 = Graphics[Text[Style["[EmptySquare]", 25], #] & /@ mark6];
L = 1;
beta1 = 4.7300, 7.8532, 10.9956, 14.1372;
modefunction = ((Cos[b*x2] -
Cosh[b*x2]) - (((Cos[b*L] - Cosh[b*L])/(Sin[b*L] -
Sinh[b*L]))*(Sin[b*x2] - Sinh[b*x2])));
m3 = modefunction /. b -> beta1[[2]];
m4 = modefunction /. b -> beta1[[3]];
m5 = modefunction /. b -> beta1[[4]];
p10 = Plot[m3, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Tiny],
AxesStyle -> Black, PlotRange -> All];
p11 = Plot[m4, x2, 0, L,
PlotStyle -> Black, Thickness[0.004], Dashing[Large],
AxesStyle -> Black, PlotRange -> All];
p12 = Plot[m5, x2, 0, L, PlotStyle -> Black, Thickness[0.004],
AxesStyle -> Black, PlotRange -> All];
fig = Show[p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12,
PlotRange -> All, AxesStyle -> Black,
Frame -> True, True, True, False,
FrameLabel -> "Beam Length", "Non-dimensional [Beta]", ,
"Mode Shapes", PlotLabel -> None,
LabelStyle -> FontFamily -> "Arial", 40, GrayLevel[0]];
fig = Style[fig, GraphicsBoxOptions -> ImageSize -> 1000]
plotting legending style
plotting legending style
asked Feb 6 at 6:03
acousticsacoustics
44119
asked Feb 6 at 6:03
acousticsacoustics
44119
asked Feb 6 at 6:03
acousticsacoustics
44119
asked Feb 6 at 6:03
acousticsacoustics
44119
asked Feb 6 at 6:03
acousticsacoustics
44119
44119
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
5
$begingroup$
You can use PlotTheme -> "Monochrome" as follows:
if1, if2, if3 = Interpolation /@ data1, data2, data3;
Quiet@Plot[ m3, m4, m5, if1[x2], if2[x2], if3[x2], x2, 0, L,
PlotTheme -> "Monochrome", AxesStyle -> Black, PlotRange -> All,
PlotLegends -> LineLegend["m3", "m4", "m5", "data1", "data2", "data3"],
ImageSize -> Large, Frame -> True, Axes -> False,
GridLines -> None, 0, 5,
GridLinesStyle -> Directive[Gray, Dashing[]],
FrameLabel -> StringPadLeft["Non-dimensional β", 60],
StringPadRight[ "Mode shapes", 70], "Beam Length", None,
Epilog -> ListPlot[data1, data2, data3, MaxPlotPoints -> 30,
PlotStyle -> Black, PlotTheme -> "OpenMarkers"][[1]]]
Use Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to get
answered Feb 6 at 7:09
kglrkglr
186k10203422
$endgroup$
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
1
$begingroup$
@acoustics, useEpilog -> (First /@ p4, p5, p6, p7, p8, p9)to add your markers, and useGridLines -> None, 0to remove the horizontal line at 5.
$endgroup$
– kglr
Feb 6 at 7:50
1
$begingroup$
@acoustics, tryPlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]
$endgroup$
– kglr
Feb 6 at 9:38
1
$begingroup$
@acoustics, replaceTopwithScaled[.5, 1.]and add the optionPlotRangeClipping->False.
$endgroup$
– kglr
Feb 6 at 9:55
|
show 4 more comments
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f190977%2flimited-line-style-for-differentiating-curves-in-the-plot%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
5
$begingroup$
You can use PlotTheme -> "Monochrome" as follows:
if1, if2, if3 = Interpolation /@ data1, data2, data3;
Quiet@Plot[ m3, m4, m5, if1[x2], if2[x2], if3[x2], x2, 0, L,
PlotTheme -> "Monochrome", AxesStyle -> Black, PlotRange -> All,
PlotLegends -> LineLegend["m3", "m4", "m5", "data1", "data2", "data3"],
ImageSize -> Large, Frame -> True, Axes -> False,
GridLines -> None, 0, 5,
GridLinesStyle -> Directive[Gray, Dashing[]],
FrameLabel -> StringPadLeft["Non-dimensional β", 60],
StringPadRight[ "Mode shapes", 70], "Beam Length", None,
Epilog -> ListPlot[data1, data2, data3, MaxPlotPoints -> 30,
PlotStyle -> Black, PlotTheme -> "OpenMarkers"][[1]]]
Use Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to get
answered Feb 6 at 7:09
kglrkglr
186k10203422
$endgroup$
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
1
$begingroup$
@acoustics, useEpilog -> (First /@ p4, p5, p6, p7, p8, p9)to add your markers, and useGridLines -> None, 0to remove the horizontal line at 5.
$endgroup$
– kglr
Feb 6 at 7:50
1
$begingroup$
@acoustics, tryPlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]
$endgroup$
– kglr
Feb 6 at 9:38
1
$begingroup$
@acoustics, replaceTopwithScaled[.5, 1.]and add the optionPlotRangeClipping->False.
$endgroup$
– kglr
Feb 6 at 9:55
|
show 4 more comments
5
$begingroup$
You can use PlotTheme -> "Monochrome" as follows:
if1, if2, if3 = Interpolation /@ data1, data2, data3;
Quiet@Plot[ m3, m4, m5, if1[x2], if2[x2], if3[x2], x2, 0, L,
PlotTheme -> "Monochrome", AxesStyle -> Black, PlotRange -> All,
PlotLegends -> LineLegend["m3", "m4", "m5", "data1", "data2", "data3"],
ImageSize -> Large, Frame -> True, Axes -> False,
GridLines -> None, 0, 5,
GridLinesStyle -> Directive[Gray, Dashing[]],
FrameLabel -> StringPadLeft["Non-dimensional β", 60],
StringPadRight[ "Mode shapes", 70], "Beam Length", None,
Epilog -> ListPlot[data1, data2, data3, MaxPlotPoints -> 30,
PlotStyle -> Black, PlotTheme -> "OpenMarkers"][[1]]]
Use Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to get
answered Feb 6 at 7:09
kglrkglr
186k10203422
$endgroup$
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
1
$begingroup$
@acoustics, useEpilog -> (First /@ p4, p5, p6, p7, p8, p9)to add your markers, and useGridLines -> None, 0to remove the horizontal line at 5.
$endgroup$
– kglr
Feb 6 at 7:50
1
$begingroup$
@acoustics, tryPlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]
$endgroup$
– kglr
Feb 6 at 9:38
1
$begingroup$
@acoustics, replaceTopwithScaled[.5, 1.]and add the optionPlotRangeClipping->False.
$endgroup$
– kglr
Feb 6 at 9:55
|
show 4 more comments
5
5
5
$begingroup$
You can use PlotTheme -> "Monochrome" as follows:
if1, if2, if3 = Interpolation /@ data1, data2, data3;
Quiet@Plot[ m3, m4, m5, if1[x2], if2[x2], if3[x2], x2, 0, L,
PlotTheme -> "Monochrome", AxesStyle -> Black, PlotRange -> All,
PlotLegends -> LineLegend["m3", "m4", "m5", "data1", "data2", "data3"],
ImageSize -> Large, Frame -> True, Axes -> False,
GridLines -> None, 0, 5,
GridLinesStyle -> Directive[Gray, Dashing[]],
FrameLabel -> StringPadLeft["Non-dimensional β", 60],
StringPadRight[ "Mode shapes", 70], "Beam Length", None,
Epilog -> ListPlot[data1, data2, data3, MaxPlotPoints -> 30,
PlotStyle -> Black, PlotTheme -> "OpenMarkers"][[1]]]
Use Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to get
answered Feb 6 at 7:09
kglrkglr
186k10203422
$endgroup$
You can use PlotTheme -> "Monochrome" as follows:
if1, if2, if3 = Interpolation /@ data1, data2, data3;
Quiet@Plot[ m3, m4, m5, if1[x2], if2[x2], if3[x2], x2, 0, L,
PlotTheme -> "Monochrome", AxesStyle -> Black, PlotRange -> All,
PlotLegends -> LineLegend["m3", "m4", "m5", "data1", "data2", "data3"],
ImageSize -> Large, Frame -> True, Axes -> False,
GridLines -> None, 0, 5,
GridLinesStyle -> Directive[Gray, Dashing[]],
FrameLabel -> StringPadLeft["Non-dimensional β", 60],
StringPadRight[ "Mode shapes", 70], "Beam Length", None,
Epilog -> ListPlot[data1, data2, data3, MaxPlotPoints -> 30,
PlotStyle -> Black, PlotTheme -> "OpenMarkers"][[1]]]
Use Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to get
answered Feb 6 at 7:09
kglrkglr
186k10203422
edited Feb 6 at 7:48
answered Feb 6 at 7:09
kglrkglr
186k10203422
answered Feb 6 at 7:09
kglrkglr
186k10203422
answered Feb 6 at 7:09
kglrkglr
186k10203422
186k10203422
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
1
$begingroup$
@acoustics, useEpilog -> (First /@ p4, p5, p6, p7, p8, p9)to add your markers, and useGridLines -> None, 0to remove the horizontal line at 5.
$endgroup$
– kglr
Feb 6 at 7:50
1
$begingroup$
@acoustics, tryPlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]
$endgroup$
– kglr
Feb 6 at 9:38
1
$begingroup$
@acoustics, replaceTopwithScaled[.5, 1.]and add the optionPlotRangeClipping->False.
$endgroup$
– kglr
Feb 6 at 9:55
|
show 4 more comments
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
1
$begingroup$
@acoustics, useEpilog -> (First /@ p4, p5, p6, p7, p8, p9)to add your markers, and useGridLines -> None, 0to remove the horizontal line at 5.
$endgroup$
– kglr
Feb 6 at 7:50
1
$begingroup$
@acoustics, tryPlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]
$endgroup$
– kglr
Feb 6 at 9:38
1
$begingroup$
@acoustics, replaceTopwithScaled[.5, 1.]and add the optionPlotRangeClipping->False.
$endgroup$
– kglr
Feb 6 at 9:55
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
actually, I have marked some maximum points in my OP, where I have used the triangle, circle, and squares. Now the thing is even we have a limited number of markers right. How to mark these point differentely
$endgroup$
– acoustics
Feb 6 at 7:30
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
$begingroup$
I used your code, But I am getting some unnecessary horizontal line near 5. How to avoid this
$endgroup$
– acoustics
Feb 6 at 7:38
1
1
$begingroup$
@acoustics, use
Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to add your markers, and use GridLines -> None, 0 to remove the horizontal line at 5.$endgroup$
– kglr
Feb 6 at 7:50
$begingroup$
@acoustics, use
Epilog -> (First /@ p4, p5, p6, p7, p8, p9) to add your markers, and use GridLines -> None, 0 to remove the horizontal line at 5.$endgroup$
– kglr
Feb 6 at 7:50
1
1
$begingroup$
@acoustics, try
PlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]$endgroup$
– kglr
Feb 6 at 9:38
$begingroup$
@acoustics, try
PlotLegends -> Placed[LineLegend["m3", "m4", "m5", "data1", "data2", "data3", LegendLayout -> "Row", 1], Top]$endgroup$
– kglr
Feb 6 at 9:38
1
1
$begingroup$
@acoustics, replace
Top with Scaled[.5, 1.] and add the option PlotRangeClipping->False.$endgroup$
– kglr
Feb 6 at 9:55
$begingroup$
@acoustics, replace
Top with Scaled[.5, 1.] and add the option PlotRangeClipping->False.$endgroup$
– kglr
Feb 6 at 9:55
|
show 4 more comments
draft saved
draft discarded
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f190977%2flimited-line-style-for-differentiating-curves-in-the-plot%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
