Trying a overlapping but piecewise plot

2022 10 31
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更新时间：2022 10 31
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Here is my code:
clear all
close all
clc
syms a(x)
N1_0 = - (3*x^5)/16 + (5*x^3)/8 - (15*x)/16 + (1/2);
N2_0 = (3*x^5)/16 - (5*x^3)/8 + (15*x)/16 + 1/2;
N1_1 = - (3*x^5)/16 + x^4/16 + (5*x^3)/8 - (3*x^2)/8 - (7*x)/16 + 5/16;
N2_1 = - (3*x^5)/16 - x^4/16 + (5*x^3)/8 + (3*x^2)/8 - (7*x)/16 - 5/16;
N1_2 = - x^5/16 + x^4/16 + x^3/8 - x^2/8 - x/16 + 1/16;
N2_2 = x^5/16 + x^4/16 - x^3/8 - x^2/8 + x/16 + 1/16;
x1 = 0;
x2 = 0.25;
x3 = 0.5;
x4 = 0.75;
x5 = 1;
a(x) = piecewise(x1<=x<=x2,0,x4<=x<=x5,0,x3<=x<=x4,N1_0,x2<=x<=x3,N2_0,x2<=x<=x3,N1_1,x3<=x<=x4,N1_1,x2<=x<=x3,N2_0,x2<=x<=x3,N2_1,x3<=x<=x4,N2_2)
fplot(a)
The idea is to overlap N1_0 to N2_2 on to 0.5, without a residual solution, but the functions should overlap each other on the same plot/line
This is the pencil sketch of how it should look like:
Feel free to ask if you want to know anything about this
Using piecewise function was my idea (coz I thought it would work but it didn't) but it is not necessary.
Feel free to modify the code as you please
Using MATLAB online
Please help
Thanks

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Star Strider
Star Strider 2022-10-31
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0 个投票

Ran in:
The problem description leaves much to the imagination. If you want to offset them on the x-axis, this likely requires a loop. (I also made them functions in the event that the function argument was to be shifted, so for example the first would be ‘N1_0(x)’ the second ‘N1_0(x+0.5)’ and so for the others.) Here, I just shifted the fplot evaluation intervals.
syms a(x)
N1_0(x) = - (3*x^5)/16 + (5*x^3)/8 - (15*x)/16 + (1/2);
N2_0(x) = (3*x^5)/16 - (5*x^3)/8 + (15*x)/16 + 1/2;
N1_1(x) = - (3*x^5)/16 + x^4/16 + (5*x^3)/8 - (3*x^2)/8 - (7*x)/16 + 5/16;
N2_1(x) = - (3*x^5)/16 - x^4/16 + (5*x^3)/8 + (3*x^2)/8 - (7*x)/16 - 5/16;
N1_2(x) = - x^5/16 + x^4/16 + x^3/8 - x^2/8 - x/16 + 1/16;
N2_2(x) = x^5/16 + x^4/16 - x^3/8 - x^2/8 + x/16 + 1/16;
Nc = {N2_0; N1_1; N2_1; N1_2; N2_2};
x1 = 0;
x2 = 0.25;
x3 = 0.5;
x4 = 0.75;
x5 = 1;
% a(x) = piecewise(x1<=x<=x2,0,x4<=x<=x5,0,x3<=x<=x4,N1_0,x2<=x<=x3,N2_0,x2<=x<=x3,N1_1,x3<=x<=x4,N1_1,x2<=x<=x3,N2_0,x2<=x<=x3,N2_1,x3<=x<=x4,N2_2)
% fplot(a)
xv = [0 5];
figure
fplot(N1_0,xv)
hold on
for k = 1:numel(Nc)
fplot(Nc{k},[xv(1)+0.5*k xv(2)])
end
hold off
grid
The piecewise approach would work for discontinuous funcitons (so each defined over different, consecutive intervals of ‘x’), however that is not my impression of what you want to do.
.

8 个评论
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Saim
Saim 2022-10-31
编辑：Saim 2022-10-31
Thanks for the help.
Your concept is cool but it doesn't achieve the "sketched" output I attached in the post.
Basically, each function that is orignially within the range [-1 1] is being compressed to 0.25 with a horizontal shift. The shape of the function in [-1 1] should remain the same but its length should now be 0.25 and each function has its own specified region. The final output is between x = 0 to x=1, just as I have shown in my sketch
Thanks again
Star Strider
Star Strider 2022-10-31
‘Your concept is cool but it doesn't achieve the "sketched" output I attached in the post.’
I don’t understand the ‘sketched output’ because it bears no resemblance to any of the actual functions.
‘Basically, each function that is orignially within the range [-1 1] is being compressed to 0.25 with a horizontal shift.’
This makes no sense to me.
.
Saim
Saim 2022-10-31
lets say the function N1_0, it is originally being considered only in the range x=-1 and x=+1. This shape should not change in the final output.
That is what I have shown in the sketch, if you look carefully makred as N(subscript1)(superscript0)
but what is different for the output is that with the same shape in mind (the height can change but not the shape it gives), it should compress to a range of x = 0 to x = 0.25 but shifted from x = 0.5 to 0.75 (as shown in sketch).
Something like this:
Star Strider
Star Strider 2022-10-31
Ran in:
Ran in:
It took a few minutes for me to figure out the best way to do this.
Still using fplot, this appears to work —
syms a(x)
N1_0(x) = - (3*x^5)/16 + (5*x^3)/8 - (15*x)/16 + (1/2);
N2_0(x) = (3*x^5)/16 - (5*x^3)/8 + (15*x)/16 + 1/2;
N1_1(x) = - (3*x^5)/16 + x^4/16 + (5*x^3)/8 - (3*x^2)/8 - (7*x)/16 + 5/16;
N2_1(x) = - (3*x^5)/16 - x^4/16 + (5*x^3)/8 + (3*x^2)/8 - (7*x)/16 - 5/16;
N1_2(x) = - x^5/16 + x^4/16 + x^3/8 - x^2/8 - x/16 + 1/16;
N2_2(x) = x^5/16 + x^4/16 - x^3/8 - x^2/8 + x/16 + 1/16;
Nc = {N1_0; N2_0; N1_1; N2_1; N1_2; N2_2};
x1 = 0;
x2 = 0.25;
x3 = 0.5;
x4 = 0.75;
x5 = 1;
% a(x) = piecewise(x1<=x<=x2,0,x4<=x<=x5,0,x3<=x<=x4,N1_0,x2<=x<=x3,N2_0,x2<=x<=x3,N1_1,x3<=x<=x4,N1_1,x2<=x<=x3,N2_0,x2<=x<=x3,N2_1,x3<=x<=x4,N2_2)
% fplot(a)
lgdc = {'N_1^0','N_2^0','N_1^1','N_2^1','N_1^2','N_2^2'};
xv = [-1 1];
figure
hold on
for k = 1:numel(Nc)
hfp{k} = fplot(Nc{k},xv, 'DisplayName',lgdc{k});
end
hold off
grid
title('Original')
legend('Location','NE')
xv = [-1 1];
figure
hold on
for k = 1:numel(Nc)
hfp{k} = fplot(Nc{k},xv);
hfp{k}.Visible = 'off';
x = hfp{k}.XData;
y = hfp{k}.YData;
hp{k} = plot(x*0.125 + 0.125 + 0.5*k, y , 'DisplayName',lgdc{k});
end
hold off
grid
xlim([0 max(xlim)])
title('X-Scaled & X-Shifted')
legend([hp{:}],'Location','best')
I am not certain that I understood exactly the result you want, so make appropriate changes to get it.
The ‘x’ calculation is:
x*0.125 + 0.125 + 0.5*k
↑← SF ↑← CO ↑← VO
where ‘SF’ is the scaling factor to get the ‘x’ values to span 0.25, ‘CO’ is a constant offset, and ‘VO’ is the variable offset that increments with the loop. Change those as necessary to get the desired result.
.
Saim
Saim 2022-10-31
Thank you so much All I have to do is make some minor adjustments to match my first sketch but this is more than enough. Thanks a lot
Star Strider
Star Strider 2022-10-31
As always, my pleasure!
Saim
Saim 2022-10-31
编辑：Saim 2022-10-31
check this out, gives the exact first sketch output.
figure
hold on
for k = [1 4 6]
hfp{k} = fplot(Nc{k},xv);
hfp{k}.Visible = 'off';
x = hfp{k}.XData;
y = hfp{k}.YData;
hp{k} = plot(x*0.125 +.625, y , 'DisplayName',lgdc{k});
end
for k = [2 3 5]
hfp{k} = fplot(Nc{k},xv);
hfp{k}.Visible = 'off';
x = hfp{k}.XData;
y = hfp{k}.YData;
hp{k} = plot(x*0.125 +.375, y , 'DisplayName',lgdc{k});
end
hold off
grid
xlim([0 1])
title('X-Scaled & X-Shifted')
legend([hp{:}],'Location','best')
Still, all credit goes to you
PS I dont know how you run it here with the graphical and numerical output but still thanks a lot for all the help
Star Strider
Star Strider 2022-10-31
Ran in:
Ran in:
As always, my pleasure!
Thank you!
I was curious, so I ran it to see what it looked like —
syms a(x)
N1_0(x) = - (3*x^5)/16 + (5*x^3)/8 - (15*x)/16 + (1/2);
N2_0(x) = (3*x^5)/16 - (5*x^3)/8 + (15*x)/16 + 1/2;
N1_1(x) = - (3*x^5)/16 + x^4/16 + (5*x^3)/8 - (3*x^2)/8 - (7*x)/16 + 5/16;
N2_1(x) = - (3*x^5)/16 - x^4/16 + (5*x^3)/8 + (3*x^2)/8 - (7*x)/16 - 5/16;
N1_2(x) = - x^5/16 + x^4/16 + x^3/8 - x^2/8 - x/16 + 1/16;
N2_2(x) = x^5/16 + x^4/16 - x^3/8 - x^2/8 + x/16 + 1/16;
Nc = {N1_0; N2_0; N1_1; N2_1; N1_2; N2_2};
x1 = 0;
x2 = 0.25;
x3 = 0.5;
x4 = 0.75;
x5 = 1;
lgdc = {'N_1^0','N_2^0','N_1^1','N_2^1','N_1^2','N_2^2'};
xv = [-1 1];
figure
hold on
for k = [1 4 6]
hfp{k} = fplot(Nc{k},xv);
hfp{k}.Visible = 'off';
x = hfp{k}.XData;
y = hfp{k}.YData;
hp{k} = plot(x*0.125 +.625, y , 'DisplayName',lgdc{k});
end
for k = [2 3 5]
hfp{k} = fplot(Nc{k},xv);
hfp{k}.Visible = 'off';
x = hfp{k}.XData;
y = hfp{k}.YData;
hp{k} = plot(x*0.125 +.375, y , 'DisplayName',lgdc{k});
end
hold off
grid
xlim([0 1])
title('X-Scaled & X-Shifted')
legend([hp{:}],'Location','best')
.

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