Trying a overlapping but piecewise plot

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

Answer 1

[Star Strider]

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.

.

[Saim]

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]

‘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]

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]

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]

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]

As always, my pleasure!

[Saim]

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]

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')

.