Constraints on meshgrid. Remove points outside function

I need help constraining the entries in my meshgrid. So far the entries take values on the entire x-axis and y-axis.

I have a figure consisting of an upper curve and a lower curve. Any point outside the curves should be equal to nan and not be coloured.

M  = 3749.41;                                   %MeV
m1 = 3728.4;                                   %MeV
m2 = 0.5109989461;                              %MeV
m3 = 0.5109989461;                              %MeV
lambda = @(x,y,z) (x-y-z).^2-4*y*z;             %Triangle function
s = M^2;                                        %Mass of the decaying particle squared
s1 = linspace((m1+m2).^2,(sqrt(s)-m3)^2,1000); %s1 = s12
s2 = linspace((m2+m3).^2,(sqrt(s)-m1)^2,1000); %s2 = s23
s3 = linspace((m1+m3).^2,(sqrt(s)-m2)^2,1000); %s3 = s31

s11 = @(s2) m1^2+m2^2-1./(2*s2).*((s2-s+m1^2).*(s2+m2^2-m3^2)-lambda(s2,s,m1^2).^(1/2).*lambda(s2,m2^2,m3^2).^(1/2)); %upper half of boundary curve
s12 = @(s2) m1^2+m2^2-1./(2*s2).*((s2-s+m1^2).*(s2+m2^2-m3^2)+lambda(s2,s,m1^2).^(1/2).*lambda(s2,m2^2,m3^2).^(1/2)); %lower half of boundary curve
hold on
plot(s2,s11(s2),'r','LineWidth',2)
plot(s2,s12(s2),'r','LineWidth',2)
mr = 0.0167*1000;                                %Pole mass in MeV
gamma01 =   0.002*1000;                         %Decay width in MeV
A1 =@(a) sqrt(a)./(mr^2-a-1i*gamma01*sqrt(a));  %Breit-Wigner

T0 = 1;
Matrixelement = @(b) T0.*A1(b);

costheta = @(s1) 2.*(sqrt(s1)-min(sqrt(s1)))./(max(sqrt(s1))-min(sqrt(s1)))-1;
lpol = @(s1) legendreP(1,costheta(s1));
A1 =@(a) sqrt(a)./(mr^2-a-1i*gamma01*sqrt(a));

[x,y] = meshgrid(s2,[s11(s2),s12(s2)]);
hold on
mscale1 = @(x) (Matrixelement(s2) - min(Matrixelement(s2)))./( max(Matrixelement(s2)) - min(Matrixelement(s2))); %normalize
mscale2 = @(a) (Matrixelement(s2) - min(Matrixelement(s2)))./( max(Matrixelement(s2)) - min(Matrixelement(s2))); %normalize
z = (mscale1(x).*conj(mscale1(x))).*costheta(y).^2;             %abs(1/2.*(3.*costheta(y).^2-1)); %remember spin
contourf(x,real(y),real(z),'edgecolor','none')
plot(s2,s11(s2),'r','LineWidth',2)
plot(s2,s12(s2),'r','LineWidth',2)
colorbar

All I need is to make the meshgrid only to take values inside the curve.

Answer 1

[Matt J]

Just apply logical indexing on the appropriate region and set it to NaN,

bad=(y<s11(s2)) | (y>s12(s2));

z(bad)=nan;

[Martin Mikkelsen]

Thank you for your answer. I appreciate it. Is there a way to apply this in

[x,y] = meshgrid(s2,[s11(s2),s12(s2)]);

Instead of removing it? Maybe with inpolygon

[Matt J]

You could remove the unwanted x,y prior to the calculation of z and just work with the list of valid values. That might be more efficient:

[xrect,yrect] = meshgrid(s2,[s11(s2),s12(s2)]);
 
[x,y]=deal(xrect,yrect);

x(bad)=[];
y(bad)=[];
z=...

For plotting purposes, however, you would have to re-insert the calculated z into a rectangular array,

zrect=nan(size(xrect));
zrect(~bad)=z;

contourf(xrect,real(yrect),real(zrect),'edgecolor','none')

[Martin Mikkelsen]

Like this?

[xrect,yrect] = meshgrid(s2,[s11(s2),s12(s2)]);
 
[x,y]=deal(xrect,yrect);

bad=(y<s11(s2)) | (y>s12(s2));

x(bad)=[];
y(bad)=[];

mscale1 = @(x) (Matrixelement(s2) - min(Matrixelement(s2)))./( max(Matrixelement(s2)) - min(Matrixelement(s2))); %normalize
z = abs(Matrixelement(x)).^2+costheta(y); %abs(1/2.*(3.*costheta(y).^2-1)); %remember spin

zrect=nan(size(xrect));
zrect(~bad)=z;

contourf(xrect,real(yrect),real(zrect),'edgecolor','none')

There seems to be only one value of zrect not equal to nan now. Am I missing something?

[Matt J]

Check to make sure you’ve constructed the logical array “bad” correctly.

[Martin Mikkelsen]

I changed it to

bad=(y>=s11(s2)) | (y<=s12(s2));

And that fixed the problem. Thank you so much! I really appreciate it.