Point array to generate meshgrid

I have a point array describing the equal-spacing points in a hexagon, how can I use this array to generate a meshgrid with identical points so that I can use pcolor?

Answer 1

[Walter Roberson]

Xu = uniquetol(X(:) );
Yu = uniquetol(Y(:) );
[Xg, Yg] = meshgid(Xu, Yu);
F = scatteredInterpolant(X(:), Y(:), Z(:)) ;
Zg = F(Xg, Yg);
pcolor(Xg, Yg, Zg);

[Huiyuan Zheng]

Sorry but I don't understand this answer. I don't lack sample points in the hexagon. The problem is, if I directly use x and y of the point array to generate meshgrid, the plot area will be in shape of square but not hexagon.

[Walter Roberson]

The locations that are outside of the convex hull of the original points, will interpolate to NaN, and pcolor() displays NaN as transparent.

[Huiyuan Zheng]

My point array is the points in the following code. While I try to put it in your code, I don't know the result.

I divide the point array into three sections with different orientations so that the hexagonal boudnaries are all smooth. However, the problem is that, there are three blank lines in between each sections. (I delete the boundary to avoid overcounting since the hexagon is a cell in a periodic function.)

q1 = [1/2;sqrt(3)/2]; % lattice vector 1
q2 = [1/2;-sqrt(3)/2]; % lattice vector 2 
q3 = -(q1+q2); % the compensated vector

np = 100;
% delete one boundary to avoid repeating calculation
r1 = linspace(0,1,np+1); r1(end) = [];
r2 = linspace(0,1,np+1); r2(1) = [];
[R1,R2] = meshgrid(r1,r2);
section1 = [q2,q3]*[R1(:),R2(:)].';
section2 = [q3,q1]*[R1(:),R2(:)].';
section3 = [q1,q2]*[R1(:),R2(:)].';
points = [section1,section2,section3];

KX1 = reshape(section1(1,:),np,np);
KY1 = reshape(section1(2,:),np,np);
KX2 = reshape(section2(1,:),np,np);
KY2 = reshape(section2(2,:),np,np);
KX3 = reshape(section3(1,:),np,np);
KY3 = reshape(section3(2,:),np,np);

figure; hold on;
pcolor(KX1,KY1,KX1*0+1);
pcolor(KX2,KY2,KX2*0+2);
pcolor(KX3,KY3,KX3*0+3);
shading interp; axis equal;

Answer 2

[Steven Lord]

I don't believe pcolor allows you to create elements with more or fewer than 4 sides. What I think you want to do is either create various patch objects or perhaps create an array of polyshape objects and use some of the object functions (rotate, scale, translate) to create an array of polyshape objects to plot.

H = nsidedpoly(6);
plot(H)
axis equal

H(2) = translate(H, 2, 0); % Now H has 2 hexagons
H(3:4) = translate(H, 0, 2); % Now it has 4, both of the previous two translated up 2 units
figure
plot(H)
axis equal

[Huiyuan Zheng]

Yes, to plot a filled hexagon uses patch is enough, while what I need is a point array describing the the equal-spacing points inside a hexagon. As you said, it seems forbidden to use a create elements with more or fewer than 4 sides, so I divide it into three sections (you can find it in the discussion of the first answer):

Strictly speaking, I have another requirement, which is to avoid the overcounting the boundary since the hexagon is a cell in a periodic function. That's why I made those modifications in my code. However, the problem is, the pcolor of the three sections are not connected, there is a blank line in between.