MATLAB: 2D Histograms in Planes XZ, YZ

2d3dhistogramprojectxzyz

Hello, I am trying to get a representation similar to the one attached to this message. That is to say, I would like to represent two 2D-histogram, one in the plane XZ and the other in the plane YZ. In X and Y, the magnitude to be displayed is the same, but the thing is that the Z-axis is different. As I want to make the representation clearer, I would add additional information in the plane Z=0, that is the reason for which I have not used the 2D-histogram with two different Y-axes. It would be very nice if you could help me to solve this. Thanks in advance, Manuel.

Best Answer

OK, here's a simple example where you plot a few pieces together...

% First some "test-data":
x = randn(500,1);
x = x-min(x)+0.5;
y = randn(500,1);
y = y-min(y)+0.5;
y = y.^1.5+1*x;  
z = exp(-abs(2*x-y)/4); % Just to get something similar to the figure linked to in your reference 
[Nx,xH] = hist(x,9);  % Histogram of X-values
[Ny,yH] = hist(y,11); % and Y
dX = gradient(xH);    % Spacing between histogram bin centres   
dY = gradient(yH); 
%%Plot stuff...
scatter3(x,y,z,15,z,'filled') % The points
for i1 = 1:length(xH), % And the X-histogram bars
  pHmyX(i1) = patch(xH(i1)+dX(i1)*[-1 1 1 -1 -1]/2,...
                    [0 0 0 0 0],...
                    [0 0 Nx(i1)*[1 1] 0],rand(1,3));         
end
for i1 = 1:length(yH),
  pHmyY(i1) = patch([0 0 0 0 0],...
                    yH(i1)+dY(i1)*0.9*[-1 1 1 -1 -1]/2,...
                    [0 0 Ny(i1)*[1 1] 0],rand(1,3));            
end

You should be able to modify and extend that to suit your needs.

HTH

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Your post is not clear (see our comments). However I guess what you want is approximate the volume of the (cone) object from the point cloud.

% Cone parameters
R = 10;
h = 20;
N = 10000;
% Generate points in cone
dx = (pi*R^2*h/3/N)^(1/3);
rvec = linspace(-R,R,ceil(2*R/dx));
hvec = linspace(0,h,ceil(h/dx));
[X,Y,Z] = ndgrid(rvec,rvec,hvec);
is_in_cone = (X.^2+Y.^2) <= (R/h*(h-Z)).^2;
x = X(is_in_cone);
y = Y(is_in_cone);
z = Z(is_in_cone);
% Method1: Estimate the volume of the 3D object assuming the object is convex
tri = delaunay(x,y,z);
trisurf(tri,x,y,z)
% indices of triangle
i1 = tri(:,1);
i2 = tri(:,2);
i3 = tri(:,3);
i4 = tri(:,4);
% Method1: Volume by summing tetrahedron
v1 = [x(i1)-x(i2) y(i1)-y(i2) z(i1)-z(i2)];
v2 = [x(i1)-x(i3) y(i1)-y(i3) z(i1)-z(i3)];
v3 = [x(i1)-x(i4) y(i1)-y(i4) z(i1)-z(i4)];
A = 1/2*cross(v1,v2,2);                     % surface of a triangle
V = 1/3*dot(A,v3,2);                        % volume of a tetrahedron
format long
V = sum(abs(V))
% Method2: use CONVHULL
[~,V]=convhull(x,y,z)
% Method3: theoretical volume of a cone computed directly from base radius and heigh
V = pi*R^2*h/3

MATLAB: Projection of 3D positions histograms in planes XY, YZ, and XZ

Here is an example

m = 20;
    % generate some data
n = 500;
x = randn(500,1);
y = randn(500,1);
z = randn(500,1);
    % create regular grid
x1 = linspace(min(x),max(x),m);
y1 = linspace(min(y),max(y),m);
[X,Y] = meshgrid(x1,y1);
    % calculate density matrix
xy = hist3([x y],[m m]);
plot3(x,y,z,'.r')
surface(X,Y,xy*0-5,'cdata',xy)
axis vis3d

Best Answer

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