I have a function which takes a voxel representation of a 3D landscape and can plot a X-Y section to show the middle of the landscape. The voxel representation is stored in a 3 dimensional matrix with a number that represents something important. Obviously the matrix is
1,1,1
2,2,2
in terms of accessing the elements but the actual 3D locations are found in the following method:
(index-1)*resolution+0.5*resolution+minPos;
where resolution is the grid size :
resolution
<-->
__ __ __
|__|__|__|
<- Min pos
and minPos is where the grid starts.
Now in terms of the actual question, i would like to extract a single X-Y section of this voxel representation and display it as a surf. This can be done by just doing this:
surf(voxel(:, :, section))
however then you get this:
The obvious problem is that the grid will start at 0 because that is how the matrix representation is. How can i set the minimum and cell size for surf, ie so that the grid will start at the minimum (shown above) and will have the grid spacing of resolution (shown above).
Read the documentation of surf, you can also provide x and y coordinates corresponding to your data points.
surf(X,Y,Z)
X and Y can be either vectors or matrices:
surf(X,Y,Z) uses Z for the color data and surface height. X and Y are vectors or matrices defining the x and y components of a surface. If X and Y are vectors, length(X) = n and length(Y) = m, where [m,n] = size(Z). In this case, the vertices of the surface faces are (X(j), Y(i), Z(i,j)) triples. To create X and Y matrices for arbitrary domains, use the meshgrid function
Example
Z=[ 0 1 2 3;
7 6 5 4;
8 9 10 11];
x=[-1 0 1 2];
y=[-2 0 2];
surf(x,y,Z);
Of course you have to match Z, x and y matrices/vectors as clearly described in the doc^^
Just remember that elements in columns of Z are surf'ed as values along the y-axis, elements in rows of Z are surf'ed as values along the x-axis. This is clearly to be seen in the example picture.
Solution
I think you switched the x and y-axis around, which you can fix by just transposing z:
s = size(voxel);
xi = (minPosX:resolution:(minPosX+resolution*s(1)-1));
yi = (minPosY:resolution:(minPosY+resolution*s(2)-1));
z = (voxel(:,:,section));
surf(xi, yi, z');
or that you're picking the wrong numbers for constructing xi and yi and it should be this instead:
xi = (minPosX:resolution:(minPosX+resolution*s(2)-1));
yi = (minPosY:resolution:(minPosY+resolution*s(1)-1));
z = (voxel(:,:,section));
surf(xi, yi, z);
So it was easy enough to do:
lets say we have a 3D matrix "voxel";
s = size(voxel);
xi = (minPosX:resolution:(minPosX+resolution*s(1)-1));
yi = (minPosY:resolution:(minPosY+resolution*s(2)-1));
z = (voxel(:,:,section));
[x y] = meshgrid(xi, yi);
x = x';
y = y';
surf(x, y, z);
Provides the following plot:
This is rotated which is annoying, I cant seem to get it to rotate back (I could just visualise around the other way but that's ok)
Related
I have 3 axes: X of size N, Y of size M and Z of size O, which correspond to the coordinates of my data.
I have a matrix: DATA of size MxNxO, which corresponds to the module for each points.
I would like to plot the MATLAB figure of coordinate X, Y, Z and color the point depending of the value of the matrix DATA of size MxNxO.
I tried lots of functions such as scatter3, surf, plot3, but none is working as I wanted.
This is what I tried:
n = 10;
x = linspace(0,10,n);
y = linspace(0,10,n);
z = linspace(0,10,n);
DATA = randn(n,n,n);
scatter3(x,y,z,DATA);
This code didn't work because DATA is not the same size as x, y, z. I also tried with:
[X,Y,Z] = ndgrid(x,y,z)
scatter3(X,Y,Z,DATA);
but this didn't work either.
The trick with scatter3() is to "unroll" your matrices to a column vector, and don't forget that the fourth argument is size, rather than colour:
n = 10;
x = linspace(0,10,n);
y = linspace(0,10,n);
z = linspace(0,10,n);
[X,Y,Z] = ndgrid(x,y,z);
DATA = randn(n,n,n);
% here 3 is the size. You can set it to a different constant, or vary it as well
scatter3(X(:), Y(:), Z(:), 3, DATA(:));
Results in
You can colour a surface, see its documentation, however, it doesn't seem to make much sense in your case, given you have a full cube of data points. A surface is 2D, whereas your data is 3D. For a 2D surface, simply follow the example in the docs:
n = 10;
x = linspace(0,10,n);
y = linspace(0,10,n);
Z = rand(n);
DATA = randn(n);
surf(x, y, Z, DATA);
Images rendered in R2007b, syntax cross-checked with the documentation.
If you've got a surface defined by an M -by- 4 array containing X, Y, Z and Data, you can use delaunay() to create a Delaunay triangulation of your points and then trisurf() to plot that. Note that this still requires a 2D surface, albeit it can vary in three dimensions. The cube of data in your example still doesn't make sense to plot as a surface, even with this method.
I want to create a non-rectangular meshgrid in matlab.
Basically I have a polygon shaped feasible set I need to make a grid of in order to interpolate 3D data points in this set. The function for interpolation is given and requires finite (x, y, z) inputs. Where x is nx1, y is 1xm and z is nxm. Right now I have the mesh set up with linspace and set all NaN (infeasible) values to 0 before using my function, which is wrong of course (third figure).
Is there a simple solution for this?
I added a picture illustrating what I'm currently doing: First plot is the feasible set, second plot are solved sample data points in this set and third plot is the interpolation (currently still with rectangular meshgrid and NaN = 0). What I need is a meshgrid looking like the first figure (red polygon) instead of a rectangular one. In the third plot you can see that the rectangular meshgrid in combination with setting NaN to 0 (=infeasible values, not included in the red polygon set) results in a wrong interpolation along the edges, because it includes infeasible regions.
Here is my code using a rectangular meshgrid:
figure (2) %sample data
plot3(X0(1,:), X0(2,:), U, 'x')
%X0(1,:) and X0(2,:) are vectors corresponding to the Z-Values (blue sample data)
%X0 and U are in the feasible set (red polygon)
xv = linspace(xLb(1), xUb(1), 100);
yv = linspace(xLb(2), xUb(2), 100); %xLb and xUb are upper and lower bounds for the rectangle mesh
[x1,x2] = meshgrid(xv, yv);
Z = griddata(X0(1,:), X0(2,:), U, x1, x2);
%This grid obviously includes values that are not in the feasible set (red polygon) by its rectangular nature
Z(isnan(Z))=0; %set infeasible values to 0, wrong of course
testMPC = someInterpolationFunction([0:length(Z)-1]',[0:length(Z)-1],Z);
testMPC.showInterpolation(20,20)
%this shows figure 3 in the attached picture
Try something like this:
nRows = 100;
nCols = 200;
x1 = #(x) max(0, x-50);
x2 = #(x) min(nCols, nCols - 50 + x);
RR = zeros(nRows, nCols);
CC = zeros(nRows, nCols);
for iRow = 1:nRows
c1 = x1(iRow);
c2 = x2(iRow);
colVec = linspace(c1, c2, nCols);
RR(iRow, :) = iRow;
CC(iRow, :) = colVec;
end
mesh(RR, CC, zeros(size(RR)))
You'd need to redefine the functions for x1 and x2 or course as well as the scaling, but this should give you an idea of how to get started.
Solution posted below function to plot bar 3 with separate x, y values and separate width and height values
bar3(x,y,z,xWidth,yWidth)
We are currently working on a project that allow one to visualize the area under a 3d function, f(x,y). The purpose of this is to demonstrate how the bars cut a 3d surface. Indirectly to visualize the desired integral.
We wish to have the bars match up with the intervals of the surface grid.
Below is a rough demonstration of the idea.
bar3 only has input for the x-values bar3(x,z), where as surf has a input for both the x and y surf(x,y,z)
Unfortunately this is what we are getting. - this is because bar3 cant be in terms of x and y
CODE:
clc;
cla;
d=eval(get(handles.edtOuterUpperB,'string'));
c=eval(get(handles.edtOuterLowerB,'string'));
b=eval(get(handles.edtInnerUpperB,'string'));
a=eval(get(handles.edtInnerLowerB,'string'));
n=eval(get(handles.edtInnerInterval,'string'));
m=eval(get(handles.edtOuterInterval,'string'));
h=(b-a)/n;
k=(d-c)/m;
[x,y] = meshgrid(a:h:b, c:k:d);
f=eval(get(handles.edtFunc,'string'));
surf(x,y,f);
hold on
bar3(f,1);
If you look closely, you will see that the XData and YData are different from the mesh to the 3D bar plot. This is because your mesh uses "real" x and y values while the bar plot uses indexes for the x and y values.
To fix this, you will want to change one or the other. For your case, the easiest one to change is going to be the surface. You can actually just omit the x and y inputs and the indexed x and y values will be used instead by default when generating the surface.
surf(f);
From the documentation for surf:
surf(Z) creates a three-dimensional shaded surface from the z components in matrix Z, using x = 1:n and y = 1:m, where [m,n] = size(Z). The height, Z, is a single-valued function defined over a geometrically rectangular grid. Z specifies the color data, as well as surface height, so color is proportional to surface height.
Update
If you want to keep the non-indexed values on the x and y axes, you will want to convert the bar3 plot instead. Unfortunately, MATLAB provides a way to specify the x axis bot not the y axis. You can take one of two approaches.
Change the XData
You can get the XData property of the resulting bar objects and change them to the data you want.
x = a:h:b;
y = c:k:d;
%// Anonymous function to scale things for us
scaler = #(vals)x(1) + ((vals-1) * (x(end) - x(1)) / (numel(x) - 1));
%// Create the bar plot
bars = bar3(y, f);
%// Change the XData
xdata = get(bars, 'XData');
xdata = cellfun(scaler, xdata, 'uni', 0);
set(bars, {'XData'}, xdata);
set(gca, 'xtick', x)
%// Now plot the surface
surf(x,y,f);
And just to demonstrate what this does:
x = linspace(0.5, 1.5, 5);
y = linspace(2.5, 4.5, 4);
f = rand(4,5);
scaler = #(vals)x(1) + ((vals-1) * (x(end) - x(1)) / (numel(x) - 1));
bars = bar3(y, f);
set(bars, {'XData'}, cellfun(scaler, get(bars, 'XData'), 'uni', 0))
set(gca, 'xtick', x)
axis tight
Change the XTickLabels
Instead of changing the actual data, you could simply change the values that are displayed to be what you want them to be rather than the indexed values.
x = a:h:b;
y = c:k:d;
labels = arrayfun(#(x)sprintf('%.2f', x), x, 'uni', 0);
bar3(y, f);
set(gca, 'xtick', 1:numel(x), 'xticklabels', labels);
hold on
%// Make sure to use the INDEX values for the x variable
surf(1:numel(x), y, f);
We found a user contributed function scatterbar3, which does what we want, in a different way than what bar3 uses:
http://www.mathworks.com/matlabcentral/fileexchange/1420-scatterbar3
There was however a slight hiccup that we had to correct:
hold on
scatterbar3(x,y,f,h);
scatterbar3 does not have separate inputs for the width and height of the bars, thus large gaps occur when the intervals do not equal one another. Demonstrated below.
We thus edited the scatterbar3 function in order to take both the width and height of the bars as inputs:
Edited scatterbar3 function:
function scatterbar3(X,Y,Z,widthx,widthy)
[r,c]=size(Z);
for j=1:r,
for k=1:c,
if ~isnan(Z(j,k))
drawbar(X(j,k),Y(j,k),Z(j,k),widthx/2,widthy/2)
end
end
end
zlim=[min(Z(:)) max(Z(:))];
if zlim(1)>0,zlim(1)=0;end
if zlim(2)<0,zlim(2)=0;end
axis([min(X(:))-widthx max(X(:))+widthx min(Y(:))-widthy max(Y(:))+widthy zlim])
caxis([min(Z(:)) max(Z(:))])
function drawbar(x,y,z,widthx,widthy)
h(1)=patch([-widthx -widthx widthx widthx]+x,[-widthy widthy widthy -widthy]+y,[0 0 0 0],'b');
h(2)=patch(widthx.*[-1 -1 1 1]+x,widthy.*[-1 -1 -1 -1]+y,z.*[0 1 1 0],'b');
h(3)=patch(widthx.*[-1 -1 -1 -1]+x,widthy.*[-1 -1 1 1]+y,z.*[0 1 1 0],'b');
h(4)=patch([-widthx -widthx widthx widthx]+x,[-widthy widthy widthy -widthy]+y,[z z z z],'b');
h(5)=patch(widthx.*[-1 -1 1 1]+x,widthy.*[1 1 1 1]+y,z.*[0 1 1 0],'b');
h(6)=patch(widthx.*[1 1 1 1]+x,widthy.*[-1 -1 1 1]+y,z.*[0 1 1 0],'b');
set(h,'facecolor','flat','FaceVertexCData',z)
Finally the working solution in action:
hold on
scatterbar3(x,y,f,h,k);
So, I'm really new to MatLab, and I was trying to make a cylinder using [X Y Z] = cylinder;.Then I got these 3 matrices: X Y and Z that generate an actual cylinder if I mesh them. Now, what I need help to do is rotate this [X Y Z] cylinder 90 degrees clockwise in the y axis. I know there is this command called rotate but my teacher wants me to use rotation and translation matrices explicitly. How could I create these matrices and multiply them to the cylinder?Is there a better way to make the cylinder? I'm really not used to matlab, if you could explain in a detailed form, I would be very thankful.
You should use a rotation matrix for the R^3 which serves as a linear map. There are built in fucntions in MATLAB for that but I guess you are not allowed to use them.
Here is a quick and dirty solution:
[X Y Z] = cylinder;
figure;
surf(X,Y,Z);
% set up rotation matrix:
angle_in_degrees = 90;
angle_in_rad = angle_in_degrees* pi/180;
rotationMatrix = [cos(angle_in_rad) 0 sin(angle_in_rad); 0 1 0; -sin(angle_in_rad) 0 cos(angle_in_rad)];
% get points at the two rings and rotate them separately:
positionOld1 = [X(1,:)',Y(1,:)',Z(1,:)'];
positionOld2 = [X(2,:)',Y(2,:)',Z(2,:)'];
positionNew1 = positionOld1*rotationMatrix;
positionNew2 = positionOld2*rotationMatrix;
% reassemble the two sets of points into X Y Z format:
X = [positionNew1(:,1),positionNew2(:,1)];
Y = [positionNew1(:,2),positionNew2(:,2)];
Z = [positionNew1(:,3),positionNew2(:,3)];
figure;
surf(X,Y,Z);
I've got a 250 x 250 image, I want to have a scatter plot of the intensity of every pixel and its nearest neighborhood. This is my code:
I = imread(image);
i = [1,249];
j = [1,250];
X = I(i,j);
Y = I(i+1,j);
scatter(X,Y);
why do I get the " X and Y vectors must be the same length" error? They are the same length !
Because scatter(X, Y) is only used for vectors, not matrix. In your example, both X and Y are 2x2 matrices, not vectors.
From its documentation:
scatter(X,Y) displays circles at the locations specified by the vectors X and Y. This type of graph is also known as a bubble plot.
Edit: if you want to plot matrix, use plotmatrix() instead:
plotmatrix(X,Y)
Scatter(X,Y) is used only for vectors as herohuyongtao correctly mentioned. You could try to do the following:
m = 250;
X = I(m+1:end);
Y = I(1:end-m);
scatter(X,Y);
You convert your image matrix I into a vector X while ignoring the first column and in a vector Y while ignoring the last column. X(n) is thus the neighbour of Y(n) on the right side.
I hope this helps!