I'm using the surfnorm matlab function to calculate the surface normal. When I use it as: surfnorm(pcloud(:,:,1),pcloud(:,:,2),pcloud(:,:,3)); the figure of the surface normal appears but the normal values are not saved. So I used :[Nx,Ny,Nz]=surfnorm(pcloud(:,:,1),pcloud(:,:,2),pcloud(:,:,3)); but not its saving the normal values in [Nx,Ny,Nz] but not displaying the normal figure. So how to make both?
According to the documentation the two actions you want to perform simultaneously appear to be mutually exclusive:
[Nx,Ny,Nz] = SURFNORM(X,Y,Z) returns the components of the 3-D
surface normal for the surface with components (X,Y,Z). The
normal is normalized to length 1.
[Nx,Ny,Nz] = SURFNORM(Z) returns the surface normal components
for the surface Z.
Without lefthand arguments, SURFNORM(X,Y,Z) or SURFNORM(Z)
plots the surface with the normals emanating from it.
SURFNORM(AX,...) plots into AX instead of GCA.
However, once created you can retrieve the normal vector data from the surface normal figure, as follows:
h=figure;
surfnorm(pcloud(:,:,1),pcloud(:,:,2),pcloud(:,:,3));
axesObjs = get(h, 'Children');
dataObjs = get(axesObjs, 'Children');
[Nx,Ny,Nz] = deal(get(dataObjs(1), 'XData').', get(dataObjs(1), 'YData').', get(dataObjs(1), 'ZData').');
It seems convoluted but if it's computational expense you are seeking to avoid this is probably the best way to do this.
Edit:
(1) You can substitute h=figure with a call to figure followed by h=gcf.
(2) My interpretation of the Nx, Ny, Nz vectors is that contain coordinates for the position and direction (not necessarily normalized) of the vectors drawn by surfnorm, as well as additional NaN values, so if you print out [Nx,Ny,Nz] you should see something like:
0 0 -1.0000 <-- position of origin
0 0 -1.0000 <-- direction of vector
NaN NaN NaN <-- nonsense
-0.5878 0 -0.8090
-0.7036 -0.0344 -0.9684
NaN NaN NaN
-0.9511 0 -0.3090
-1.1341 -0.0543 -0.3685
NaN NaN NaN
-0.9511 0 0.3090
-1.1341 -0.0543 0.3685
NaN NaN NaN
....
Related
I have some observational data that is relatively complete, but contains some NaN values, in an matrix in matlab and I want to interpolate them to a more evenly spaced grid using interp2
So, to keep things simple lets say I have one complete (no NaN values) matrix, and one that looks something like:
A = [ 1 2 3 4;
2 3 2 NaN;
0 2 3 4;
0 NaN 4 5 ]
with B and C being complete matrices, interp2 won't accept an input matrix with NaN values. So if I do something like this:
[AI,BI] = meshgrid(a,b) %# matrices to interpolate data to, arbitrary
CI = interp2(A,B,C,AI,BI) %# interpolation, A has NaN values
I get an error:
Error using griddedInterpolant
The coordinates of the input points must be finite values; Inf and NaN are not permitted.
Can anyone suggest either a solution, or reasonable work around that doesn't obstruct my data?
Sorry the quick fix I gave in comment does not work directly for 2D data (it does work that simply with interp1 though, if you ever need it).
For gridded data, if you have NaNs in your grid then you do not have a uniform grid and you cannot use interp2 directly. In this case you have to use griddata first, to re-interpolate your data over a uniform grid (patch the holes basically).
(1) Let's show an example inspired from the Matlab doc:
%% // define a surface
[A,B] = meshgrid(-3:0.25:3);
C = peaks(A,B);
%// poke some holes in it (in every coordinate set)
A(15,3:8) = NaN ;
B(14:18,13) = NaN ;
C(8,16:21) = NaN ;
(2) Now let's fix your data on a clean grid:
%// identify indices valid for the 3 matrix
idxgood=~(isnan(A) | isnan(B) | isnan(C));
%// define a "uniform" grid without holes (same boundaries and sampling than original grid)
[AI,BI] = meshgrid(-3:0.25:3) ;
%// re-interpolate scattered data (only valid indices) over the "uniform" grid
CI = griddata( A(idxgood),B(idxgood),C(idxgood), AI, BI ) ;
(3) Once your grid is uniform, you can then use interp2 if you want to mesh on a finer grid for example:
[XI,YI] = meshgrid(-3:0.1:3) ; %// create finer grid
ZI = interp2( AI,BI,CI,XI,YI ) ; %// re-interpolate
However, note that if this is all what you wanted to do, you could also use griddata only, and do everything in one step:
%// identify indices valid for the 3 matrix
idxgood=~(isnan(A) | isnan(B) | isnan(C));
%// define a "uniform" grid without holes (finer grid than original grid)
[XI,YI] = meshgrid(-3:0.1:3) ;
%// re-interpolate scattered data (only valid indices) over the "uniform" grid
ZI = griddata( A(idxgood),B(idxgood),C(idxgood), XI, YI ) ;
This produces the exact same grid and data than we obtained on step (3) above.
Last note: In case your NaNs are on the border of your domain, by default these functions cannot "interpolate" values for these border. To force them to do so, look at the extrapolation options of these functions, or simply interpolate on a slightly smaller grid which doesn't have NaN on the border.
I have a 3D matrix (19-by-21-by-23) of mean AOD values. My dataset consists of NaN values at many positions in the matrix. I wish to calculate the trend of each grid of the matrix, but I am somehow getting incorrect results and mostly NaN value as the trend. Help me in correcting the code. The code I wrote is below:
y=1:21;
% = mat2cell(y,1*ones(1,1),21);
% Mcell = mat2cell(aa,19,repmat(1,21,1));
kq= zeros(19,2);
X = mat2cell(winter,1*ones(19,1),21);
for i=1:19;
for k=1:23;
u(i,:,:)= winter(i,:,:);
kq(i,:,:)= polyfit(u(i,:,:),y,1);
end
end
Well, I don't know how to describe my problem with a title, I hope the one I got is correct.
I have a matrix (Min the example below) that is a 3D image, composed, in this case, by 11x11x11 voxels (I made it logical just for easiness, and size is just an example also).
In my code, I need to reach the 26 neighbors of some voxels, and for that I use some fancy linear indexing found in: http://www.mathworks.com/matlabcentral/answers/86900-how-to-find-all-neighbours-of-an-element-in-n-dimensional-matrix
The problem is that if the point is in the "boundary" of M some out of bounds values are tried to be accessed, and that will generate an error.
To solve this problem, a good approach would be to create a boundary around M making it +2 size in every dimension, and populate that with zeros, however I really would like to avoid changing M, as my code is quite more complex that the one in the example.
I cant find any way of doing it, i'm a bit stuck here. Any suggestion?
EDIT: #Dan answer works, however I would like to see if there is a possible solution using this linear indexing method.
% Example data
M=round(randn(11,11,11))~=0;
% Fancy way of storing 26 neigh indices for good accesing
s=size(M);
N=length(s);
[c1{1:N}]=ndgrid(1:3);
c2(1:N)={2};
neigh26=sub2ind(s,c1{:}) - sub2ind(s,c2{:});
point=[5 1 6];
% This will work unless the point is in the boundary (like in this example)
neighbours=M(sub2ind(s,point(1),point(2),point(3))+neigh26)
Is that linear indexing stuff essential? Because it's pretty easy to handle boundary conditions is you use subscript indexing and min and max like this:
p = [5, 1, 6];
neighbourhood = M(max(1,p(1)-1)):min(p(1)+1,end),
max(1,p(2)-1)):min(p(2)+1,end),
max(1,p(3)-1)):min(p(3)+1,end))
%// Get rid of the point it self (i.e. the center)
neighbours = neighbourhood([1:13, 15:end])
This way you can also easily generalize this if you want a broader neighbourhood:
p = [5, 1, 6];
n = 2;
neighbourhood = M(max(1,p(1)-n)):min(p(1)+n,end),
max(1,p(2)-n)):min(p(2)+n,end),
max(1,p(3)-n)):min(p(3)+n,end))
%// Get rid of the point it self (i.e. the center)
mid = ceil(numel(neigbourhood)/2);
neighbours = neighbourhood([1:mid-2, mid+1:end])
or if you liked to keep the cube shape then maybe:
neighbours = neighbourhood;
neighbours(mid) = NaN;
If you want to use this many times in your code it's probably best to refactor it as an m-file function that just returns the indices:
function ind = getNeighbours(M,p,n)
M = zeros(size(M));
M(max(1,p(1)-n)):min(p(1)+n,end), max(1,p(2)-n)):min(p(2)+n,end), max(1,p(3)-n)):min(p(3)+n,end)) = 1;
M(p(1), p(2), p(3)) = 0;
ind = find(M);
end
Basic theory: Extend input array to left-right, up-down, one more on each sides of the third dimension with NaNs. This would allow us to use a uniform 3x3x3 grid and then later on use those NaNs to detect elements that go beyond the boundaries of input array and as such are to be discarded.
Code
%// Initializations
sz_ext = size(M)+2; %// Get size of padded/extended input 3D array
M_ext = NaN(sz_ext); %// Initialize extended array
M_ext(2:end-1,2:end-1,2:end-1) = M; %// Insert values from M into it
%// Important stuff here : Calculate linear offset indices within one 3D slice
%// then for neighboring 3D slices too
offset2D = bsxfun(#plus,[-1:1]',[-1:1]*sz_ext(1)); %//'
offset3D = bsxfun(#plus,offset2D,permute([-1:1]*sz_ext(1)*sz_ext(2),[1 3 2]));
%// Get linear indices for all points
points_linear_idx = sub2ind(size(M_ext),point(:,1)+1,point(:,2)+1,point(:,3)+1);
%// Linear indices for all neighboring elements for all points; index into M_ext
neigh26 = M_ext(bsxfun(#plus,offset3D,permute(points_linear_idx,[4 3 2 1])))
How to use: Thus, each slice in the 4th dimension represent the 27 elements (neighboring plus the element itself) as 3x3x3 array. Hence, neigh26 would be a 3x3x3xN array where N is the number of points in point array.
Example: As an example, let's assume some random values in M and Point -
M=rand(11,11,11);
point = [
1 1 4;
1 7 1]
On running the earlier code with these inputs, I get something like this -
neigh26(:,:,1,1) =
NaN NaN NaN
NaN 0.5859 0.4917
NaN 0.6733 0.6688
neigh26(:,:,2,1) =
NaN NaN NaN
NaN 0.0663 0.5544
NaN 0.3440 0.3664
neigh26(:,:,3,1) =
NaN NaN NaN
NaN 0.3555 0.1257
NaN 0.4424 0.9577
neigh26(:,:,1,2) =
NaN NaN NaN
NaN NaN NaN
NaN NaN NaN
neigh26(:,:,2,2) =
NaN NaN NaN
0.7708 0.3712 0.2866
0.7088 0.3743 0.2326
neigh26(:,:,3,2) =
NaN NaN NaN
0.4938 0.5051 0.9416
0.1966 0.0213 0.8036
This is my attempt to simulate the water surface. It works fine when I use the surf() function. But when I change it to bar3(), this error occurs: "Matrix dimensions must agree, not rendering mesh". Can some one please tell me how to fix this? Here's my code:
n=60;
i = 2:n-1;
j = 2:n-1;
H = ones(n,n);
Dropx=30; %x and y coordinate of the droplet
Dropy=30;
width=20;
r=width/2;
dt=0.1;
dx=0.3;
%%% add droplet to the surface %%%
[x,y] = ndgrid(-1.5:(2/(width/1.5-1)):1);
D = 8*exp(-5*(x.^2+y.^2));
w = size(D,1);
i2 = (Dropx-r):w+(Dropx-r)-1;
j2 = (Dropy-r):w+(Dropy-r)-1;
H(i2,j2) = H(i2,j2) + D;
oldH=H;
newH=H;
h=surf(newH); % cannot change this to bar3
axis([1 n 1 n -2 8]);
k=0.2; %damping constant
c=2; %wave speed
while 1==1
newH(i,j)=H(i,j)+(1-k*dt)*(H(i,j)-oldH(i,j))-...
dt^2*c^2/dx^2*((4*H(i,j)-H(i+1,j)-H(i-1,j)-H(i,j+1)-H(i,j-1))...
+0.4*(4*H(i,j)-H(i+1,j+1)-H(i+1,j-1)-H(i-1,j+1)-H(i-1,j-1)));
set(h,'Zdata', newH(i,j));
oldH=H;
H=newH;
pause(0.05);
end
The problem, as stated by David, is that bar3 transforms the original data matrix into a special ZData. This new one is a cell array of patches, of length n (60 in your code), each of them is an array of size [n*6,4]. So you cannot assign directly your new matrix to ZData.
There is one solution, besides recreating the plot each time. Basically, it modifies directly ZData. You can directly modify element by element Zdata. For that, try the following code instead of calling set(h,'Zdata', newH(i,j));:
for ih=j
set(h(ih), 'ZData', kron(newH(i,ih),[nan 0 0 nan;0,1,1,0;0,1,1,0;nan 0 0 nan;nan 0 0 nan;nan nan nan nan]));
end
h is the handle of the plot; in the case of bar3, its length is n, the first dimension of your matrix. So, for each bar column, you set the ZData according to its format. Each element V of the matrix is transformed to this matrix:
NaN 0 0 NaN
0 V V 0
0 V V 0
NaN 0 0 NaN
NaN 0 0 NaN
NaN NaN NaN NaN
So, in order to build the complete ZData of each column, you call the function kron with the column of the updated matrix and with this atomic matrix.
This is not very fast; on my computer, the display lags time to time, but it is faster than recreating the bar plot each time. Using surf is more faster because there is less patches to draw.
The problem lies in the way you handle the plotting.
h=bar3(newH);
plots the data and stores handles to patch graphic objects in h. When you write the following :
set(h,'Zdata', newH(i,j));
you assume that the handle 'Zdata' is a 60x60 array, which is not the case for bar3. Just write
output = get(h,'Zdata')
to see that. It requires a bit more data handling to do it this way but that seems tedious.
I propose an easy solution to this, simply replotting at every timestep :
oldH=H;
newH=H;
h=bar3(newH);
axis([1 n 1 n -2 8]);
k=0.2; %damping constant
c=2; %wave speed
while 1==1
newH(i,j)=H(i,j)+(1-k*dt)*(H(i,j)-oldH(i,j))-...
dt^2*c^2/dx^2*((4*H(i,j)-H(i+1,j)-H(i-1,j)-H(i,j+1)-H(i,j-1))...
+0.4*(4*H(i,j)-H(i+1,j+1)-H(i+1,j-1)-H(i-1,j+1)-H(i-1,j-1)));
h=bar3(newH);
axis([1 n 1 n -2 8]);
oldH=H;
H=newH;
pause(0.05);
end
I've got a 2-D histogram (the plot is 3D - several histograms graphed side by side) that I've generated with the bar3 plot command. However, all the zero values show up as flat squares in the x-y plane. Is there a way I can prevent MATLAB from displaying the values? I already tried replacing all zeros with NaNs, but it didn't change anything about the plot. Here's the code I've been experimenting with:
x1=normrnd(50,15,100,1); %generate random data to test code
x2=normrnd(40,13,100,1);
x3=normrnd(65,12,100,1);
low=min([x1;x2;x3]);
high=max([x1;x2;x3]);
y=linspace(low,high,(high-low)/4); %establish consistent bins for histogram
z1=hist(x1,y);
z2=hist(x2,y);
z3=hist(x3,y);
z=[z1;z2;z3]';
bar3(z)
As you can see, there are quite a few zero values on the plot. Closing the figure and re-plotting after replacing zeros with NaNs seems to change nothing:
close
z(z==0)=NaN;
bar3(z)
One solution is to modify the graphics objects created by bar3. First, you have to get the handles returned from bar3:
h = bar3(z);
In your case, h will be a 3-element vector of handles, one for each set of colored bars. The following code should then make the bins with counts of zero invisible:
for i = 1:numel(h)
index = logical(kron(z(:, i) == 0, ones(6, 1)));
zData = get(h(i), 'ZData');
zData(index, :) = nan;
set(h(i), 'ZData', zData);
end
And here's an illustration (with obligatory free-hand circles):
How it works...
If your vector of bin counts is N-by-1, then bar3 will plot 6*N rectangular patches (i.e. the 6 faces of a cuboid for each bin). The 'ZData' property for each set of patch objects in h will therefore be (6*N)-by-4, since there are 4 corners for each rectangular face. Each cluster of 6 rows of the 'ZData' property is therefore a set of z-coordinates for the 6 faces of one bin.
The above code first creates a logical vector with ones everywhere the bin count equals 0, then replicates each element of this vector 6 times using the kron function. This becomes an index for the rows of the 'ZData' property, and this index is used to set the z-coordinates to nan for the patches of empty bins. This will cause the patches to not be rendered.
EDIT:
Here's a slightly modified version of the code that makes it more general by fetching the bar height from the 'ZData' property of the plotted bars, so all that's needed for it to work are the handles returned from bar3. I've also wrapped the code in a function (sans error and input checking):
function remove_empty_bars(hBars)
for iSeries = 1:numel(hBars)
zData = get(hBars(iSeries), 'ZData'); % Get the z data
index = logical(kron(zData(2:6:end, 2) == 0, ones(6, 1))); % Find empty bars
zData(index, :) = nan; % Set the z data for empty bars to nan
set(hBars(iSeries), 'ZData', zData); % Update the graphics objects
end
end
Here is an example that shows how to hide bars with zero-values. We start with a normal BAR3 plot:
x = 1:7;
Y = jet(numel(x));
h = bar3(x,Y,'detached');
xlabel x; ylabel y; zlabel z; box on;
Note that the variable h contains an array of surface handles (3 in this case, one for each "group" of bars. The groups correspond to the columns of the Y matrix, each represented by a different color).
And now the code to hide zero values:
for i=1:numel(h)
%# get the ZData matrix of the current group
Z = get(h(i), 'ZData');
%# row-indices of Z matrix. Columns correspond to each rectangular bar
rowsInd = reshape(1:size(Z,1), 6,[]);
%# find bars with zero height
barsIdx = all([Z(2:6:end,2:3) Z(3:6:end,2:3)]==0, 2);
%# replace their values with NaN for those bars
Z(rowsInd(:,barsIdx),:) = NaN;
%# update the ZData
set(h(i), 'ZData',Z)
end
Explanation:
For each group of bars, a surface graphic object is created (with handle stored in h(i)). It's Z-coordinates matrix ZData is represented as a 6*N-by-4 matrix (same thing for XData, YData, and CData matrices), where N is the number of rectangular bars in each group or 7 in the example above.
This way each rectangle is represented with 6x4 matrices (one for each of X/Y/Z coordinates). For example the coordinates of one such rectangle would look like:
>> xx = get(h(3),'XData'); yy = get(h(3),'YData'); zz = get(h(3),'ZData');
>> xx(1:6,:)
ans =
NaN 2.6 3.4 NaN
2.6 2.6 3.4 3.4
2.6 2.6 3.4 3.4
NaN 2.6 3.4 NaN
NaN 2.6 3.4 NaN
NaN NaN NaN NaN
>> yy(1:6,:)
ans =
NaN 0.6 0.6 NaN
0.6 0.6 0.6 0.6
1.4 1.4 1.4 1.4
NaN 1.4 1.4 NaN
NaN 0.6 0.6 NaN
NaN NaN NaN NaN
>> zz(1:6,:)
ans =
NaN 0 0 NaN
0 1 1 0
0 1 1 0
NaN 0 0 NaN
NaN 0 0 NaN
NaN NaN NaN NaN
The second column of each traces the points along the left face, the third column traces the points along the right face, and when the two are connected would draw 4 faces of the rectangle:
>> surface(xx(1:6,2:3), yy(1:6,2:3), zz(1:6,2:3), cc(1:6,2:3))
>> view(3)
The first and last columns would draw the two remaining faces by closing the sides of the rectangle.
All such matrices are concatenated as one tall matrix, and the rectangles are all drawn using a single surface object. This is achieved by using NaN values to separate the different parts, both inside the points of the same rectangle, and in-between the difference rectangles.
So what the above code does is to look for rectangles where the Z-height is zero, and replace all its values with NaN values which effectively tells MATLAB not to draw the surfaces formed by those points.
My problem was not zero values, but NaN values (which are converted into zero values inside of bar3).
I wanted to keep displaying elements with values zero, but not the elements with value nan.
I adjusted the code slightly, and it worked perfectly:
for i = 1:numel(h)
index = logical(kron(isnan(z(:,i)),ones(6,1)));
zData = get(h(i),'ZData');
zData(index,:) = nan;
set(h(i),'ZData',zData);
end
Thanks!