I am having some trouble understanding contours.
What I have understood so far is that contours are a way to represent a 3d figure in a 2d plane. It does so by plotting a function of 2 variables as curves along which the function has same value.
Now if I do:
z=[1 4; 10 7];
contour(z);
I get this:
I read the documentation and it says:
contour(Z) draws a contour plot of matrix Z, where Z is interpreted as
heights with respect to the x-y plane. Z must be at least a 2-by-2
matrix that contains at least two different values. The x values
correspond to the column indices of Z and the y values correspond to
the row indices of Z. The contour levels are chosen automatically.
Thus for x=1,y=1: z=1, x=2,y=1: z=4 and so on. However I can't understand how to interpret this as the contour plot shown above.
And if I write:
contour(X1, X2, vals, [0.5 0.5], 'b'); where X1, X2 and vals are equal sized matrices and vals is a matrix of only 0s and 1s. I can't understand what does the argument [0.5 0.5] do. I read the documentation which states:
contour(Z,v) draws a contour plot of matrix Z with contour lines at
the data values specified in the monotonically increasing vector v. To
display a single contour line at a particular value, define v as a
two-element vector with both elements equal to the desired contour
level.
and I am unable to understand this statement.
The problem of the first contour is that there are just 4 values. Try something like
x = 0:0.1:10;
y = 0:0.1:10;
z = sin(x') * cos(y);
contour(z)
For the second thing, this means that if you want to see just particular contours, input them as vector v. In the example above:
contour(z, [0.1, 0.2, 0.3])
will show contour lines of 0.1, 0.2 and 0.3.
To have a single contour line, you can't have just (z, 0) but require (z, [0,0])
How would I plot in 3D space (plot3() I presume) from a matrix containing N rows of coordinates where column 1 is x, column 2 is y and column 3 is z?
Given that your matrix is in X, it's as simple as:
plot3(X(:,1), X(:,2), X(:,3), 'b.');
plot3 takes in three arguments as a base. The first argument are the x coordinates, the second are the y coordinates and the third are the z coordinates. Because you have all three coordinates conveniently in a matrix and each are in separate columns, you just have to pluck out each coordinate and put that into plot3. I'm also assuming that the points are discrete and you don't want to join any of the points together, so the fourth argument denotes both the colour of the points as well as the style of the points. Here, I've made them blue and single dots.
Another option would be scatter3.
X = rand(30,3);
scatter3(X(:,1), X(:,2), X(:,3), 'b.');
I want to draw a contour plot for 3D data.
I have a force in x,y,z directions I want to plot the contour3 for that
the dimensions of the Fx = 21x21X21 same for Fy and Fz
I am finding force = f*vector(x,y,z)
Then
Fx(x,y,z) = force(1)
Fy(x,y,z) = force(2)
Fz(x,y,z) = force(3)
I did the following but it is not working with me ?? why and how can I plot that
FS = sqrt(Fx.^2 + Fy.^2 + Fz.^2);
x = -10:1:10;
[X,Y] = meshgrid(x);
for i=1:length(FS)
for j = 1:length(FS)
for k=1:length(FS)
contour3(X,Y,FS(i,j,k),10)
hold on
end
end
end
This is the error I am getting
Error using contour3 (line 129)
When Z is a vector, X and Y must also be vectors.
Your problem is that FS is not the same shape as X and Y.
Lets illustrate with a simple example:
X=[1 1 1
2 2 2
3 3 3];
Y=[1 2 3
1 2 3
1 2 3];
Z=[ 2 4 5 1 2 5 5 1 2];
Your data is probably something like this. How does Matlab knows which Z entry corresponds to which X,Y position? He doesnt, and thats why he tells you When Z is a vector, X and Y must also be vectors.
You could solve this by doing reshape(FS,size(X,1),size(X,2)) and will probably work in your case, but you need to be careful. In your example, X and Y don't seem programatically related to FS in any way. To have a meaningful contour plot, you need to make sure that FS(ii,jj,k)[ 1 ] corresponds to X(ii,jj), else your contour plot would not make sense.
Generally you'd want to plot the result of FS against the variables your are using to compute it, such as ii, jj or k, however, I dont know how these look like so I will stop my explanation here.
[ 1 ]: DO NOT CALL VARIABLES i and j IN MATLAB!
I'm not sure if this solution is what you want.
Your problem is that contour and contour3 are plots to represent scalar field in 2D objects. Note that ball is 2D object - every single point is defined by angles theta and phi - even it is an object in "space" not in "plane".
For representation of vector fields there is quiver, quiver3, streamslice and streamline functions.
If you want to use contour plot, you have to transform your data from vector field to scalar field. So your data in form F = f(x,y,z) must be transformed to form of H = f(x,y). In that case H is MxN matrix, x and y are Mx1 and Nx1 vectors, respectively. Then contour3(x,y,H) will work resulting in so-called 3D graph.
If you rely on vector field You have to specify 6 vectors/matrices of the same size of corresponding x, y, z coordinates and Fx, Fy, Fz vector values.
In that case quiver3(x,y,z,Fx,Fy,Fz) will work resulting in 6D graph. Use it wisely!
As I comment the Ander's answer, you can use colourspace to get more dimensions, so You can create 5D or, theoretically, 6D, because you have x, y, z coordinates for position and R, G, B coordinates for the values. I'd recommend using static (x,y,R,G,B) for 5D graph and animated (x,y,t,R,G,B) for 6D. Use it wisely!
In the example I show all approaches mentioned above. i chose gravity field and calculate the plane 0.25 units below the centre of gravity.
Assume a force field defined in polar coordinates as F=-r/r^3; F=1/r^2.
Here both x and yare in range of -1;1 and same size N.
F is the MxMx3 matrix where F(ii,jj) is force vector corresponding to x(ii) and y(jj).
Matrix H(ii,jj) is the norm of F(ii,jj) and X, Y and Z are matrices of coordinates.
Last command ensures that F values are in (-1;1) range. The F./2+0.5 moves values of F so they fit into RGB range. The colour meaning will be:
black for (-1,-1,-1),
red for (1,-1,-1),
grey for (0,0,0)
Un-comment the type of plot You want to see. For quiver use resolution of 0.1, for other cases use 0.01.
clear all,close all
% Definition of coordinates
resolution=0.1;
x=-1:resolution:1;
y=x;
z=-.25;
%definition of matrices
F=zeros([max(size(x))*[1 1],3]); % matrix of the force
X=zeros(max(size(x))*[1 1]); % X coordinates for quiver3
Y=X; % Y coordinates for quiver3
Z=X+z; % Z coordinates for quiver3
% Force F in polar coordinates
% F=-1/r^2
% spherical -> cartesian transformation
for ii=1:max(size(x))
for jj=1:max(size(y))
% temporary variables for transformations
xyz=sqrt(x(ii)^2+y(jj)^2+z^2);
xy= sqrt(x(ii)^2+y(jj)^2);
sinarc=sin(acos(z/xyz));
%filling the quiver3 matrices
X(ii,jj)=x(ii);
Y(ii,jj)=y(jj);
F(ii,jj,3)=-z/xyz^2;
if xy~=0 % 0/0 error for x=y=0
F(ii,jj,2)=-y(jj)/xyz/xy*sinarc;
F(ii,jj,1)=-x(ii)/xyz/xy*sinarc;
end
H(ii,jj)=sqrt(F(ii,jj,1)^2+F(ii,jj,2)^2+F(ii,jj,3)^2);
end
end
F=F./max(max(max(F)));
% quiver3(X,Y,Z,F(:,:,1),F(:,:,2),F(:,:,3));
% image(x,y,F./2+0.5),set(gca,'ydir','normal');
% surf(x,y,Z,F./2+.5,'linestyle','none')
% surf(x,y,H,'linestyle','none')
surfc(x,y,H,'linestyle','none')
% contour3(x,y,H,15)
I have 3 dimensional (X-Y-Z) data which includes-
11 Y vectors (100*1 each (range 0:0.01:1)) each is unique and correspond to the same X vector (100*1 (range 0:0.01:1)). Thus, Y can be treated as matrix with dimension 100*11.
Different Y vectors correspond to different Z values on Z axis (11 values of Z ranging from 0 to 1).
e.g. => Every value of Z on Z axis i.e. Z1=0.05 ... Z11=0.95 has different Y vector for the same X vector. Thus it is like: X-Y1-Z1, X-Y2-Z2, X-Y3-Z3...X-Y11-Z11 (Z1 to Z11 are fixed values like 0.05, 0.1 ,..., 0.95 which are repeated equal to the length of X and Y).
I have already plotted this data as 11 discrete contour lines stacked one above other in 3D space using plot3 hold on. But, I want to create surface out of it. I think I can use interpolation using griddata but I didn't understand how to approach this problem. Can anybody help?
I have a file with data arranged in three columns. I am trying to make 2D contour plot of these values, where the values in the third column (Z) is projected on the space formed by values in the first (X) and second column (Y). But usual matlab commands like 'contour' and 'imagesc' take the Z-values in the matrix format. Is there a way out in Matlab to plot these values in a 2D-plane?
Contour usually works with two vectors (X and Y) and a matrix (Z). So for each elements of the two vectors (X(i) , Y(i)), there should be a value in the matrix (Z(i,j)). Thus the size of the matrix Z should be equal to the size of the first vector (X) multiplied by the size of the second vector (Y).
if the x,y,z have the same size then you can do something like this:
[X,Y,Z] = meshgrid(x,y,z);
contour(X,Y,Z)
on the other hand if you manage to make the sizes correct then you can do something like this example:
x = linspace(-2*pi,2*pi);
y = linspace(0,4*pi);
[X,Y] = meshgrid(x,y);
Z = sin(X)+cos(Y);
figure
contour(X,Y,Z)