How to find an exact value on a plot? - matlab

I have a plot which is drawn from points.
I can identify the coordinates values with the brush tool. However I'd be interested in the specific value of a certain x when y value is 0. With the brush tool I cannot pick it exactly.
Is there a way to have the specific y value for x = 0 approximated from the graph?

Related

How to have a log scale plot so that the smallest value on the vertical axis is a power of 10

I have the following logarithmic plot shown below:
I want to change this plot so that the "x axis" is such that the vertical value lies at the smallest possible power of 10. What I mean by this is that I would like to make sure that the horizontal axis seen at the bottom of the plot is perhaps y = 10e-2 such that the rightmost group of bars in the above plot can be above the "x axis". I tried 'xaxislocation' but it doesn't work. In hindsight, I suppose the y=10e0 line is not the x axis anyway.
% plot group_err
data_names = cell(1,8);
data_names{1}='1'; data_names{2}='2';
data_names{3}='3'; data_names{4}='4';
data_names{5}='5'; data_names{6}='6';
data_names{7}='7'; data_names{8}='8';
h = bar(group_err);
grid on;
set(gca,'xticklabel',data_names,'YScale','log','FontSize',14);
ylabel('Error rate (%))','FontSize',14);
xlabel('Dataset','FontSize',14);
title('Error rate of sequential algorithms','FontSize',14);
ylim([0.01 100]);
group_err:
79.0407673860911 80.6235000000000 80.3837000000000
28.2600000000000 24.3600000000000 25.0200000000000
2.18055555555556 1.44290190000000 1.92145600000000
34.1692954784437 14.9053400000000 17.9127200000000
0.0551724137931035 0.0298850500000000 0.0459770500000000
33.2005921539600 22.4352400000000 25.6802200000000
0.0979391960824322 0.0685568400000000 0.155070440000000
Now that we've seen your edit, that's very straight forward. Simply find whatever y value is the smallest and you need to round this down so that the resulting value is a power of 10 and is smaller than the smallest y value you're looking at.
To do this, you want to the floor of the following relationship where given your minimum value ymin, it satisfies this relationship:
10^floor(x) = ymin
Re-arranging this equation by taking the log of both sides, we get:
x = log(ymin) / log(10)
... and we now take the floor of x to get what you need. Take special note that you need to take the floor as it rounds down to minus infinity. Don't use fix as this rounds towards 0 so for negative values, this will add 1 to negative values and not what you want. Specifically, this will ensure that you find the smallest power x that respects negative powers when the above relationship is less than 1.
The value of x serves as the smallest power of 10 that satisfies what you need. You will the need to take 10^x to complete the task. This is the smallest power of 10 that will serve as the horizontal axis of your plot. You then use ylim to limit the vertical axis so that you see what the smallest and largest values you have. Because you are using a semi-logarithmic plot, to do what you need you must specify these values as powers of 10. This is the whole reason why we need to determine the smallest power of 10 to serve as the minimum limit or the x axis of your data.
Therefore, assuming you have your plot already open, simply do the following:
x = floor(log(min(y)) / log(10));
ylim([10^x max(y)]);
ylim takes two values: The minimum value and maximum value of the y axis you would like to see. I've made sure that the largest value to visualize is just the largest value in your data itself.
what you want in to change the 'BaseValue' property of your bar plot, in your case would be:
set(h,'BaseValue',0.01)
You will get something like this:

How to make a plot of a circle with dashed coloured border in MATLAB?

So i have this code to obtain radial gravity on Earth in function of the latitude:
G=6.6e-11;
M=5.976e24;
N=1000;
r=6371000;
w=2*pi/(24*3600);
for i=1:1:360
Theta=i*pi/180;
x(i)=i;
Vi(i)=-G*M/(r*r);
Phii(i)=r*w*w*sin(Theta)*sin(Theta);
gr(i)=Vi(i)+Phii(i);
end
plot(x,gr)
And it runs well. I want to make a graph of a circle made of a border of points (representing angle (i)) that change colour according to the value of gr(I want to set ranges of values of gr so that if the value obtained falls in a specific category, the point will have a specific colour).
I'm really new to MATLAB. Is there any possible way to make this?
Thanks in advance.
Here is the basic algorithm that I would do:
Determine how many colours you want to represent in your plot.
Create a colour map that has this many points for what you want to compute.
Determine a linearly increasing vector that varies from the minimum value of gr to the maximum value of gr with as many points as you have determined in Step #2
For each point in gr:
a. Determine which point yields the closest distance of this point to the vector in Step #3
b. Use this to index which colour you want.
c. Convert your angle into Cartesian co-ordinates, then plot this point with the colour found in Step 4b.
Let's tackle each point in detail.
Step #1 - Determine how many colours you want
This is pretty simple. Just determine how many colours you want. For now, let's assume that you want 20 colours, so:
num_colours = 20;
Step #2 - Create a colour map
What we can do is create a 20 x 3 matrix where each row determines a RGB tuple that denotes the amount of red, green and blue that each colour will occupy. MATLAB has built-in colour maps that will help you facilitate this. Here are all of the available colour maps that MATLAB has:
Each colour map has a special variable where you can provide it an integer number, and it'll return this 2D matrix of as many rows as the number you have provided. Each row gives you an RGB triplet which denotes the proportion of red, green and blue respectively. This matrix varies from the beginning of the colour map (top row) to the end (bottom row). All you have to do is use any name seen in the figure I've shown you above to create a colour map of that type. For example, if you wanted to get a bones colour map of 15 points, simply do:
colour_map = bones(15);
If you wanted to get a jet colour map of 25 points, simply do:
colour_map = jet(25);
.... you get the idea right? I like hsv so let's use the HSV colour map. You can use any colour map you want, but let's just stick with HSV for the sake of this example.
As such:
colour_map = hsv(num_colours);
Step #3 - Get that linearly increasing vector
You want certain colours to map into certain ranges, which is why this step is important. Given a value in gr, we want to figure out which colour we want to choose, and all you have to do is determine which value in gr is the closest to a value in this vector in Step #3. Therefore, you can use linspace to do this for you:
bin_vector = linspace(min(gr), max(gr), num_colours);
This will create a num_colours 1D array where the beginning of this array starts at the minimum value of gr and varies up to the maximum value of gr and each value is equally spaced such that we generate a num_colours array.
Step #4 - Bring it all home
Now, for each point in gr, we need to figure out which point is the closest to that vector in Step #3, we then use this to figure out the colour we want, then we need to convert our angle into Cartesian co-ordinates, then plot this point.
For illustration purposes, I'm going to assume your radius is 1. You can figure out how to get the x and y co-ordinates by simply doing cos(theta) and sin(theta), where theta is the angle you are examining. Since your gr array has 360 slots, I'm going to assume a resolution of 1 degree per slot. Therefore, you can easily do this in a for loop. Make sure you use hold on because we are going to call plot multiple times, and we don't want to overwrite the plot each time we call plot. You want all of the points to stay in the plot.
Without further ado:
figure; %// Create blank figure
hold on; %// Remember all points
%// For each point in our array...
for idx = 1 : 360
%// Find the closest slot between gr and our vector in Step #3
[~,min_idx] = min(abs(gr(idx) - bin_vector));
%// Grab this colour
clr = colour_map(min_idx,:);
%// Plot the point with this colour
plot(cosd(idx), sind(idx), '.', 'Color', clr, 'MarkerSize', 10);
end
Take notice that cosd and sind take in degrees as the input argument while cos and sin take in radians. Also, take note that I also changed the size of the point so that it's bigger. With the above logic, and your array in gr, this is what I get:
If you want the radius to get larger, all you have to do is multiply each cosd and sind term with your radius. Therefore, you can do something like this:
radius = 2;
for idx = 1 : 360
... %// Insert colour code here
...
...
%// Now plot
plot(radius*cosd(idx), radius*sind(idx), '.', 'Color', clr, 'MarkerSize', 10);
end
Just leave the code the same, but for the plot command, just multiply each x and y value by the radius.
Minor note in efficiency
The way you're calculating your gr array is using an inefficient for loop. There are some situations (like mine above) where you need to use a for loop, but for simple computations there is no need. It's better if you vectorize its creation. Therefore, you can get rid of the for loop to calculate your gr array like so:
x = 1 : 360;
Theta = x*pi/180;
Phii = r*w*w*sin(Theta).*sin(Theta);
Vi = -G*M/(r*r);
gr = Vi + Phii;
x is simply a vector going from 1 to 360, and that's done in the first line. Also, Vi is just an array which contains a single value and if you know how operations work between a scalar and an array, you can just do an addition with this single value and it'll add every value in your array by this much. As such, there's no need to create an array for Vi. Also, take a look at how I calculated Phii. I'm using element-by-element operations as Theta is now an array. You want to create an array Phii that takes corresponding values of Theta, and applies that formula to each value in Theta to produce Phii.
Hope this helps. Good luck!

3D scatter plot with 4D data

I need to plot a 3D figure with each data point colored with the value of a 4th variable using a colormap. Lets say I have 4 variables X,Y,Z and W where W = f(X,Y,Z). I want a 3D plot with X, Y, and Z as the three axis. The statement scatter3(X,Y,Z,'filled','b') gives me a scatter plot in 3D but I want to incorporate the value of Z in the graph by representing the points as an extra parameter (either with different areas :bigger circles for data points with high value of Z and small circles for data points with low value of Z or by plotting the data points with different colors using a colormap). However, I am a novice in MATLAB and dont really know how to proceed. Any help will be highly appreciated.
Thanks in advance!
So just use z for the size vector (4th input) as well as the color vector (5th input):
z = 10*(1:pi/50:10*pi);
y = z.*sin(z/10);
x = z.*cos(z/10);
figure(1)
scatter3(x,y,z,z,z)
view(45,10)
colorbar
The size vector needs to be greater 0, so you may need to adjust your z accordingly.
You are already nearly there... simply use
scatter3(X,Y,Z,s,W);
where s is the point size (scalar, e.g. 3) and W is a vector with your W values.
You might also want to issue an
set(gcf, 'Renderer','OpenGL');
where gcf gets your current figure you are plotting in to significantly increase responsiveness when scattering a lot of data.

Find closest point in matlab grid

G'day
I'm trying to program a smart way to find the closest grid points to the points along a contour.
The grid is a 2-dimensional grid, stored in x and y (which contain the x and y kilometre positions of the grid cells).
The contour is a line, made up of x and y locations, not necessarily regularly spaced.
This is shown below - the red dots are the grid, and the blue dots are the points on the contour. How do I find the indices of the red dot closest to each blue dot?
Edit - I should mention that the grid is a latitude/longitude grid, of an area fairly close to the south pole. So, the points (the red dots) are the position in metres from the south pole (using a polar stereographic representation). Since the grid is a geographic grid there is unequal grid spacing - with slightly different shaped cells (where the red dots define the vertices of the cells) due to the distortion at high latitudes.
The result is that I can't just find which row/column of the x and y matrix corresponds closest to the input point coordinates - unlike a regular grid from meshgrid, the values in the rows and columns vary...
Cheers
Dave
The usual method is to go:
for every blue point {
for every red point {
is this the closest so far
}
}
But a better way is to put the red data into a kd tree. This is a tree that splits the data along its mean, then splits the two data sets along their means etc until you have them separated into a tree structure.
This will change your searching effeciancy from O(n*m) to O(log(n)*m)
Here is a library:
http://www.mathworks.com.au/matlabcentral/fileexchange/4586-k-d-tree
This library will provide you the means to easily make a kd tree out of the data and to search for the closest point in it.
Alternatively you can use a quadtree, not as simple but the same idea. (you may have to write your own library for that)
Make sure the largest data set (in this case your red points) go into the tree as this will provide the greatest time reduction.
I think I've found a way to do it using the nearest flag of griddata.
I make a matrix that is the same size as the grid x and y matrices, but is filled with the linear indices of the corresponding matrix element. This is formed by reshaping a vector (which is 1:size(x,1)*size(x,2)) to the same dimensions as x.
I then use griddata and the nearest flag to find the linear index of the point closest to each point on my contour (blue dots). Then, simply converting back to subscript notation with ind2sub leaves me with a 2 row vectors describing the matrix subscripts for the points closest to each point on the blue-dotted contour.
This plot below shows the contour (blue dots), the grid (red dots) and the closest grid points (green dots).
This is the code snippet I used:
index_matrix1 = 1:size(x,1)*size(x,2);
index_matrix1 = reshape(index_matrix1,size(x));
lin_ind = griddata(x,y,index_matrix1,CX,CY,'nearest'); % where CX and CY are the coords of the contour
[sub_ind(1,:),sub_ind(2,:)] = ind2sub(size(x),lin_ind);
I suppose that in the stereographic representation, your points form a neat grid in r-theta coordinates. (I'm not too familiar with this, so correct me if I'm wrong. My suggestion may still apply).
For plotting you convert from the stereographic to latitude-longitude, which distorts the grid. However, for finding the nearest point, consider converting the latitude-longitude of the blue contour points into stereographic coordinates, where it is easy to determine the cell for each point using its r and theta values.
If you can index the cell in the stereographic representation, the index will be the same when you transform to another representation.
The main requirement is that under some transformation, the grid points are defined by two vectors, X and Y, so that for any x in X and y in Y, (x, y) is a grid point. Next transform both the grid and the contour points by that transformation. Then given an arbitrary point (x1, y1), we can find the appropriate grid cell by finding the closest x to x1 and the closest y to y1. Transform back to get the points in the desired coordinate system.
dsearchn: N-D nearest point search.
[k, d] = dsearchn(A,B) : returns the distances, d, to the closest points. d is a column vector of length p.
http://au.mathworks.com/help/matlab/ref/dsearchn.html?s_tid=gn_loc_drop

OpenNI range of returned coordinates

I am using the HandsGenerator class of OpenNI, and I want to use it to track the users' movements.
I've registered my own callback for getting the updated position of the hand, and everything works fine, except I can't find information about the coordinate system etc. of the returned XnPoint3D. Is there a spec somewhere that precisely specifies the X,Y,Z ranges, and perhaps scaling information (so that I would know that say a change of 100 in the XnPoint3D's X corresponds to a movement of 10 centimeters, or something).
The HandsGenerator returns real world coordinates in millimeters from the sensor. This means that depth points that are right in the middle of the depthmap will have an X and Y of 0.
A change of 100 (in X, Y, or Z) is indeed a change of 10 centimeters (100mm = 10cm).
The range of the X an Y values depends on the Z value of the hand point. Assuming you have a hand point at the top left of the depthmap (or 0,0 in projective coordinates) the possible X and Y values depend on how far away the hand is. The closer the hand, the smaller X and Y. To get the max range your hand positions can be you should choose an arbitrary max Z value and then find the X & Y values of the corners of the depth map at that distance. Or in other words - convert the projective coordinates (0,0,maxZ) and (DepthmapWidth,DepthmapHeight,maxZ) to real world coordinates. All hand points that have a Z value less than maxZ will fall between those 2 real world coordinates)
Note that you can convert projective coordinates to real world using DepthGenerator::ConvertProjectiveToRealWorld.