Gnuplot: how to eliminate gap between minimum value and "floor" - range

I use
splot "merged2.dat" using 9:10:11
to draw my points.
No matter what values i use for 'set zrange', there is always a huge 'gap' between the point with minimal z value and the 'floor' (i.e. the rectangle bounded by the x and y axes), about a third of the z-axis.
Is there a way to reduce or remove this gap?

I think you are looking for the set xyplane relative <frac> command, where:
The form set xyplane relative <frac> places the xy plane below the range in Z, where the distance from the xy plane to Zmin is given as a fraction of the total range in z. The default value is 0.5.
The default value 0.5 explains the "one third" which you are experiencing. Setting it to 0.0 should remove the gap.
The xy-plane can be set to an absolute value withset xyplane at <zlevel>.

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 find an exact value on a plot?

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?

Principal direction in a binary image

As shown in image, there is a binary polygonal image. I want to find the principal direction in the image with respect to X-axis. I have shown the principal direction and X-axis with blue line. This can be done using PCA but my problem is such a small rectangle will have around 1000 pixels and I have to find Principal directions for around 100 polygons (polygon can be of arbitrary shape).
One approach that I have thought is:
Project that rectangle onto a line which is oriented at degrees at an interval (say) 5 degrees. The projection which has the maximum variance is the desired projection axis, and thus that is the desired angle. But this also falls under a greedy approach and thus will take time. Is there a smarter approach?
Also, if anybody could explain the exact procedure to do this using PCA, it would be helpful. I know the steps:
1. Take the covariance matrix.
2. Get the top eigenvector corresponding to largest eigenvalue -> that will be the principal direction.
But I am confused in the following statement which I often read everywhere:
A column vector: [0.5 0.5] is the first principal component and it gives the direction of the maximum variance. So can do I exactly calculate the angle by which I should rotate the data so that it will become parallel to X-axis.
Compute the eigenvector associated with the highest eigen value. Call that v. Normalize v. v = v/norm(v);
Compute angle between that and the horizontal direction: angle=acos(sum(v.*[1,0]))
Rotate by -angle, transformation matrix T = [cos(-angle) -sin(-angle); sin(-angle) cos(-angle)], multiply all points by that matrix. Do that for all polygons.

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.

How can I calculate the distance between two points along a complex path?

I have a set of lines that define a W shape. On each line I have then defined a set of M points that separated by a fixed width. Now I'd like to calculate the MxM matrix of distances where the value of (i,j) contains the along-the-path-distance between the points i and j.
Here is an of the along-the-path-distance between two points.
How can I calculate this distance in Matlab?
It mostly comes down to whether a simple algorithm that only works for this sort of shape is sufficient or if you'll need to also find the distance with different complex paths. If it's just this shape then it's rather trivial
Here the yHoriz is the y value of the horizontal line that connects the vertical lines and x and y I and J are the x and y values of the points i and j.
distance= abs(yI - yHoriz) + abs(xJ-xI) + abs(yJ - yHoriz)
You would need to check if the the points are on the same vertical line and just find the difference in their y values instead of the above value if they are on the same line.