I am trying to generate a plot which uses arrows as markers in Gnuplot. These arrows I want to turn in a specific angle which I know. So I have value triples of x1 ... xn, y1...yn, alpha1...alphan. Sorry, I wasn't able to include a pic from my hard drive to illustrate what I want to achieve.
Basically, for every (15th or so) x-y pair, the marker should be an arrow which uses a certain angle.
The measured data is tightly packed so I suppose I will have to define an increment between the markers. The length of the arrow can be the same all over.
I would appreciate your ideas.
Gnuplot has a plot mode with vectors that is what you want
Given that your file has the following format, x y angle and assuming that
your angle is in radians, you have to take into account that
with vectors requires 4 parameters, namely x y dx dy where dx
and dy are the projections of the lenght of the arrow.
this draws only the arrows, if you want a line you have to make
two passes on the data.
you want to draw an arrow for a data point over, say, 10 points.
That said, I'd proceed like this
dx(a) = 0.2*cos(a) # 0.2 is an arbitrary scaling factor
dy(a) = 0.2*sin(a)
# this draws the arrows
plot 'mydata.dat' every 10 using 1:2:(dx(a)):(dy(a)) with vectors
# this draws the line
plot 'mydata.dat'
You may want to use help plot to find the detailed explanation of all the parameters that you can apply to a with vectors plot.
Credits: An article on the gnuplotting site
Related
I am trying to reproduce a plot as in the attached image below.
In this picture, the position of the vectors is fixed at a specific position (let's say in a 10×10 grid), and the orientation of the vectors represents the magnitude of the x and y coordinate. In contrast, the color represents the magnitude of the z coordinate.
I need help with Gnuplot codes to plot a similar one.
enter data here
enter data here
Data points for referenceenter image description here.
The key of the solution is:
plot 'DATA.dat' with vectors head size 0.08,20,60 filled lc palette
you can play with the vector's head size parameters, borders, colors etc.
I am working on a project of interpolating sample data {(x_i,y_i)} where the input domain for x_i locates in 4D space and output y_i locates in 3D space. I need generate two look up tables for both directions. I managed to generate the 4D -> 3D table. But the 3D -> 4D one is tricky. The sample data are not on regular grid points, and it is not one to one mapping. Is there any known method to treat this situation? I did some search online, but what I found is only for 3D -> 3D mapping, which are not suitable for this case. Thank you!
To answer the questions of Spektre:
X(3D) -> Y(4D) is the case 1X -> nY
I want to generate a table that for any given X, we can find the value for Y. The sample data is not occupy all the domain of X. But it's fine, we only need accuracy for point inside the domain of sample data. For example, we have sample data like {(x1,x2,x3) ->(y1,y2,y3,y4)}. It is possible we also have a sample data {(x1,x2,x3) -> (y1_1,y2_1,y3_1,y4_1)}. But it is OK. We need a table for any (a,b,c) in space X, it corresponds to ONE (e,f,g,h) in space Y. There might be more than one choice, but we only need one. (Sorry for the symbol confusing if any)
One possible way to deal with this: Since I have already established a smooth mapping from Y->X, I can use Newton's method or any other method to reverse search the point y for any given x. But it is not accurate enough, and time consuming. Because I need do search for each point in the table, and the error is the sum of the model error with the search error.
So I want to know it is possible to find a mapping directly to interpolate the sample data instead of doing such kind of search in 3.
You are looking for projections/mappings
as you mentioned you have projection X(3D) -> Y(4D) which is not one to one in your case so what case it is (1 X -> n Y) or (n X -> 1 Y) or (n X -> m Y) ?
you want to use look-up table
I assume you just want to generate all X for given Y the problem with non (1 to 1) mappings is that you can use lookup table only if it has
all valid points
or mapping has some geometric or mathematic symmetry (for example distance between points in X and Yspace is similar,and mapping is continuous)
You can not interpolate between generic mapped points so the question is what kind of mapping/projection you have in mind?
First the 1->1 projections/mappings interpolation
if your X->Y projection mapping is suitable for interpolation
then for 3D->4D use tri-linear interpolation. Find closest 8 points (each in its axis to form grid hypercube) and interpolate between them in all 4 dimensions
if your X<-Y projection mapping is suitable for interpolation
then for 4D->3D use quatro-linear interpolation. Find closest 16 points (each in its axis to form grid hypercube) and interpolate between them in all 3 dimensions.
Now what about 1->n or n->m projections/mappings
That solely depends on the projection/mapping properties which I know nothing of. Try to provide an example of your datasets and adding some image would be best.
[edit1] 1 X <- n Y
I still would use quatro-linear interpolation. You still will need to search your Y table but if you group it like 4D grid then it should be easy enough.
find 16 closest points in Y-table to your input Y point
These points should be the closest points to your Y in each +/- direction of all axises. In 3D it looks like this:
red point is your input Y point
blue points are the found closest points (grid) they do not need to be so symmetric as on image .
Please do not want me to draw 4D example that make sense :) (at least for sober mind)
interpolation
find corresponding X points. If there is more then one per point chose the closer one to the others ... Now you should have 16 X points and 16+1 Y points. Then from Y points you need just to calculate the distance along lines from your input Y point. These distances are used as parameter for linear interpolations. Normalize them to <0,1> where
0 means 'left' and 1 means 'right' point
0.5 means exact middle
You will need this scalar distance in each of Y-domain dimension. Now just compute all the X points along the linear interpolations until you get the corresponding red point in X-domain.
With tri-linear interpolation (3D) there are 4+2+1=7 linear interpolations (as on image). For quatro-linear interpolation (4D) there are 8+4+2+1=15 linear interpolations.
linear interpolation
X = X0 + (X1-X0)*t
X is interpolated point
X0,X1 are the 'left','right' points
t is the distance parameter <0,1>
I have a set of data, looks like:
x y z
1 1 2 1
2 3 5 7
3 -3 2 4
4 -2 1 1
so each row record the dot coordinate in a 3-D space. I want to plot all the dot as points except for one, say no.15 as a translucent sphere, with radius I can set. Then I can see from the plot that which of those points in the data are included in the sphere. I'm using RGL package right now and did the following:
> open3d()
> plot3d(readin,col=3,type="p")
> plot3d(readin[15,],col=2,add=T,type="s",radius=0.1)
So the first plot command plotted the whole set as scatter plots and the second plot command picked the 15th row of the data and plot it as a sphere and add it to the previous canvas. I just wondering if I can make the sphere translucent so that I can see which dots a included in the sphere which means those dots are very near to the one I select.
Is there a way to do this by RGL Or you can provide me another ways to complete this task?
Thanks!
I think what you are looking for is the argument alpha.
Example
df <- data.frame(x=c(1,3,-3,-2), y=c(2,5,2,1),z=c(1,7,4,1))
library(rgl)
open3d()
plot3d(df,col=3,type="p", radius=0.5)
plot3d(df,col=rgb(1,0,0.3),alpha=0.5, add=T,type="s",radius=1)
You can plot transparent spheres using the alpha argument to spheres3d. You can rotate the plot to move the box line behind the sphere to prove it's transparent.
spheres3d(dat[4,],col=rgb(1,0,0), alpha=0.9) # transparent red.
(I tried to do it with the alpha argument to rgb but it failed.)
If you just want to find out which points are within a certain radius of point 15 then you can calculate the Euclidean distance from each point to point 15 and see which of those distances are less than the radius. No plotting needed (though you could plot those points as a different color to highlight them. The dist function is one way to compute the distances, or it is simple to program yourself.
t = 0:%pi/50:10*%pi;
plot3d(sin(t),cos(t),t)
When I execute this code the plot is done but the line is not visible, only the box. Any ideas which property I have to change?
Thanks
The third argument should, in this case, be a matrix of the size (length arg1) x (length arg2).
You'd expect plot3d to behave like an extension of plot and plot2d but it isn't quite the case.
The 2d plot takes a vector of x and a vector of y and plots points at (x1,y1), (x2,y2) etc., joined with lines or not as per style settings. That fits the conceptual model we usually use for 2d plots - charting the relationship of one thing as a function of another, in most cases (y = f(x)). THere are other ways to use a 2d plot: scatter graphs are common but it's easy enough to produce one using the two-rows-of-data concept.
This doesn't extend smoothly to 3d though as there are many other ways you could use a 3d plot to represent data. If you gave it three vectors of coordinates and asked it to draw a line between them all what might we want to use that for? Is that the most useful way of using a 3d plot?
Most packages give you different visualisation types for the different kinds of data. Mathematica has a lot of 3d visualisation types and Python/Scipy/Mayavi2 has even more. Matlab has a number too but Scilab, while normally mirroring Matlab, in this case prefers to handle it all with the plot3d function.
I think of it like a contour plot: you give it a vector of x and a vector of y and it uses those to create a grid of (x,y) points. The third argument is then a matrix whose dimensions match those of the (x,y) grid holding the z-coordinates of each point. The first example in the docs does what I think you're after:
t=[0:0.3:2*%pi]';
z=sin(t)*cos(t');
plot3d(t,t,z);
The first line creates a column vector of length 21
-->size(t)
ans =
21. 1.
The second line computes a 21 x 21 matrix of products of the permutations of sin(t) with cos(t) - note the transpose in the cos(t') element.
-->size(z)
ans =
21. 21.
Then when it plots them it draws (x1,y1,z11), (x1,y2,x12), (x2,y2,z22) and so on. It draws lines between adjacent points in a mesh, or no lines, or just the surface.
I know on gnuplot you can plot some data with circles as the plot points:
plot 'data.txt' using 1:2 ls 1 with circles
How do I then set the size of the circles? I want to plot several sets of data but with different size circles for each data set.
If you have a third column in your data, the third column specifies the size of the circles. In your case, you could have the third column have the same value for all the points in each data set. For example:
plot '-' with circles
1 1 0.2
e
will plot a circle at (1,1) with radius 0.2. Note that the radius is in the same units as the data. (The special file name '-' lets you input data directly; typing 'e' ends the input. Type help special at the gnuplot console for more info.)
You can look here for more ideas of how to use circles.
I used:
plot "file" using 1:2:($2*0+10) with circles
This will fake a the third column specifying the sizes - it is probably possible to write it simpler, but this worked for me.