I have two pairs of data sets, x1 vs y1 and x2 vs y2. x1, y1, x2, y2 all have uneven distribution of data represented by the following images:
My problem is to determine the intersection of the two pairs of data sets, x1/y1 and x2/y2, shown in following image:
I tried interpolating the data points to have even spacing, but due invalid regions of x1/y1 where there are multiple solutions for the same x value.
Here is a zoom in of the x1/y1 and x2/y2 relationship, showing that there are knots within the data set that cannot be interpolated in any orientation:
It seems that x2/y2 is a smooth curve, so you should be able to interpolate it piecewise with polynomials, and get decent results. Of course you will not want to do this with x1/y1, as your data is crazy. I will refer to the independent variable in the last two images as t. You can use the matlab spline function to do this interpolation from arrays of t and x2/y2 values. Your t value array in this case should be the same size as your set of x2/y2 values. Then you could loop over your x1/y1 points, using the interpolation to estimate x2/y2 at the same value of t. Then you could subtract these values. When the sign of this value changes for two consecutive x1/y1 points, you have a point of intersection between them. Then perform a linear interpolation between those two x1/y1 points and find the intersection of that line with your interpolated x2/y2 function. The code may get a little messy, but it should work. You will want to look at the MATLAB spline documentation.
Related
I have measured electric field data in three dimensions of the following form:
pos = [x1 y1 z1
x2 y2 z2
. . .
x1000 y1000 z1000]
ef = [e_x1 e_y1 e_z1
e_x2 e_y2 e_z2
. . .
e_x1000 e_y1000 e_z1000]
The positions are located within a half sphere. I want to be able to interpolate the electric field at some point of the sphere, so that I receive all the three values of the electric field components, not just the norm of the whole field. interp3 won't work as the points are not in a grid. scatteredInterpolant needs the norm as the input, and the generated function only returns the norm. Any suggestions on what function to use or how to solve this problem?
scatteredInterpolant only interpolates one column of samples at a time, but one way to interpolate a vector field is to interpolate each component of the vector independently.
This is straightforward with scatteredInterpolant.
componentInterpolants = cellfun(#(v) {scatteredInterpolant(pos,v)}, num2cell(ef,1));
This leaves you with a cell array of three scatteredInterpolant objects, one for each cartesian component of the field. By evaluating each of them individually for the specified coordinates and concatenating the result you get an electric field vector for each given coordinates. You could define a convenience function to give you the interpolated vector field in full for a given set off coordinates:
efInterpolant = #(coords) cell2mat(cellfun(#(interpolant) {interpolant(coords)}, componentInterpolants));
Verify that this interpolates the original vector field exactly (barring floating point error):
assert(all(all(abs(ef - efInterpolant(pos)) < eps * 2)));
If interpolating each cartesian component independently doesn't maintain some relationship between the vector components you expect within this field then you might need a different numerical method – perhaps some coordinate transformation before taking the same interpolation approach – but that's probably more a question for the Mathematics Stack Exchange site.
I have a list of scattered 3D points similar to the one below:
Using MATLAB, I want to interpolate further points from the surface that those original points correspond to, in order to obtain a more complete scatter. Note that there are no particular slices defined on this scattered data. That is, the z values of the point cloud are not discrete, so it's not possible to interpolate slice by slice.
I think that the ideal way to achieve this would be to somehow obtain the smooth closed surface which best matches the scattered data, and then sample it. But I have found no straightforward way to achieve this.
The scatterinterpolant class could be a simple option.
Use scatteredInterpolant to perform interpolation on a 2-D or 3-D
Scattered Data set. For example, you can pass a set of (x,y) points
and values, v, to scatteredInterpolant, and it returns a surface of
the form v = F(x, y). This surface always passes through the sample
values at the point locations. You can evaluate this surface at any
query point, (xq,yq), to produce an interpolated value, vq.
http://au.mathworks.com/help/matlab/math/interpolating-scattered-data.html
Scattered data consists of a set of points X and corresponding values
V, where the points have no structure or order between their relative
locations. There are various approaches to interpolating scattered
data. One widely used approach uses a Delaunay triangulation of the
points.
I have plotted a piece-wise defined continuous linear function comprising of several oblique straight lines joined end-to-end:-
x=[0,1/4,1/2,3/4,1];
oo=[1.23 2.31 1.34 5.69 7] % edit
y=[oo(1),oo(2),oo(3),oo(4),oo(5)];
plot(x,y,'g--')
I now wish to sample points from this plot itself, say i want the y corresponding to x=0.89. How to achieve that using Matlab? Is there a special function in-built in Matlab?
Yes, there's a built-in function for that: interp1:
vq = interp1(x,v,xq) returns interpolated values of a 1-D function at specific query points using linear interpolation. Vector x contains the sample points, and v contains the corresponding values, v(x). Vector xq contains the coordinates of the query points.
[...]
See the linked documentation for further options. For example, you can specify the interpolation method (default is linear), or whether you want to extrapolate (i.e. allow for xq values to lie outside the original x range).
I am using matlab's interpolation feature to interpolate the values of some points inside the convex hull formed. However, some of the points inside the convex hull have noisy z value. My input points are of two dimension x & y with z giving the value at the location(x,y). In some cases the z value is particular noise value. So, how can I make sure that it doesn't affect the interpolation, I mean I don't want this value to be considered. Suggestions?
Define your criteria for the point to be 'too noisy'.
Too many standard deviations from the mean? (Calculate mean and standard deviation, then threshold at n standard deviations?)
Too different from the surrounding values? (Use a smoothing/lowpass filter.)
Some background on what this data represents, and some of its characteristics, would help here.
I have multiple vectors of varying lengths that I would like to plot next to each other in 3D space in Matlab.
As an example:
Say I have three vectors:
X is a 5x2 vector,
Y is a 10x2 vector and
Z is a 15x2 vector.
Each element of every vector has the format:
x value, y value
but the x values of the various vectors do not match.
I would like to plot these vectors in 3D space, next to each other. The reason why I don't want to plot them using "hold" is because most of the data have the same values, but I would like to see how many of the plots have the same value at a specific time.
I hope my questions makes sense. Please just ask if anyone is unsure.
I think you are looking for the function ribbon.
Documentation: http://www.mathworks.fr/help/techdoc/ref/ribbon.html
EDIT:
if your x's do not have the same length, you can combine it with interp1 as follow:
x1=0:0.1:1;
x2=0:0.02:1.5;
y1=x1.^2;
y2=sqrt(x2);
y2=interp1(x2,y2,x1);
ribbon(x1',[y1;y2]')