Interpolating specific data on Matlab - function

I am trying to analyze an image sequence of a twisting ribbon (helicoidal structure) by measuring its pitch angle but I am facing some problems in the extraction of my results.
Basically what I am trying to do is building a code that calculate the pitch angle of the helix obtained experimentally : what I have done is : calculate the width of the ribbon at every value of the height and deduce the radius of the helix. The code itself works properly and it is shown below :
%% We go to the specific file that we want to treat
clear all
path = rdir('9V\largeur.mat');
load(path{1})
%% We define the spatial scaling
% We have a picture (echelle.tiff) that tells us 10cm=565pix
echelle=565/.1; %(pixel per meter). It's the frequency
%
% for z = 1:size(largeur,1)
%
% hauteur(z) = z/echelle; %Converting the height of the image to cm
%
% end
hauteur=[1:size(largeur,1)]/echelle;
for t = 1:size(largeur,2)
signal_spatial=largeur(:,t)/echelle;
signal_spatial=(signal_spatial-min(signal_spatial));
radius = max(signal_spatial); % The radius corresponds to the maximum of the ribbon's width
theta(:,t)=acos(signal_spatial/radius); % theta = acos(x/R)
% figure(3)
% title('Angle theta en fonction de la hauteur')
% Plotting the angle theta as a function of the height z
%
%hold on
%plot(hauteur,signal_spatial)
%xlabel('hauteur (cm)')
%ylabel(['theta(z,t=',num2str(t),')'])
%title(num2str(t))
% hold off
end
%cd('6V');
%save('theta','theta');
%cd ..
plot(hauteur,theta(:,401)) % we plot for the last image ranked 401
After that, I plot the values :
plot(hauteur,-theta(:,t),'r')
And I obtain this result :
And this is my problem : now I want to get rid of some branches in order to obtain the linear evolution of the angle as a function of the height: typically my goal is to "select" the first red branch and the second blue one in order to obtain a kind of "straight" line but I don't know how to do it ?
I have thought about trying to do it by working on the fact that the wanted branches correspond to the "increasing" part of the respective functions but how to do so ?
Could you suggest a way to do it please ?
Thank you !
PS : any suggestions please ?

Related

Convert Autodesk Viewer Units to Inches

I am using the viewer with the Edit2D library and am trying to convert the length between two x and y points into real measurements.
For example, after a shape is drawn using the polygon tool, I want to get the length of the first edge.
I get the drawn shape and the first two points on the event shown below, get 2 points, and get the distance between them. It seems they are in Autodesk Units or something. Is there an easy way to convert the units to feet or inches?
I have found
Edit2DExtension.defaultContext.unitHandler.fromDisplayUnits()
as well as
Edit2DExtension.defaultContext.unitHandler.toDisplayUnits()
and also
Autodesk.Viewing.Private.convertUnits().
I've tried all three, but am unsure how to use them and haven't found any good results with them yet.
There may be a way to do it through Edit2d but I haven't found a way yet and there is next to no documentation I can find on this library.
beforeEdit2DAction(event) {
console.log('After Shape has been drawn -> ', event);
let shape = event.action.shape;
let pointA = shape._loops[0][0]; // Value: {x: 21.393766403198242, y: 20.934386880096092}
let pointB = shape._loops[0][1]; // Value: {x: 25.082155227661133, y: 20.934386880096092}
// Distance between 2 points (Assuming Autodesk units)
let length = Autodesk.Edit2D.Math2D.distance2D(pointA, pointB); // 3.6883888244628906
// Need to convert to real world units (preferably ft or inches)
}
The real length is 29.5 FEET
Any ideas, or comments are welcome! Thanks
Edit: Trying Petr's suggestion here's what it returned:
That's an interested question. The "unit handler" keeps track of two types of units:
layer units (Edit2DExtension.defaultContext.unitHandler.config.layerUnits, can be inch for example)
display units (Edit2DExtension.defaultContext.unitHandler.config.displayUnits)
These two properties control how the actual lengths and areas are displayed. For example, the unit handler's toDisplayUnits method is implemented like so:
toDisplayUnits(fromUnits, value) {
this.updateConfig();
return Autodesk.Viewing.Private.convertUnits(fromUnits, this.config.displayUnits, this.config.scaleFactor, value);
}
With that, configuring fromUnits and displayUnits (and scale) properly should give you the real measurements you need.

Cut ultrasound signal between specific values using Octave

I have an ultrasound wave (graph axes: Volt vs microsecond) and need to cut the signal/wave between two specific value to further analyze this clipping. My idea is to cut the signal between 0.2 V (y-axis). The wave is sine shaped as shown in the figure with the desired cutoff points in red
In my current code, I'm cutting the signal between 1900 to 4000 ms (x-axis) (Aa = A(1900:4000);) and then I want to make the aforementioned clipping and proceed with the code.
Does anyone know how I could do this y-axis clipping?
Thanks!! :)
clear
clf
pkg load signal
for k=1:2
w=1
filename=strcat("PCB 2.1 (",sprintf("%01d",k),").mat")
load(filename)
Lthisrun=length(A);
Pico(k,1:Lthisrun)=A;
Aa = A(1900:4000);
Ah= abs(hilbert(Aa));
step=100;
hold on
i=1;
Ac=0;
for index=1:step:3601
Ac(i+1)=Ac(i)+Ah(i);
i=i+1
r(k)=trapz(Ac)
end
end
ok, you want to just look at values 'above the noise' in your data. Or, in this case, 'clip out' everything below 0.2V. the easiest way to do this is with logical indexing. You can take an array and create a sub array eliminating everything that doesn't meet a certain logical condition. See this example:
f = #(x) sin(x)./x;
x = [-100:.1:100];
y = f(x);
plot(x,y);
figure;
x_trim = x(y>0.2);
y_trim = y(y>0.2);
plot(x_trim, y_trim);
From your question it looks like you want to do the clipping after applying the horizontal windowing from 1900-4000. (you say that that is in milliseconds, but your image shows the pulse being much sooner than 1900 ms). In any case, something like
Ab = Aa(Aa > 0.2);
will create another array Ab that will only contain the portions of Aa with values above 0.2. You may need to do something similar (see the example) for the horizontal axis if your x-data is not just the element index.

Freefem++: Solving poisson equation with numerical function

I am using Freefem++ to solve the poisson equation
Grad^2 u(x,y,z) = -f(x,y,z)
It works well when I have an analytical expression for f, but now I have an f numerically defined (i.e. a set of data defined on a mesh) and I am wondering if I can still use Freefem++.
I.e. typical code (for a 2D problem in this case), looks like the following
mesh Sh= square(10,10); // mesh generation of a square
fespace Vh(Sh,P1); // space of P1 Finite Elements
Vh u,v; // u and v belongs to Vh
func f=cos(x)*y; // analytical function
problem Poisson(u,v)= // Definition of the problem
int2d(Sh)(dx(u)*dx(v)+dy(u)*dy(v)) // bilinear form
-int2d(Sh)(f*v) // linear form
+on(1,2,3,4,u=0); // Dirichlet Conditions
Poisson; // Solve Poisson Equation
plot(u); // Plot the result
I am wondering if I can define f numerically, rather than analytically.
Mesh & space Definition
We define a square unit with Nx=10 mesh and Ny=10 this provides 11 nodes on x axis and the same for y axis.
int Nx=10,Ny=10;
int Lx=1,Ly=1;
mesh Sh= square(Nx,Ny,[Lx*x,Ly*y]); //this is the same as square(10,10)
fespace Vh(Sh,P1); // a space of P1 Finite Elements to use for u definition
Conditions and problem statement
We are not going to use solve but we ll handle matrix (a more sophisticated way to solve with FreeFem).
First we define CL for our problem (Dirichlet ones).
varf CL(u,psi)=on(1,2,3,4,u=0); //you can eliminate border according to your problem state
Vh u=0;u[]=CL(0,Vh);
matrix GD=CL(Vh,Vh);
Then we define the problem. Instead of writing dx(u)*dx(v)+dy(u)*dy(v) I suggest to use macro, so we define div as following but pay attention macro finishes by // NOT ;.
macro div(u) (dx(u[0])+dy(u[1])) //
So Poisson bilinear form becomes:
varf Poisson(u,v)= int2d(Sh)(div(u)*div(v));
After we extract Stifness Matrix
matrix K=Poisson(Vh,Vh);
matrix KD=K+GD; //we add CL defined above
We proceed for solving, UMFPACK is a solver in FreeFem no much attention to this.
set(KD,solver=UMFPACK);
And here what you need. You want to define a value of function f on some specific nodes. I'm going to give you the secret, the poisson linear form.
real[int] b=Poisson(0,Vh);
You define value of the function f at any node you want to do.
b[100]+=20; //for example at node 100 we want that f equals to 20
b[50]+=50; //and at node 50 , f equals to 50
We solve our system.
u[]=KD^-1*b;
Finally we get the plot.
plot(u,wait=1);
I hope this will help you, thanks to my internship supervisor Olivier, he always gives to me tricks specially on FreeFem. I tested it, it works very well. Good luck.
The method by afaf works in the case when the function f is a free-standing one. For the terms like int2d(Sh)(f*u*v), another solution is required. I propose (actually I have red it somewhere in Hecht's manual) an approach that covers both cases. However, it works only for P1 finite elements, for which the degrees of freedom are coincided with the mesh nodes.
fespace Vh(Th,P1);
Vh f;
real[int] pot(Vh.ndof);
for(int i=0;i<Vh.ndof;i++){
pot[i]=something; //assign values or read them from a file
}
f[]=pot;

AS3 Polar coordinate from Cartesian coordinate

I'm playing with body animation in AS3. I did a body with all parts (excluding fingers) and make a XML with the "skeleton". The XML got the instances of each part and the place of the articulation of the next part. I make it work with cardinal coordinates (x,y) and the body moves when I rotate a part and recalculate all the links again (each part in each articulation).
However, this will demand some calculation each little modification of the body, so now I'm optimizing it. As for de design x,y is easier, so when the body instance is created, the class re-build the XML converting coordinates to Polar system (r,t), like this ("Quadro" is the node with coordinates):
dx = Quadro.#x;
dy = Quadro.#y;
Quadro.#r = Math.sqrt(Math.pow(dx,2) + Math.pow(dy,2));
Quadro.#t = (dy>0)? Math.asin(dx/Quadro.#r) : Math.acos(dy/Quadro.#r);
I did some changes to make it work but at list one quadrant is always wrong! In this case, the upper left is wrong. The neck and the head should be in this place and they are in upper right (mirrored).
Any tips for a right conversion in AS3?
Try to use this:
Quadro.#t=Math.atan2(dy,dx);
From Wikipedia:
The Cartesian coordinates x and y can be converted to polar
coordinates r and φ with r ≥ 0 and φ in the interval (−π, π] by:

Given an R,G,B triplet and a factor F, how do I calculate a “watermark” version of the color?

I have an (R, G, B) triplet, where each color is between 0.0 and 1.0 . Given a factor F (0.0 means the original color and 1.0 means white), I want to calculate a new triplet that is the “watermarked” version of the color.
I use the following expression (pseudo-code):
for each c in R, G, B:
new_c ← c + F × (1 - c)
This produces something that looks okayish, but I understand this introduces deviations to the hue of the color (checking the HSV equivalent before and after the transformation), and I don't know if this is to be expected.
Is there a “standard” (with or without quotes) algorithm to calculate the “watermarked” version of the color? If yes, which is it? If not, what other algorithms to the same effect can you tell me?
Actually this looks like it should give the correct hue, minus small variations for arithmetic rounding errors.
This is certainly a reasonable, simple was to achieve a watermark effect. I don't know of any other "standard" ones, there are a few ways you could do it.
Alternatives are:
Blend with white but do it non-linearly on F, e.g. new_c = c + sqrt(F)*(1-c), or you could use other non-linear functions - it might help the watermark look more or less "flat".
You could do it more efficiently by doing the following (where F takes the range 0..INF):
new_c = 1 - (1-c)/pow(2, F)
for real pixel values (0..255) this would convert into:
new_c = 255 - (255-c)>>F
Not only is that reasonably fast in integer arithmetic, but you may be able to do it in a 32b integer in parallel.
Why not just?
new_c = F*c
I think you should go first over watermarking pixels and figure out if it should be darker or lighter.
For lighter the formula might be
new_c=1-F*(c-1)