I made the wrap angle code in the Modelica like below.
thetta_eq=mod(thetta, 720);
thetta keep increasing 0 to infinite angle and thetta_eq is the wrapped angle 0 to 720deg.
However, the problem is occurring when i differentiate the wrapped angle.
Furthermore, i'm not able to use the wrapangle block in the Modelica Standard Library 3.2.3 because i have to use 3.2.2 version.
Does anyone have solution for this problem? Code, Logic or options?
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I already know that it's not possible to differentiate when angle drops 720 to 0 deg, because it's discontinuous.
So, What i'd like to ask was making it continuous even the falling region.
Acutually, above picture is sigmoid function and i thought i can use this function when the wrap angle falls 720 to 0 deg.
If i make the sigmoid function's inclination really high, i thought this can be functioning like original wrap angle. And the derivative is not infinite or -infinite so it can be differentiated.
How do you think? and How can i make the logic for this idea?
ps) I really appreciate your reply!
Like matth commented, you can not differentiate a variable with discontinuities.
What would you expect for the derivative when theta jumps from 720 to 0?
Instead of using the wrapped angle, you can use the derivative of the original angle.
model Demo
Modelica.SIunits.Angle theta = 100*sin(time);
Modelica.SIunits.Angle theta_wrap;
Modelica.SIunits.AngularVelocity w;
equation
w = der(theta);
theta_wrap=mod(theta, 2*Modelica.Constants.pi);
end Demo;
Note: I used the proper SIunit type for theta, so I have to wrap to 2*pi radians, instead of 720 degree.
Related
(I use MATLAB R2015a). I have a plot of edge points of an object (obtained using edge detection), and I have a plot of the template of the object. I want to rotate the template until it matches with the detected edge points. (Figure link included: solid blue - template, red dots - edge detected points; the rotation is subtle, but it's there.)
I plan to rotate the template in a loop about the centroid through different values of thetas (which I know how to do), and ask the code to 'stop executing when it matches with the edge' (which is what I want to know how) and return the corresponding theta.
The number of points making up the template and that making up the edges are not the same, so splitting the plots into 3 lines and 1 (half) ellipse and directly comparing does not work.
Using regionprops 'orientation' does not give the expected result for each frame because of the way the edges are being detected in each frame. (I can elaborate more on this if required)
I have intentionally plotted points using plot, rather than keeping the edge as a BW image because, otherwise, I'm having to round off indices while creating the template, and for my application, I cannot afford to lose precision like that.
I'm not lazy, I don't want somebody to just code it up for me. None of my ideas worked and I'm unable to think any differently, so perhaps somebody with a fresh mind and more experience in Matlab will have some idea.
Assuming both image and template are bitmaps (= template isn't given as 3x lines + half of ellipse), and you know the position and size of the template, just not the angle:
For each edge, find the closest point on the template, and sum all the distances, or perhaps sum of sqrt of distances, or some other metric that penalizes many small outliers - many points will be slightly wrong if rotation is slightly wrong. Few points that are completely wrong are noise to ignore. So, something like:
minDist = inf;
minAngle = -1;
for t = 1 : length(thetas)
templatePoints = ...; % calculate template points.
for i = 1 : length(edges)
edge = edges(i); % assuming this edge is (x, y) edge point
mind = inf; % Min distance
for j = 1 : length(templatePoints)
d = sum(sqrt((edge - templatePoints).^2));
if (d < mind)
mind = d;
end
end
end
currentDist = sum(mind);
if (currentDist < minDist)
...
end
When you complete the full circle of template rotation select the rotation with the lowest difference.
This procedure might be a bit problematic because you might have template rotated by 10.5 deg and you are going in a step of 1 deg, so you will not have totally optimal angle in the end. Plus you will try tons of completely wrong angles, slowing you down.
But to find the optimal angle you can change angle step, say you first try every 10 deg rotation, then every 1deg around the minimum, then every 0.1deg etc. Or use optimization method. Gradient descent should work fine if you don't have too much noise, use simulated annealing for noisy images. Use the same code as above, currentDist is a good enough optimization parameter - it should be as close to 0 as possible.
If you have unknown template size too, or unknown template position, you definitely should use simulated annealing, gradient descent will almost surely get stuck in a local minimum. Use code similar to above to calculate difference between the edges and template, and put all the unknown parameters to the method.
One option is to make an image of your result for each rotation, but do not make it binary, make it grayscale. There are ways of making this so the "maximum interpolated edge" is where your continuous function is (such as Xiaolin Wu's line algorithm, for example).
As you are matching an image, you are not loosing precision, but putting the precision of your target to the same level as your image.
Once you get this, for each rotation, use a metric to evaluate how the 2 grayscale (yes, not binary) images match, using i.e. correlation coefficient, mutual information, universal quality index (UQI), etc.
Given parametrization of points on line L(t,θ) is
x(s):= t cos θ − s sin θ
y(s):= t sin θ + s cos θ, where t is the distance from the origin to the line at the angle θ from x-axis, and s is some point on the line.
How to take projections of image Img at this line L(t,θ) with specific step size s. Using this I have to implement a radon transform further.
My question is how to define step size s and value of t ?
Also, do I need to rotate Img or without rotation is it possible?
Please help.
I suggest you have a look at the multiple Open source software that are around.
In tomography, rotating the image is the same as rotating the machine around, so you could change the source/detector position per angle and then compute the line that joins them. Then, the step size is up to you. Research has shown (I have tested this) that a good value is s=pixel_size/2 or 0.5 if you are working in standard pixels.
If you are doing 2D parallel beam then you can forget about all the geometric transformations that need to be performed and generate projections by using imrotate. If you are using fan beam or cone beam, then the code gets a bit more complicated.
I want to compute the Euler angles from a rotation matrix in order to find out the orientation associated to that rotation. For that purpose, I am using MATLAB and the function rotm2eul that gives me the rotation first about x-axis, then about y-axis and finally the z-axis.
I am using a signal with 1000 frames and for each frame a rotation matrix is computed, as well, the three Euler angles. However, when I am going to see the Euler angles' curve, there is some "jumps" as I shown on the figures below.
On Technique 1, I think it jumps from -180º to 180º which should be the same. In fact, the upper portion of the plot seems a continuation of the lower portion. So in this case I thought I could subtract 360º to the upper portion to get the plot. But I am not sure if I do this I am falsifying the results.
On Technique 2, it makes a jump with a different reason of the previous one. I think it must be because the angle associated with the y-axis reaches 90º which should be a boundary case. But in this case I don't know how should I correct the data or , like previously, if I want to correct the plot is falsifying the euler angle result.
Technique 2: This is a Gimbal lock, known feature of Euler angles. You can't avoid it completely. You can change the rotation order, but it will appear in another position.
Still need the math: I am trying to calculate the yxy rotation sequence given a quaternion transformation. I can easily do this using Matlab's quat2angle function. However, I need to calculate this by hand using a python script.
This part solved: Please look at this awesome presentation which helped me resolve these issues below:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CCoQFjAC&url=http%3A%2F%2Fwww.udel.edu%2Fbiology%2Frosewc%2Fkaap686%2Freserve%2Fshoulder%2Fshoulder%2FBluePresentation.ppt&ei=jgRAVLHfOsSrogTJiYHABQ&usg=AFQjCNGFmwh11jEZen80jc3tM4f7HUQcNw&sig2=Dlr8_7TIFPLyUfJy6-pSJA&bvm=bv.77648437,d.cGU
Also, with Matlab, I am seeing strange results with the way they calculate yxy. I have a quaternion transformation of [1.0000 -0.0002 -0.0011 -0.0006] and I get y = 112.4291 x = -0.0719 y1 = -112.5506 (in degrees).
I don't expect to see any rotations here (my sensors aren't rotating). Why is Matlab showing me rotation? And when I try to just move in the x rotation, I see y and y1 also rotate, however, I don't expect y or y1 to be rotating. Any thoughts?
UPDATE:
When I add y + y1 I seem to get the value for the first y (when doing simple rotation around the first y), and this smooths out the data. However, when I combine the three rotations of the shoulder, the data doesn't make sense. I am trying to define shoulder movement based on plane of elevation, elevation and rotation (yxy) in a way that's easy to interpret. When I rotate around x, then the second y, I get "clipping" (data goes to 180 then -180 following positive trend for y1 and opposite happens for y), even though I start my sensors at the zero position. Also, If I try to rotate only around the second y, I see rotation in the x. That doesn't make any sense either. Any additional thoughts?
Note:
I am using 2 IMU sensors, taring them in the same orientation, holding one constant and rotating the other, calculating the relative rotation between them using quaternions, and then calculating the yxy rotation sequence angles.
In case anyone is interested in quaternion calculations and transformations. I solved it using this transformations library:
http://www.lfd.uci.edu/~gohlke/code/transformations.py.html
There are several functions in here using matrices, quaternions, and Euler rotations. And you can convert quaternions to several different Euler rotation sequences. Give thanks to the person who created this script.
I am trying to convert an array of velocity values to acceleration values. I understand that acceleration is the integral of velocity, but don't know how to acheive this. I am using MATLAB, so if anyone can offer a solution in this language, I would be very grateful! See the graph below:
The yellow line plots the velocity and the vertical dotted lines show the peaks and troughs of that waveform (peaks and troughs found using peakdet). The green horizontal stuff in the middle is unrelated to this question.
What I am trying to isolate is the steepest part of the large downward slopes on the curve above. Can anyone offer any advice on how to calculate this?
P.S. I am aware that quad() is the function used to integrate in MATLAB but don't know how to implement it in this situation.
Acceleration is a derivative of velocity.
If your velocity values are stored in v, you can get a quick numerical derivative of v with
a = diff(v)
Be aware that if v is a real rather than synthetic signal, a is likely to be pretty noisy, so some smoothing may be in order, depending on how you're going to use it.