Measure of angle from XYZ positions

I made a 3D particle tracking image. It is (in this example) 17 tracks including the point of start in 0,0,0 (XYZ). Some of them didn't start the part of track (tracking problem), but it is not serious.


I also have a digital picture with any XYZ positions for each particle in the following frames. Now my question: is it possible in LabView to measure the initial angle (start) for each track of the first 10 frames (1-10)? On the photo above shows could be an angle for part of the beaches marked in red. There are only the initial angle, another part of the beaches is not bad actually.


Greetings to you.

OK, it is not too difficult.  You have a point P (I will choose 20, 34.5, 20), origin O (10, 10, 10) and you want to know the angle between the line of origin upside (call this OP line) and the line that is the projection of OP on the plan through the origin XZ.

Let's start with the passage of the origin 0, 0, 0.  We do this simply by subtracting O p, which gives us a new point P' = 10, 24.5, 10.  The point on the XZ plane is simply P' with its component is returned to zero, 10, 0, 10.  Since our origin is (now) to (0, 0, 0), points P' and the projection of P' also represent vectors from the origin (that is, they are 'lines').

We now use the fact that the scalar product of two vectors is simply the product of the length of the two vectors times the cosine of the angle between them.  I assume you know how to calculate a scalar product (if not, there is a function "Dot product" practical mathematics, algebra linear subpallet) and the length of a vector (vector Norm, even under Palette).  The division, take the arc-cosine, and you should get (approximately) pi/3 (I took 24.5 = 10 * sqrt (6) I figured it would give me this angle).

If you write this as a Subvi with particle XYZ and XYZ origin (2-3 items 1-D tables) and Theta as output, you can put this inside a loop For that subscribe to all of the 2-D array of particles and the only original value and it will return an array of Angles.

I hope it's clear.

Bob Schor

Tags: NI Software

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