hi,
before, happy new year..

i have perhaps a simple question, but for me, it's not..

i try to measure angle between 3 points.
My problem is i don't know where start..
i find acos function, and trigonometric function.. But there is no informations on this..
Please, someone can explain me very very slowly how create this?
Thank you very much for all help.

Sorry for my english..

Best regards

angle in radians is acos(dot(v1, v2))
v1 and v2 are the normalized edgevectors that define the angle

I'm not really a math guy, so here's my artists explanation.

The first thing you want to do is get the two vectors that form the edges of the angle you are measuring. A vector can be found by subtracting one points position from another one. The direction the vector is pointing is dependent on the subtraction order of operations. So for example:

A - B points from B to A.
B - A points from A to B.

When doing this for points in 3D space you need to subtract all of the X/Y/Z positions to get a 3D vector. So that looks like this:

Bx - Ax
By - Ay
Bz - Az

Then you make a vector out of those 3 floats. This is pretty easy in Houdini because you can add a float vector 3 parameter to just about any node. After this you can plug in these vectors into the formula above. You have to account for Houdini's syntax which can be a little weird, so I've attached an example .hip file where I'm finding the angle between the edges 0->1 and 0->2

Here is some explanation of the syntax used in my example. Look at the “measure_angle” node to see the values and formulas.

point(“../single_triangle”, 1, “P”, 0) - point(“../single_triangle”, 0, “P”, 0)
This subtracts the X position of point 1 from the X position of point 0. You can read more about point() here http://www.sidefx.com/docs/houdini12.0/expressions/point [sidefx.com]. I do this for X, Y and Z in my example to get the vectors from 0->1 and 0->2.

acos(dot(normalize(vector3(ch(“vec_p0_p1x”), ch(“vec_p0_p1y”), ch(“vec_p0_p1z”))), normalize(vector3(ch(“vec_p0_p2x”), ch(“vec_p0_p2y”), ch(“vec_p0_p2z”)))))
This looks like a lot, but what I've done is what sanostol posted above, acos(dot(v1, v2)) where v1 and v2 are normalized vectors. I'm referencing the channels where I stored the output of the vectors to make the expression smaller and easier to read.

Hi,

You can also use this VOP to do it for you:
http://www.orbolt.com/asset/animatrix::angleBetween::1.00 [orbolt.com]

It's open source if you want to know how it works.

hi, thank you very much for your help..
for this moment, i want try orbolt.. it seem best way for me…
but now, i must find how it work..
i created a vopsop node.. but where i connect?
I search..
thank you very much.
Best regard

i say you when i succeed

to mattv,
Thank you very much for your file.. it’s really perfect for me..
now, i want check your file for learn..

very thank you.

Best regard and see you.

Hi,

It's very easy. Just provide 2 vectors calculated from your 3 points. Assuming they are like this:



then (B-A) for the first input, (C-A) for the second input.