I would like to define a Center of mass - Wikipedia
At first by help one experiment
and then (after a scanning the figure) by Mathcad help
Do you know more quickly method?
Solved! Go to Solution.
Here is how I would have approached:
Or, programmatically:
Both of these methods calculate almost instantly.
Quickly looking at your calculations, I did not follow what you were doing. What's wrong with my approach compared to yours?
I have got the solution but it needed... 5 hr. Not from me but from my PC
Valery,
I believe you made the following error:
The matrix indices should be i1 and j1.
As a result, you found the center of the picture frame:
350 / 2 = 175
385 / 2 = 192.5
Thanks, Mark
Now I am going to bed. I will say tomorrow the resultat
You can integrate the boundary curves.
45 minutes start to finish:
Thanks, Fred!
But I see one error
Well done! I guess I would have rather used linear interpolation.
But the method would not work for something like the following, right?
We would have to resort to algorithms from computer graphics to determine the boundary, but I am too lazy to dig in an implement it. maybe its less work to digitize the outline by other means and import the result into Mathcad.
Then we could use the formula for polygons rather than using integrals, like so (this for the original graphics using your X, X.l and X.r):
Regards,
Werner
Werner,
You'd have to break a complex shape into several simpler ones (that you could integrate. Once you have areas and CG's for each finding whole is simple
Yes, but its quite some efforts to do it automatically in an all purpose CG finding routine, I guess.
Werner Exinger написал(а):
Well done! I guess I would have rather used linear interpolation.
But the method would not work for something like the following, right?
Better
Using my method (see post below), I calculate the COM for your woman to be (169.545, 388.775).
The image is 336 x 897 pixels.
Thanks? bot it is too simple...
I would argue that your method is too complex.
Sorry,
we must find a center of mass, not a center of gravity
Valery Ochkov wrote:
Sorry,
we must find a center of mass, not a center of gravity
When is it different?
"Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish. That means that for any rigid body, the two points are the same, because you can model rigid bodies in free fall as if gravity acted only on the center of mass, and forces on the center of mass make no torque."
Fred Kohlhepp написал(а):
Valery Ochkov wrote:
Sorry,
we must find a center of mass, not a center of gravity
When is it different?
The different is when we have non parallel gravity field - a big body in space near Earth. I think so.
Mark Gase написал(а):
I would argue that your method is too complex.
But I can have this figure
Or so
Mark Gase написал(а):
Using my method (see post below), I calculate the COM for your woman to be (169.545, 388.775).
She (from the famous movie) has the COM in the other point as by us
Here is how I would have approached:
Or, programmatically:
Both of these methods calculate almost instantly.
Quickly looking at your calculations, I did not follow what you were doing. What's wrong with my approach compared to yours?
EXCELLENT!
You've replaced my integration (with it's troublesome edge/function needs) with the simple summations.
Impressive!
Here is another simpler approach if the area is given by a pixel graphics
EDIT: Oops, sorry. Had not seen that Mark already suggested this approach.
You can find CG by using our Monte-Carlo method
(from Kirsanov book http://vuz.exponenta.ru/PDF/tm2.pdf)