Re: how to compute the surface defined by a given contour?

[Ben Abbott]

On Dec 11, 2010, at 12:46 PM, Christophe Trophime wrote:

> 
> On Dec 11, 2010, at 5:58 PM, Ben Abbott wrote:
> 
>> 
>> On Dec 11, 2010, at 4:18 AM, Christophe Trophime wrote:
>> 
>>> 
>>> On Dec 11, 2010, at 2:17 AM, Ben Abbott wrote:
>>> 
>>>> On Dec 10, 2010, at 9:29 AM, trophime wrote:
>>>> 
>>>>> Hi,
>>>>> I am a newbie to octave.
>>>>> I have X Y Z data. I have manage to plot contour of Z as a function of
>>>>> X,Y using something like :
>>>>> 
>>>>> x = linspace(0, 0.1197, 101);
>>>>> y = linspace(0.113258, 0.377527, 101);
>>>>> Z = load("data");
>>>>> 
>>>>> [X,Y] = meshgrid(x, y);
>>>>> surf(X,Y,Z)
>>>>> contour (X, Y, Z)
>>>>> 
>>>>> Then I have selected a given contour :
>>>>> 
>>>>> VN = [0.5, 0.5];
>>>>> contour (Z, VN);
>>>>> [C, LEV] = contourc (X, Y, Z, VN);
>>>>> 
>>>>> Now I would like to get the surface (in the (X,Y) plane) defined by this
>>>>> contour?
>>>>> Is it possible to compute the gravity point of the contour?
>>>>> 
>>>>> Thanks for your helps
>>>> 
>>>> If I understand what you'd like to do, an approximation to the center of 
>>>> gravity can be calculated as ...
>>>> 
>>>>    center = sum (((X+1i*Y).*Z)(:)) / sum (Z(:))
>>>>    x_center = real (center)
>>>>    y_center = imag (center)
>>> 
>>> Yes but I want the center of gravity of the surface defined by a given 
>>> contour?
>>> I other words I want to extract X and Y from C provided by "contourc" for a 
>>> given value to define a surface,
>>> compute its area and its center of gravity.
>>> 
>>> Thanks
>>> C.
>> 
>> You'd like to treat the distributed mass as proportional to the surface's 
>> area?
>> 
>> Do I understand correctly? 
> 
> It seems that I am not very clear.
> I am doing some finite element calculation in cylindrical reference frame.
> I would like to compute the volume corresponding to a given isovalue of the 
> unknown of my fem problem
> using the Guldin's theorem. So I need a way to compute the area of the 
> surface (in the cylindrical reference frame) 
> and its center of gravity (with Z=1 in your proposed formula).
> 

Ok. I'm unfamiliar with Guldin's theorem and my FEM studies are too distant a 
memory for me to be helpful.

Ben