Geometrical properties of arbitrary sections (2D)

Click For Summary
SUMMARY

The discussion focuses on calculating geometrical properties of arbitrary 2D sections, specifically area, centroid, and moment of inertia. The user is attempting to automate these calculations using programming, relying on straight lines defined by coordinate points. They are exploring the applicability of Green's Theorem for these calculations but express uncertainty regarding its effectiveness with numerous coordinate points and arbitrary shapes. The conversation highlights the need for clarity on the limitations of Green's Theorem in this context and seeks alternative algorithms for accurate computation.

PREREQUISITES
  • Understanding of Green's Theorem in calculus
  • Familiarity with coordinate geometry
  • Basic programming skills for algorithm implementation
  • Knowledge of moment of inertia calculations
NEXT STEPS
  • Research the limitations of Green's Theorem for arbitrary coordinate systems
  • Explore algorithms for calculating area and centroid of polygonal shapes
  • Learn about numerical integration techniques for complex shapes
  • Investigate libraries or tools for computational geometry, such as CGAL or Shapely
USEFUL FOR

Mathematicians, engineers, and software developers interested in computational geometry and automated calculations of geometrical properties in 2D spaces.

cigarette
Messages
9
Reaction score
0
Hi all, i am interested in finding out the Geometrical properties of an arbitrary section, which means 2D area. Rather than having to perform manual calculations everytime, i am trying to write a program to help me with this. There is a problem however. I cannot seem to find the appropriate mathematical expressions to help me obtain the following :

(1) Area
(2) Centroid
(3) Moment of Inertia

To help make the program easier to write, i have decided that all lines drawn are straight lines, therefore eliminating the tedious curves. Hence i can easily calculate the length of each lines and sum them up to obtain the perimeter. This is possible, because i have all the co-ordinate points. Now, what about area? I have tried using the Green's Theorem for calculations, but i am not sure whether it works for sections which have a large number of co-ordinate points. Also the centroid can also be worked out using Green's Theorem, and once again, it is not known whether it works for arbitrary co-ordinates. Does it have any limitations?

Can anyone help explain to me whether Green's Theorem is good for this application? Or does anyone have a clearer or better algorithm which i can use?

Thanks in advance ... it's rather urgent.. :confused:
 
Last edited:
Physics news on Phys.org
This same question was asked in "General Mathematics". Please do not post the same question multiple times.
 
Green th is using on partial differentials eq , for the variational formulation than for finite element
 

Similar threads

Undergrad Green's Theorem->Does it work for ?
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Differentiability of a Multivariable function
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Converse of focus-directrix property of conic sections
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Discretisation of a PDE in Lagrangian coordinates
  • · Replies 4 ·
Replies
4
Views
3K
Misc. Yarn cross-section and path length
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Proof that lattice points can't form an equilateral triangle
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Prove that the geometric mean is always the same
  • · Replies 2 ·
Replies
2
Views
2K
Insights The Art of Integration
  • · Replies 10 ·
Replies
10
Views
5K
Undergrad How to understand this property of Geometric Distribution
  • · Replies 1 ·
Replies
1
Views
1K
MHB What Property Connects the Steps in a Geometric Series Calculation?
  • · Replies 3 ·
Replies
3
Views
2K