Hi everyone ,I'm doing a momentum curvature usign Popovic's Method and found a big problem beacuse to divide a polygon(convex and concave) into small fiber like this image but with more lines:


it's not so easy to do an algorithm. I did a smath file when the polygon it's rectangular but for more general case my smath code doesn't work, I'd like know an algorithm, code or function if it's posible in smath or other language to develop.

Best regards.
Jesus.

Verificacion_de_fluencia_en_acero_fiber_method_degradation_forum.pdf (550.67 KiB) downloaded 562 time(s).

If I understand ...
Your polygon has 9 vertices, we can try a circular spline.
That will add as many points between vertices, is it ?
From there: Area, Perimeter, Center of Gravity.
Give the vertices... Jean.

Hi Jean, exactly I need to known the area, center of gravity and perimeter of the division but the polygon doesn't need to have 9 vertices, this is an example in this case. In general ,I'd like to calculate for n vertices polygon(convex or concave),let me give an example in smath for regular polygon.



polygon_2.sm (36.33 KiB) downloaded 914 time(s).

Best regards.
Jesus.

Hi Jean, it was a good solution and you give some ideas to do a code but I'd like to do for more lines and I'd like to optimize the code or algorithm. I did a code in smath maybe need to optimize some parts and get some interesting results, i hope you take a look because a I'd like to aply to convex and no convex polygon, I think it's so hard but I'd like to know the algorithm or code that other programs use. My code doesn't work for some slopes though

Page5 Polygon Copy.sm (116.59 KiB) downloaded 1097 time(s).

Best regards.
Jesus.

Wrote

Hi everyone ,I'm doing a momentum curvature usign Popovic's Method and found a big problem beacuse to divide a polygon(convex and concave) into small fiber like this image but with more lines:


it's not so easy to do an algorithm. I did a smath file when the polygon it's rectangular but for more general case my smath code doesn't work, I'd like know an algorithm, code or function if it's posible in smath or other language to develop.

Best regards.
Jesus.

Verificacion_de_fluencia_en_acero_fiber_method_degradation_forum.pdf (550.67 KiB) downloaded 562 time(s).

This might be an application for the GPC wrapper plugin by Davide.

gpc1.sm (12.5 KiB) downloaded 942 time(s).

Thank you so much, mkraska and Jean, I'll take a look this package (GPC wrapper).

Best regards

Jesús.

Ok Jean, I hope You'll find an algorithm to solve that problem.

Best regards
Jesus

very exciting project!

Hi Jean it's an excellent solution, thank you so much , I did a code with GPC plugin and I could get this results.





polygon_irregular_fiber_borrador1.sm (34.31 KiB) downloaded 953 time(s).

polygon_regular_fiber_borrador1.sm (35.48 KiB) downloaded 926 time(s).

Best regards

Jesus

Wrote

very exciting project!

... algo style to collapse in utilities.

General hatching procedure for arbitrary contours


gpc2.sm (42.6 KiB) downloaded 947 time(s).

Hi. In the attached, a function for see if a point is inside or outside a polygon, and a code for double integrals using Gauss-Legendre coefficients.

InPoly.pdf (97.1 KiB) downloaded 505 time(s).
InPoly.sm (43.3 KiB) downloaded 910 time(s).

Best regards.
Alvaro.

Wow!
Will we be able to calculate the static moment and the moment of inertia of any section with these tools?

gpc3.sm (135.5 KiB) downloaded 982 time(s).

That's superb!

Thanks a lot!

Has anyone worked on polyhedra, convex hulls and polar polyhedra?

... refreshed for convenience.

Maths Polygon Create.sm (99.71 KiB) downloaded 922 time(s).

Wrote

Has anyone worked on polyhedra, convex hulls and polar polyhedra?

I may have something on convex hull
Polyhedra, we have C_60 extracted from the adjacency matrix.
Jean

anything on the adjacency matrix I am super interested!
Handling the adjacency matrix is the only difficulty in fact. Polarity of points-planes is easy.

Wrote

anything on the adjacency matrix I am super interested!
Handling the adjacency matrix is the only difficulty in fact. Polarity of points-planes is easy.

1. In the attached Buckyball, adjacency matrix is from Mathsoft,
Mathsoft borrowed fro Matlab.
2. I have the Mathcad convex hull ORIGIN 0
RemToDo ORIGIN 1 for Smath coding.
Cheers ... Jean.

Buckyball Adjacency.sm (16.36 KiB) downloaded 896 time(s).
0Anim Buckyball.sm (107.29 KiB) downloaded 911 time(s).
Buckyball.sm (176.41 KiB) downloaded 936 time(s).

Wrote

gpc3.sm (135.5 KiB) downloaded 982 time(s).

I guess we can not use the same matrix of contour point to get the area and de center of mass ... Or am I wrong ?