My problem is like this:

I have a 2 dimensional domain

Now, that domain is made up of eleemnts- these elemnts are triangular

or quadrilateral in shape. Each triangualr and quadrilateral element has 3 and 4 vertices (a triangular element has 3 vertices and quadrilateral has 4 vertices).

We have fixed function values at these vertices- the function is (Say) F

In that 2-D domain we define a strip (a strip is just a part of the area of that domain), A strip may have several sections - (those) lines as in attached figure (summary-figure.jpg)- the vertical lines are sections.

What I need is::

I need to integrate the resultant (function) along the length of each design strip section and

hence across the width of the design strip.

I could think to proceed in the following steps::

The inputs are:

A) All the triangle/quadrilateral vertices

B) Function values at all the vertices

C) The line over which you want to integrate

D)geometry of the strip

The broad algorithm would be like this:

1. Find which quadrilaterals/triangles this line intersects

2. Find the function values at the points of intersection of the line with the sides of these quadrilatrals/triangles

3. Use numerical integration to integrate the function from these values

Can anyone help me with a better algorithm?

Also, how would I proceed with 3 above?What would be the best for numerical integration?

Someone suggested about Chebyshev polynomials- but I do not have any idea of it!

Please please can anyone help?