Defining points of a polygon for use in finding area of triangle.

My problem is I need a way to take the points from a convex polygon and later use those points to calculate the area of triangles that make of the polygon. How would I define the points [x1 x2 x3...] and [y1 y2 y3...] in a way they can be used later in a loop to find the areas of a triangle? Thanks?

Answer 1

[Bruno Luong]

For polygon (x1,y1) ... (xn,yn) Why not breaking up with respect to the first vertex:

T1 = (x1,y1)(x2,y2)(x3,y3)
T2 = (x1,y1)(x3,y3)(x4,y4)
T3 = (x1,y1)(x4,y4)(x5,y5)
...
Tn-2 = (x1,y1)(xn-1,yn-1)(xn,yn)

Answer 2

[Walter Roberson]

The list you already show is as good as any representation for that purpose.

You have more of a problem in defining the "triangles that make up the polygon". There is no unique decomposition of a polygon of 4 or more points in to triangles, even when the polygon is constrained to be convex. The decomposition becomes even less special if you are allowed to introduce new interior points.

By the way, are you aware of the polyarea() call?

[Austin Hoffeditz]

Thanks for the reply,

I am, but it doesn't help my case. This is for a project and we have to break it up a n-sided polygon into n-2 triangles. From here we need to be able to find the area of each triangle and this is where I'm stuck.

[Walter Roberson]

newx = [x x(1) x(2)];

newy = [y y(1) y(2)];

for K = 1:length(x)

find the area of triangle defined by newx(K:K+2), newy(K:K+2)

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