Tabulation of a function
At the beginning F is the following. You can change it however you want.
function F(x) { with(Math) {
return sqrt(1-x*x)
}}
An example of use.
I want to determine the centroid of:
To find the center of a polygon I can use this script. I have to approximate the figure with a polygon (of a few hundred sides).
I use F(x) = sqrt(1-x*x):
I add as a starting point (0,−1):
I can approximate the centroid with (0, 0.12966).
With some theoretical reasoning I could get the ordinate 1/(3*(1+π/2)) = 0.1296615
(the exact value of the perimeter is π+2*√2 = 5.97002).