#27 Calculating areas and volumes using bezier curve parameters
Hi, thanks for creating Asymptote and offering it for free. I have used Asymptote in physics and there is sometimes need to integrate experimental curves. It is possible to define a function which picks up values of bezier curve and to integrate that using simpson but that may be quite a slow process. I thought it might be possible to calculate the integrals using the parameters of the bezier curve and found a reference, see bezierintegral.asy. To my surprise, the method also works on a closed curve, so that you can use it to calculate the area of a closed curve. The package also includes the calculation of the area of the sector and the volume and area of the body of revolution. For polynoms up to third degree the result is exact which is not suprising because it uses cubic bezier curves.
In the package attached you find the module candidate bezierintegral.asy and some examples of the usage. I have compared the numeric results of simple curves to the algebraic results and it seems to work. In each example the points used for the generation of the bezier curve are also marked. Of course, increasing the number of points improves the accuracy. One example uses the integral to calculate a moving average of an experimental curve, which was my original goal.
I forgot the experimental curve data