Date: Jan 19, 2013 6:50 PM
Subject: Re: create polygon coordinates
"Roger Stafford" wrote in message <email@example.com>...
> "Jessica" wrote in message <firstname.lastname@example.org>...
> > I have coordinates such as this:
> > 384 360 60 69
> > that represent the left, top, width, and height of an ellipse. How can I turn these values into a list that specifies a polygon?
> > I would like to use this polygon list to find out whether particular X and Y coordinates fall inside this ellipse:
> > k_inside1= inpolygon(X_Coordinate, Y_Coordinate, X_Polygon3, Y_Polygon3);
> > Thanks!
> - - - - - - - - -
> It seems a shame to approximate an ellipse with a polygon to see if points lie inside it, when a direct test with the simple equation of the ellipse would accomplish the same thing with much better accuracy and simplicity.
> However, here are n vertices of a polygon approximating an ellipse. Let the ellipse be defined by the equation
> (x-x0)^2/a^2 + (y-y0)^2/b^2 = 1
> Then the vertices are given by:
> t = linspace(0,2*pi,n); % <-- You choose n
> x = a*cos(t)+x0;
> y = b*sin(t)+y0;
> Note: The spacing along the polygon is not uniform here. To do that would require the use of elliptic integrals.
> Roger Stafford
Thanks for the tip! Do you mind explaining how I could test whether a coordinate falls within an ellipse using just the equation of an ellipse and not converting it to polygon coordinates?