"Roger Stafford" wrote in message <firstname.lastname@example.org>... > "Jessica" wrote in message <email@example.com>... > > 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?