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Re: create polygon coordinates
Posted:
Jan 19, 2013 2:14 PM


"Jessica" wrote in message <kdenag$nth$1@newscl01ah.mathworks.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
(xx0)^2/a^2 + (yy0)^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



