Calculates polar coordinates of a point at angle (theta) on ellipse.
[theta, rho [, z]] = mathieu_ell_in_pol(a, b, theta [, z])
major ellipse semiaxis (on x axis).
major ellipse semiaxis (on y axis).
(optional) polar height (cylindrical case).
polar angle of a point on ellipse..
polar radius on ellipse.
(optional) polar height (cylindrical case).
Calculates polar coordinates of a point at angle θ on ellipse with major semiaxis a and minor semiaxis b with the following formulas:
eccentricity
;
ellipse in polar coordinates
.
// draw the ellipse a = 5; b = 4; e = sqrt (a^2 - b^2) / a; // parameters of ellipse tht = linspace(0, 2*%pi, 100); [thta, rho] = mathieu_ell_in_pol(a, b, tht); [x, y] = mathieu_pol2cart(thta, rho); polarplot(thta, rho); plot(x, y, 'c:'); xgrid; h=gca(); h.isoview='on'; xtitle('Ellipse in polar and Cartesian coordinates', 'x', 'y'); legend('polar','Cartesian'); | ![]() | ![]() |
R.Coisson and G. Vernizzi, Parma University
X. K. Yang
2011 - DIGITEO - Michael Baudin
N. O. Strelkov, NRU MPEI