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mathieu_ell_in_pol

Calculates polar coordinates of a point at angle (theta) on ellipse.

Calling Sequence

[theta, rho [, z]] = mathieu_ell_in_pol(a, b, theta [, z])

Parameters

a

major ellipse semiaxis (on x axis).

b

major ellipse semiaxis (on y axis).

z

(optional) polar height (cylindrical case).

theta

polar angle of a point on ellipse..

rho

polar radius on ellipse.

z

(optional) polar height (cylindrical case).

Description

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 .

Examples

// 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');

See Also

Authors

R.Coisson and G. Vernizzi, Parma University

X. K. Yang

2011 - DIGITEO - Michael Baudin

N. O. Strelkov, NRU MPEI


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