VMath matricese:optimize:distancee:apollonius_e
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2026-10-13T05:30:06+0300VMath
http://vmath.ru/vf5/
http://vmath.ru/vf5/lib/tpl/vf5/images/favicon.icotext/html2020-03-11T14:00:22+0300Anonymous (anonymous@undisclosed.example.com)References
http://vmath.ru/vf5/matricese/optimize/distancee/apollonius_e/hofault?rev=1583924422&do=diff
Author --- Русская версия
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Distance approximations
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In , the following formula is suggested for an approximation of the distance from a point to an ellipse in the plane:
$$ d \approx d_{HO} = \sqrt{-B_4/B_3} \, . $$
where $ B_3 $ and $ B_4 $ are the coefficients of the distance equation:
$$
\begin{array}{ll}
B_3(x_0,y_0)&=-2\,a^2b^2\bigg\{a^2b^2T_0G_0^2 -\bigg[(a^2+b^2)T_0^2+3\,a^2b^2T_0-6\,a^4b^4S_{4,0}\bigg]G_0 +2\,a^2b^2T_0^2S_{4,0}\bigg\} \, , \\
B_4(x_0,y_0)&=a^{4}…