Distance between ellipses with horizontal and vertical axes (here)
Example.
The distance between x=cos(t)+1, y=1.5*sin(t)+2 and
x=2*cos(t)+5, y=sin(t)+4 |
With N=6 and CLICK. The algorithm takes 2*10^7 points of the two ellipses at random. If I repeat I get slightly different values.
d = 1.5157354877226683 1.515735 (20*10^6 trials) P1=(1.7598987886578747,2.975062110709704) P2=(3.076393276713425,3.726258710583019) (1.759899,2.975062) (3.076393,3.726259) |
d = 1.515735320276885 1.515735 (220*10^6 trials) P1=(1.7598615664468806,2.975127376106839) P2=(3.076755995043274,3.725622296187349) (1.759862,2.975127) (3.076756,3.725622) |
d = 1.515735233339863 1.51573523 (2220*10^6 trials) P1=(1.759903834272297,2.9750532631508335) P2=(3.0766332895032336,3.7258374127671465) (1.75990383,2.97505326) (3.07663329,3.72583741) |
The ellipses (and the distance) with Desmos:
The ellipses with WolfranAlpha:
Another example:
d = 0.9860241507797305 0.986024 (4220*10^6 trials) P1=(2.5546884044301406,3.748087233120817) P2=(3.251945737231238,4.445278625620745) (2.554688,3.748087) (3.251946,4.445279) d = 0.9860241662756983 0.986024 (2220*10^6 trials) P1=(2.554590454246272,3.748185167806666) P2=(3.2518782140464175,4.445346151018277) (2.55459,3.748185) (3.251878,4.445346) d = 0.9860242035531152 0.986024 (220*10^6 trials) P1=(2.5548853798442934,3.7478902132314653) P2=(3.2520786639100256,4.445145729270022) (2.554885,3.74789) (3.252079,4.445146) d = 0.986026008078451 0.986026 (20*10^6 trials) P1=(2.555703244079048,3.747071082645272) P2=(3.252931565336402,4.444294114855036) (2.555703,3.747071) (3.252932,4.444294) |
If one ellipse is a point ... The distance from (10, 10) and the curve x=2*cos(t)+2, y=5*sin(t)-1 |
distance = 9.64470018696 nearest point of the curve = (2.8155786, 3.5653802)
d = 9.644700186960899 9.6447001870 (2220*10^6 trials) P1=(2.8155786459581336,3.5653802362570923) P2=(10,10) (2.8155786460,3.5653802363) (10,10) d = 9.644700186960899 9.6447001870 (220*10^6 trials) P1=(2.8155786459581336,3.5653802362570923) P2=(10,10) (2.8155786460,3.5653802363) (10,10) d = 9.644700186960902 9.6447001870 (20*10^6 trials) P1=(2.815578570087272,3.56538032096889) P2=(10,10) (2.8155785701,3.5653803210) (10,10) |