Timeline for answer to Given the y-values of points sampled at a constant angle on a circle with unknown center and radius, find corresponding x-coordinates by David K
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Oct 31, 2019 at 16:33 | comment | added | MisterH | Now that I think of it, if the horizontal coordinate of the center of the circle would always be at 0.5 times the first y-value, then the circle would go through the origin, giving you 2 points, and the third could be easily found because the arc length of the circle-segments between points on the circle would be equivalent to the distance from 0 to the first y-value, and this would be the hypotenuse of the right triangle, so via pythagoras you get your third x-value, and 3 points uniquely define a circle, so you only have to plug in the other y-values, giving you all the x-values... | |
| Oct 29, 2019 at 3:53 | comment | added | David K | I would expect to be able to rule out one of the roots. But I think this answer needs to be checked, because when I tried it on an example it did not recover the original differences in $x$ values. | |
| Oct 28, 2019 at 16:10 | comment | added | MisterH | Ok if one of the conditions: "These circles touch the Y-axis in 1 place: the first y-value (closest to the origin), where they also touch each other." is incorrect: they cross the Y-axis twice, and if you knew that the horizontal coordinate of the center of the circle would always be at 0.5 times the first y-value, would there be a different solution? Solving for the last equation for t always returns 2 real roots. | |
| Oct 18, 2019 at 22:48 | vote | accept | MisterH | ||
| Oct 6, 2019 at 3:40 | history | edited | David K | CC BY-SA 4.0 |
interpretation
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| Oct 6, 2019 at 3:33 | history | edited | David K | CC BY-SA 4.0 |
interpretation
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| Oct 6, 2019 at 3:28 | history | edited | David K | CC BY-SA 4.0 |
interpretation
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| Oct 6, 2019 at 3:22 | history | edited | David K | CC BY-SA 4.0 |
three points are not enough
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| Oct 6, 2019 at 3:15 | history | answered | David K | CC BY-SA 4.0 |