(41) Intersection points between circles

12102020, 01:34 PM
Post: #13




RE: Intersection points between circles
(12012020 02:04 PM)rawi Wrote: sx1 = x1 + r1*(cos(alpha+beta))*sg To reduce errors, it may be better if we pick circle1 with the smaller radius, r1 ≤ r2. With circle1 having smaller radius, beta could be huge. (up to pi) We could use complement of beta instead: gamma = arcsin((z²+r1²r2²)/(2*z*r1)) = pi/2  beta With gamma, the coordinates are: sx1 = x1 + r1 * sin(gammaalpha) * sg sy1 = y1 + r1 * cos(gammaalpha) sx2 = x1 + r1 * sin(gamma+alpha) * sg sy2 = y1 − r1 * cos(gamma+alpha) Prove: If x ≥ 0, sg = 1 cos(alpha ± beta) = cos(beta ± alpha) = sin(gamma ∓ alpha) * 1 sin(alpha ± beta) = ±sin(beta ± alpha) = ±cos(gamma ∓ alpha) If x <0, sg = 1, alpha should really be pi  alpha cos(pialpha ∓ beta) = cos(alpha ± beta) * 1 sin(pialpha ∓ beta) = sin(alpha ± beta) 

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Messages In This Thread 
(41) Intersection points between circles  rawi  11252020, 03:07 PM
RE: Intersection points between circles  Albert Chan  11252020, 06:16 PM
RE: Intersection points between circles  rawi  11252020, 06:48 PM
RE: Intersection points between circles  Albert Chan  11262020, 12:22 AM
RE: Intersection points between circles  Albert Chan  11302020, 02:19 PM
RE: Intersection points between circles  rawi  11302020, 05:19 PM
RE: Intersection points between circles  Albert Chan  11302020, 09:03 PM
RE: Intersection points between circles  Albert Chan  12012020, 12:17 AM
RE: Intersection points between circles  SlideRule  11302020, 08:51 PM
RE: Intersection points between circles  rawi  12012020, 09:25 AM
RE: Intersection points between circles  Albert Chan  12012020, 11:59 AM
RE: Intersection points between circles  rawi  12012020, 02:04 PM
RE: Intersection points between circles  Albert Chan  12102020 01:34 PM

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