KIRBSTER269 Very interesting approximation. How did you come up with that? Pattern spotting? Trial and error?
Obviously the approximation and the true calculation yield the same result if one of the deviations is equal to 0. Oddly enough, they yield the same result if one deviation is 8/15 of the other. For example, assume Δx = .0015 and Δy = .0008. Your approximation yields position error of 2(.0015) + .0008/2 = .0034 and the exact calculation yields .0034. In this case, Δy = 8Δx/15. You can analyze further to find a local minimum in the error function at Δy = Δx/sqrt(15), the case in which the error in the approximation is approximately 6.4% of Δx. The local maximum in the error function will be when Δy = Δx, the case in which the error in the approximation is approximately 32.8% of Δx.
I’m interested in how you discovered this approximation because I’m wondering if there is another easy approximation that has different behavior as Δx and Δy get farther apart.
KIRBSTER269 Very interesting approximation. How did you come up with that? Pattern spotting? Trial and error?
Obviously the approximation and the true calculation yield the same result if one of the deviations is equal to 0. Oddly enough, they yield the same result if one deviation is 8/15 of the other. For example, assume Δx = .0015 and Δy = .0008. Your approximation yields position error of 2(.0015) + .0008/2 = .0034 and the exact calculation yields .0034. In this case, Δy = 8Δx/15. You can analyze further to find a local minimum in the error function at Δy = Δx/sqrt(15), the case in which the error in the approximation is approximately 6.4% of Δx. The local maximum in the error function will be when Δy = Δx, the case in which the error in the approximation is approximately 32.8% of Δx.
I’m interested in how you discovered this approximation because I’m wondering if there is another easy approximation that has different behavior as Δx and Δy get farther apart.
