FractionalGeometry-Chap2

# 8 videofeedback with mirrors analog ifs 28 83

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Unformatted text preview: and S ′ × R′ ≈ 0, 0, −.25 , and so r = −.75. Finally, to ﬁnd the angles θ and ϕ, use Eq (2.17) and the cases listed afterward: θ = arctan(−.375/ − .65) − π and ϕ = arctan(−(−.25)/.43) The parameters of the transformation T are the values of r, s, θ, ϕ, e, and f we have found. This method is a straightforward application of some basic linear algebra. We apply it again in Sect. 2.8, where we use videofeednback with mirrors as an analog implementation of some IFS. Obviously, some of the transformations involve reﬂections. Practice problems Prxs 2.7.1 Given the points P1 , P2 , P3 , Q1 , Q2 , and Q3 , in the left image of Fig. 2.47, ﬁnd the parameters r, s, θ, ϕ, e, and f of the transformation T for which T (Pi ) = Qi for i = 1, 2, 3. Prxs 2.7.2 Given the points P1 , P2 , P3 , Q1 , Q2 , and Q3 , in the right image of Fig. 2.47, ﬁnd the parameters r, s, θ, ϕ, e, and f of the transformation T for which T (Pi ) = Qi for i = 1, 2, 3. Practice problem solutions Prx...
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## This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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