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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.
 Fall '14
 AmandaFolsom
 Geometry, Fractal Geometry, Limits, The Land

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