FractionalGeometry-Chap2

8 videofeedback with mirrors analog ifs 28 83

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

Ask a homework question - tutors are online