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Unformatted text preview: er2 coordinates (L,M,N;P,Q,R) of a line (see e.g. [Davidson & Hunt, 2004]). Coordinates P and Q are scaled directly on two axes in Fig. 2, but L and M are first multiplied by length j/2 to give measures L' and M' in units of [length] (see [Davidson and Shah, 2002 or Bhide, et al., 2003] for more detail). The linear relation $ = λ1 $1 + λ 2 $ 2 + λ3 $ 3 + λ 4 $ 4 + λ5 $ 5 (1) contains the coordinates λ1,…,λ5 [Coxeter, 1969], and its linearity derives from the extremely small ranges for orientational variations which are imposed by tolerance-values in a tolerance-zone. Note that the position of $ depends only on four independent ratios of these magnitudes, thereby requiring one condition among them2 and confirming 4 as the dimension of the space. When the coordinates λ1,…,λ5 are normalized by setting Σλi =1, they become areal coordinates [Coxeter,1969]. To reach all the lines in the tolerance-zone (points in the T-Map), some of the λ1,…,λ5 will be negative. Equation (1) can be used to construct the entire boundary of the T-Map (see [Bh...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.
- Spring '10
- The Land