By Virginia Woolf
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Additional resources for A Room of One's Own (Penguin Great Ideas)
Wooden “Hedgehog in a Cage” puzzle. com/. 2. 4 Some of these puzzles are extremely diﬃcult to solve, even those which have no hidden parts. Nevertheless all of these puzzles could in theory be solved by a general motion planning algorithm in “constant time,” because for any speciﬁc puzzle, the parameters are constant. 2. It consists of just two rigid parts. The cage could be represented by two squares for the top and bottom and four segments for the bars. The hedgehog could be represented by, say, a dodecahedron and 14 segment spikes (8 short, and 6 long).
11 We could retain y as a universal joint for the three links ya, yd, and yz, but at the cost of bracing ad with another link. 4 Rigid Frameworks The area of rigidity theory studies a special class of problems about linkages: can the linkage move at all? This seemingly simple question has a deep theory behind it, with many variations and characterizations. 6 (p. 93). A full survey is beyond our scope; see Connelly (1993), Graver (2001), Graver et al. (1993), and Whiteley (2004) for more information.
In this case the conﬁguration space is a torus representing two angles θ 1 and θ 2 , each with wrap-around ranges [0, 2π] (see p. 60). Their original algorithm, developed in the justly famous ﬁve “piano mover’s” Hopcroft et al. 1987papers,1 resulted in a doubly exponential algorithm. Subsequent research has improved this to singly exponential. Although we will not employ this algorithm subsequently, it is an important milestone and serves as a baseline for all subsequent work, and so it is worth stating the result more precisely.
A Room of One's Own (Penguin Great Ideas) by Virginia Woolf