Shape And Function of Solid Objects Some Examples

Cover Shape And Function of Solid Objects Some Examples
Shape And Function of Solid Objects Some Examples
Ernest Davis
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For example, an open outer cage for an object O is a triple , Q> such that C is an object (the cage), and P and Q are pseudo- objects (respectively, the shell and the opening of the cage); C is a subset of P; P JJ Q is a box; O fits inside P{JQ; and, observing the hard objects constraint, if starts inside P\JQ and O never intersects Q then O never intersects the outside of P{JQ.
For the most part, the properties of boxes translate straightforwardly into those of cages. Fact B. 4, however, is so
...mewhat tricky. We may formulate the analogue in cages as follows. Let be an open cage for object 0. Define D, a vertical segment, to be a dead zone if the following facts are true: 1) Q is entirely above D; -20- 2) D is longer than the maximum diameter of 3) In any scene in hard_obj_scenes, if O is entirely contained within D and within P\JQ, then any point where C abuts does not face upward.
The formal statement of B. 4 given on page 15 can now be asserted, substituting "cage" for "box".


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