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By E. Mach

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Extra info for Space and Geometry - In the Light of Physiol., Psych. and Physical Inquiry

Example text

Vn } be a non-degenerated component. Then, each solution for P requires at least µ(P ) = C P + DP + E P + 2F P cuts. Decomposing Octilinear Polygons into Triangles and Rectangles 27 Algorithm 1. Decomposing a non-degenerated component 1 2 3 4 5 6 7 8 9 10 11 12 13 Data: a non-degenerated component P = {v1 , v2 , . . , vn } Result: a decomposition of P into basic components foreach vertex vi of type d, e and f do divide the angle at vi by a cut that prolongs an edge incident to vi ; /* according to the proof of Theorem 3, at the end of this step, P is optimally decomposed into convex components */ end while there are convex components with at least 5 vertices do take a convex component C with at least 5 vertices; foreach vertex vi of type c do decompose C by using a nice-cut [vi , p] ; /* according to Lemma 6, there exists such a cut in C */ end end foreach convex component C with 4 vertices and different from a rectangle do decompose C ; end return the set of all the obtained basic components Remark 1.

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Phys. Eng. Sci. 455, 4131–4143 (1999) 9. : New Mathematical Diversions, Chapter 5: Paper Cutting, pp. 58–69. Simon and Schuster, New York (1966) 10. : R´ecr´eations Math´ematiques et Physiques, pp. 297–302. A. Jombert (1790) 11. : Covering a sphere by equal circles, and the rigidity of its graph. Math. Proc. Camb. Philos. Soc. fi Abstract. A shortest path joining two specified endpoint configurations that is constrained to have mean curvature at most ς on every non-zero length sub-path is called a ς-geodesic.

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Space and Geometry - In the Light of Physiol., Psych. and Physical Inquiry by E. Mach


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