A Topologically Complete Theory of Weaving
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چکیده
Recent advances in the computer graphics of woven images on arbitrary surfaces in 3-space motivate the development of weavings for higher genus surfaces. Our paradigm differs markedly from what Grünbaum and Shepard have provided for the plane. In particular, we demonstrate herein how weavings on surfaces in 3-space are inducible from graph imbeddings on surfaces in 3-space. Moreover, we show that the two most frequently invoked subdivision algorithms in computer graphics, the Catmull-Clark and Doo-Sabin algorithms, correspond nicely to topological surgery operations on the induced weavings. A considerable advantage of our model is that it is topological. This permits the graphic designer to superimpose strand colors and geometric attributes — distances, angles, and curvatures — that conform to manufacturing or artistic criteria. Version: 15:31 March 1, 2012
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تاریخ انتشار 2012