Dynamic Grid Embedding Optimizing the Compression of Partial Grids
Dynamic Grid Embedding Optimizing the Compression of Partial Grids
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Lemma 8 ("symmetric hole" PG embedding). Let PG be a rectangular grid (a X b) with exactly one "symmetric" hole, i. E. , a rectangular hole (c^d) whose sides c and d are parallel to PG's sides a and b be respectively and such that the diagonals of the PG rectangle coincide with the diagonals of the hole rectangle. Such a PG can then be embedded into its nearly ideal square with dilation • • • - r', ■ ' • • • ■ . '' . -■-"■ »• • • -•■ > • • • O - c '• • • ■ - * ^ ■•y ■ • • •••••••••• »n •••••••...•• • • • A t ^«>>i * »>»* « **t«i • •••••••••••••••••••••• •••••••••«•»••* till ^-^ iAeal sc^aar* Fig. 10: Symmetric Hole PG Embedding -18- Proof : Step 1 . Embed hole c x d into an 1 x (ex d)/2) grid and the successive layers of full grid around the hole to obtain a new rectangular grid PC which has a very narrow (1 x (ex d/2)) hole inside It.
What to read after Dynamic Grid Embedding Optimizing the Compression of Partial Grids?
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To quickly assess the difficulty of the text, read a short excerpt:
Lemma 8 ("symmetric hole" PG embedding). Let PG be a rectangular grid (a X b) with exactly one "symmetric" hole, i. E. , a rectangular hole (c^d) whose sides c and d are parallel to PG's sides a and b be respectively and such that the diagonals of the PG rectangle coincide with the diagonals of the hole rectangle. Such a PG can then be embedded into its nearly ideal square with dilation • • • - r', ■ ' • • • ■ . '' . -■-"■ »• • • -•■ > • • • O - c '• • • ■ - * ^ ■•y ■ • • •••••••••• »n •••••••...•• • • • A t ^«>>i * »>»* « **t«i • •••••••••••••••••••••• •••••••••«•»••* till ^-^ iAeal sc^aar* Fig. 10: Symmetric Hole PG Embedding -18- Proof : Step 1 . Embed hole c x d into an 1 x (ex d)/2) grid and the successive layers of full grid around the hole to obtain a new rectangular grid PC which has a very narrow (1 x (ex d/2)) hole inside It.
What to read after Dynamic Grid Embedding Optimizing the Compression of Partial Grids?
You can find similar books in the "Read Also" column, or choose other free books by Ellis John to read onlineMoreLess
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