1991 Fiscal Year Final Research Report Summary
Properties of Patterns Generated by Bivariate Residue Functions and Their Application to Graphic Design
| Project/Area Number |
02650257
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
情報工学
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| Research Institution | University of Tokyo |
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Principal Investigator |
SAKAMOTO Munekazu University, of Tokyo, Institute of Industrial Science, Research Assistant, 生産技術研究所, 助手 (70178581)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAGI Mikio University of Tokyo, Institute of Industrial Science, Professor, 生産技術研究所, 教授 (30013113)
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| Project Period (FY) |
1990 – 1991
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| Keywords | residue function / graphic representation of solutions / pattern design / geometric properties / logical composition / smoothed contour / color arrangement / source book for graphic design |
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| Research Abstract |
To plot solutions of a bivariate congruence on lattice points makes a pattern, which we named a residue pattern. We have investigated its theoretical background and applied it to graphic design as a new technique of designing planar patterns.
1. We have revealed that the geometrical properties of the residue pattern root from the algebra of the congruence. So, a residue pattern is generally a composite graph of the solutions of congruences with the same modulus. But the composition is not trivial, because man cannot recognize component elementary residue patterns except in special cases.
2. The pattern changes according to the congruence used, the lattice and other conditions. Smoothed contour and partial filling are used to make jaggy raster patterns more natural. and we can make beautiful and elaborate patterns usable for interior decoration etc. Four of them with the same period are assembled and their bit configuration at each lattice point defines the color number of that point. A palette specification, i. e. to assign color value to each color number, gives a color pattern. These processes are programmed and empirical guidelines for appropriate parameters are given.
3. We have designed some 200 patterns, of which our official report contains about 80. Our proposed technique is fertile and achieves high quality patterns. If parameters are automatically selected by better knowledge, our program can serve as a source book with infinite pages for pattern design.
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Research Products
(8 results)
