{"title":"数字几何中的一组三角形网格","authors":"B. Nagy","doi":"10.1109/ISPA.2003.1296876","DOIUrl":null,"url":null,"abstract":"In this paper we show a new geometric interpretation of the hexagonal and triangular grids. They can be considered as the sets of points of one (see (I. Her, 1995)), respectively two plane(s) in Z/sup 3/. By this approach we can build up a whole family of triangular grids (the so called n-planes triangular grids). The hexagonal and triangular grids are the first two members of this family, moreover, they are duals of each other. We investigate the three-planes grid, the third member of the family, and its dual in detail. We show that for n /spl ges/ 4 on, the n-planes triangular grids are non-planar.","PeriodicalId":218932,"journal":{"name":"3rd International Symposium on Image and Signal Processing and Analysis, 2003. ISPA 2003. Proceedings of the","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":"{\"title\":\"A family of triangular grids in digital geometry\",\"authors\":\"B. Nagy\",\"doi\":\"10.1109/ISPA.2003.1296876\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we show a new geometric interpretation of the hexagonal and triangular grids. They can be considered as the sets of points of one (see (I. Her, 1995)), respectively two plane(s) in Z/sup 3/. By this approach we can build up a whole family of triangular grids (the so called n-planes triangular grids). The hexagonal and triangular grids are the first two members of this family, moreover, they are duals of each other. We investigate the three-planes grid, the third member of the family, and its dual in detail. We show that for n /spl ges/ 4 on, the n-planes triangular grids are non-planar.\",\"PeriodicalId\":218932,\"journal\":{\"name\":\"3rd International Symposium on Image and Signal Processing and Analysis, 2003. ISPA 2003. Proceedings of the\",\"volume\":\"51 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"27\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"3rd International Symposium on Image and Signal Processing and Analysis, 2003. ISPA 2003. Proceedings of the\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISPA.2003.1296876\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"3rd International Symposium on Image and Signal Processing and Analysis, 2003. ISPA 2003. Proceedings of the","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISPA.2003.1296876","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 27
摘要
本文给出了六边形网格和三角形网格的一种新的几何解释。它们可以被认为是一个点的集合(见(I. Her, 1995))，分别是Z/sup 3/中的两个平面(s)。通过这种方法，我们可以建立一个完整的三角形网格家族(所谓的n面三角形网格)。六边形网格和三角形网格是这个家族的前两个成员，而且它们是彼此的对偶。我们研究了三平面网格，家庭的第三个成员，以及它的双重细节。我们证明了对于n /spl / 4 on, n面三角形网格是非平面的。
In this paper we show a new geometric interpretation of the hexagonal and triangular grids. They can be considered as the sets of points of one (see (I. Her, 1995)), respectively two plane(s) in Z/sup 3/. By this approach we can build up a whole family of triangular grids (the so called n-planes triangular grids). The hexagonal and triangular grids are the first two members of this family, moreover, they are duals of each other. We investigate the three-planes grid, the third member of the family, and its dual in detail. We show that for n /spl ges/ 4 on, the n-planes triangular grids are non-planar.
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