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Proof of Fundamental Theorem of Axonometric Projection(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1996年04期
Page:
52-56
Research Field:
Publishing date:

Info

Title:
Proof of Fundamental Theorem of Axonometric Projection
Author(s):
Zhou Jianping
Department of Manufacturing Engineering, NUST, Nanjing 210094
Keywords:
pro ject iv e g eomet ry g eomet ry theorem mat rices( mathemat ics) ax onometr ic project ion
PACS:
TB231
DOI:
-
Abstract:
In this paper, the basic principles o f axo nometric project ion ar e used to set up a common transformation mat rix of axo nometric project ion. According to mat rix matching method, if tw o mat rixes are equal, their corresponding element s are equal respect iv ely . This method is used to determine parameters of axonomet ric project ive t ransfo rmat ion matr ix . When an ax onometr ic project ive tr ansformat io n matr ix is appl ied to scale tet rahedr on, the scale tet rahedr on can be tr ansformed into a pur e quadrang le. The quadrangle is axo nomet ic pro jection of scale tet rahedron. So this paper applied the method to combine geomet ry w ith mathemat ics, to pr ove the Pohlke-Schwarz theo rem. It provided an ex ample of using computer and mathematics to study g raphic theory .

References:

1 叶玉驹, 简召全. 高等画法几何学. 北京: 国防工业出版社, 1990
2 徐宏文. 轴测投影. 天津: 天津大学出版社, 1986
3 Rog ers D F, Alan A J. Mathematical elements for comput er gr aphics. New Yor k: Mcg ramhill Book Company , 1976

Memo

Memo:
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Last Update: 2013-04-11