# 周期関数による幾何学模様の生成とその変換The Creation of Geometric Design by Periodic Function and Its Trasformation

## 抄録

When <I>F</I><SUB>1</SUB><I> (t), F</I><SUB>2</SUB><I> (t) </I> is expressed as periodic function of <I>t, </I> we define the figure which <I>x</I>=<I>F</I><SUB>1</SUB><I> (t) </I>, <I>y</I>=<I>F</I><SUB>2</SUB><I> (t) </I> draws as <I>pan trochoid</I>. When a circle rolls along grounds circle, including when the circle slides, a trace of point fixed on the rolling circle is contained all by this pan trochoid. And if a radius of grounds circle becomes infinity, <I>x</I> = <I>F</I><SUB>1</SUB><I> (t) </I> or <I>y</I> = <I>F</I><SUB>2</SUB><I> (t) </I> becomes a form containing linear expression of <I>t</I>, and calculated figures go straight while rolling the straight line top. Here, I use this pan trochoid going straight on as basic form for the creation of geometric figures.<BR>The purpose of this paper is to show algorithm to form geometric figures, using this pan trochoid going straight on. In other words, this paper shows settingmethod of pan trochoid going straight on and their conversion method (turn transformation, spiral transformation, affine transformation, projective transformation, compound transformation), and discusses concrete geometric figures formed by those transformation and their characterics and is going to provide the fundamental method to make unique and harmonic geometric figures quickly as plane design, decoration and art.

## 収録刊行物

• 図学研究

図学研究 32(3), 61-69, 1998-09-01

日本図学会

## 各種コード

• NII論文ID(NAID)
10002847069
• NII書誌ID(NCID)
AN00125240
• 本文言語コード
JPN
• 資料種別
ART
• ISSN
03875512
• NDL 記事登録ID
4584015
• NDL 雑誌分類
ZM1(科学技術--科学技術一般)
• NDL 請求記号
Z14-457
• データ提供元
CJP書誌  NDL  J-STAGE

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