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
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.
図学研究 32(3), 61-69, 1998-09-01