Journal of Graphic Science of Japan
Online ISSN : 1884-6106
Print ISSN : 0387-5512
ISSN-L : 0387-5512
Some properties and computational constructions of the Cartesian ovals by XY plotter
Hirotaka Ebisui
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1985 Volume 19 Issue 2 Pages 9-14

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Abstract
The Cartesian ovals are simply defined with bipolar coordinates. However it is difficult to draw them by handwriting. In this paper, therefore, we have constructed a computational drawing system by means of XY plotter that works with PC 8001mkII. And then, the ovals will show some particular properties. First, the ovals change gradually with left and right eccentricities. Second, the set of the intersections of three circles forms the oval. Third, when the eccentricities change continuously without changing the director circle and the foci, the ovals fill between the ellipse and the director circle. Forth, there can be shown two kinds of evolutes of the ovals. The one is drawn as an evelope of the straight lines, and the other with paramatric equations. In this way, these properties of the oval can be shown for the first time by using computational drawing system.
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© Japan Society for Graphic Science
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