著者

蛭子井 博孝

出版者

日本図学会

雑誌

図学研究 (ISSN:03875512)

巻号頁・発行日

vol.40, no.1, pp.21, 2006 (Released:2010-08-25)

著者

蛭子井 博孝

出版者

日本図学会

雑誌

図学研究 (ISSN:03875512)

巻号頁・発行日

vol.29, no.2, pp.3-8, 1995 (Released:2010-08-25)

参考文献数

8

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Descartes' oval is defined as mr1 + nr2 = kc by using bipolar coordinates. Where, if m=n, it is ellipse. According to this definition and a number of the properties, it can be said that the Descartes' oval is essential extension of ellipse.This time, the minor axis of oval that has the similar properties to those of the minor axis of ellipse is found. This minor axis is the segment connecting the middle point 0 of the major axis (the axis of symmetry) of oval and the point Np on the oval, which is at the shortest distance from the point 0. The length of this minor axis is expressed by α√1-eLeR, where α is a half of the length of the major axis, and eL and eR are left and right eccentricities, respectively. As for this minor axis, its proof and a number of the properties are discussed.Next, the method of defining ovaloid which is convex, closed curved surface in space by extending the oval on plane is found, therefore, it is reported. This ovaloid has, as the contours of the orthographic projection from three directions, circle, Descartes' oval and a fourth order curve like ellipse. Further, the parametric expression of this ovaloid is derived. In this way, the new properties of oval are able to be added, therefore, it is reported.

著者

蛭子井 博孝

出版者

図学研究

雑誌

図学研究 (ISSN:03875512)

巻号頁・発行日

vol.19, no.2, pp.9-14, 1985

被引用文献数

1

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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.