Properties Features of Parabola at Its Simulation

О. Графский, O. Grafskiy, Ю. Пономарчук, Yu. Ponomarchuk, В. Суриц, V. Suric
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引用次数: 4

Abstract

When studying the theory of contour construction in “Affine and Projective Geometry” course on educational program specializations “Computer-Aided Design Systems” and “Applied Informatics in Design” a unit of computational and graphic task "Contour Construction" is carrying out in structural design. In this computational and graphic task the contour constructions are carrying out by second-order curves (a circle — by the radius and graphical method; a hyperbola, an ellipse, a parabola — by means of Pascal curves, taking into account positions of engineering discriminant). The constructions of an arc of ellipse, hyperbola, and parabola are carried out based on Pascal theorem: in any hexagon, which vertices belong to a second-order series, three points of the opposite sides’ intersection lie on one straight line — the Pascal line. However, in construction of a conic (a second-order curve), it is necessary to draw students’ attention to the fact that the points belonging to a second-order series (a second-order curve, or a conic) make a geometrical locus of intersection of Pascal hexagon’s adjacent opposite sides. By this method students successfully construct conjugate arcs of an ellipse and a hyperbola with other conics. The construction of a parabola arc, conjugated with other conics, is carried out by the method of engineering discriminant (it is more convenient to divide line segments in halves: a median and a triangle side, which is opposite to its vertex lying on a parabola arc). It should be noted that theoretical and practical material on this subject corresponds to the assimilation of Study Plan’s necessary competences (in accordance with each educational program), however, some aspects of this subject are accepted by students simply by trust. The aim of this paper is research of construction methods for parabola, applied to contour simulation.
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抛物线在模拟中的性质和特征
在教育专业“计算机辅助设计系统”和“设计应用信息学”的“仿射与射影几何”课程中学习轮廓构造理论时,在结构设计中开展了计算与图形任务单元“轮廓构造”。在这个计算和图形任务中,轮廓构造是通过二阶曲线(圆-通过半径和图形方法;双曲线、椭圆、抛物线(利用帕斯卡曲线,考虑工程位置判别)。椭圆、双曲线和抛物线的弧的构造是根据帕斯卡定理进行的:在任何顶点属于二阶级数的六边形中,对边相交的三个点位于一条直线上——帕斯卡线。然而,在构造二次曲线(二阶曲线)时,有必要提请学生注意,属于二阶级数(二阶曲线或二次曲线)的点构成帕斯卡六边形相邻对边的几何交点轨迹。通过这种方法,学生成功地构造了椭圆和双曲线与其他二次曲线的共轭弧。抛物线弧的构造与其他二次曲线共轭,采用工程判别法(将线段分成两半更方便:中间和三角形边,三角形边的顶点相对于抛物线弧)。应该指出的是,这一主题的理论和实践材料符合学习计划的必要能力的同化(根据每个教育计划),然而,这一主题的某些方面被学生简单地接受了信任。本文的目的是研究抛物线的构造方法,并将其应用于等高线仿真。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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