Kassel', Germany
Non-degenerate surface of second order (PVP, quadric) is defined, if set to nine points, no three of which are collinear and no six of which lie in the same plane. The points in pairs can be imaginary. Analytic surface is defined, if recorded its the equation of three variables with numerical coefficients of F(x, y, z) = 0. Graphically, the surface is defined, if defined by its basic parameters — the lengths of its three mutually perpendicular main axes: large, medium and small. Depending on the position of the nine data points, one or two of the three axes can be imaginary. Analytical surface definition through writing her equations on the coordinates of the nine points is possible without any difficulties. But here we are interested in graphic design. This paper examines the question of determining the parameters of PVP — determination of the position of the surface in space and definition of its main axes upon prescribed points or other surface elements. Quadric has three main axes — it is three parameters. The center of the quadric may be shifted from the origin along each of three axes — it is three parameters. Quadric can be inclined to coordinate axes in each of the three coordinate planes. Total, quadric is determined by nine parameters. Nine points determine a quadric in form and position in space. Nine points is three trio points that define the three planes, inclusive these points. The article reviews the task of a quadric with nine points, of a conical and four points, three profile of a quadric. Solution of the definition of quadric in the case where five of the nine points lie in the same plane is proposed.
involution, double points, conic, quadric, assignment by nine points.
Введение
Невырожденная поверхность второго порядка (ПВП, квадрика) определена, если заданы девять ее точек, никакие три из которых не лежат на одной прямой и никакие шесть из которых не лежат в одной плоскости. Девять точек могут быть заданы своими координатами или графически своими проекциями на полях двухкартинного чертежа.
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