
Journal for Geometry and Graphics 22 (2018), No. 2, 183193 Copyright Heldermann Verlag 2018 Construction of a NinePoint Quadric Surface Viktor A. Korotkiy Inst. of Architecture and Construction, South Ural State University, 76 Lenin prospect, Chelyabinsk 454080, Russia ospolina@mail.ru The fundamental issue of constructing a ninepoint quadric was frequently discussed by mathematicians in the 19th century. They failed to find a simple linear geometric dependence that would join ten points of a quadric (similar to Pascal's theorem, which joins six points of a conic section). Nevertheless, they found different algorithms for a geometrically accurate construction (using straightedge and compass or even using straightedge alone) of a quadric that passes through nine given points. While the algorithms are quite complex, they can be implemented only with the help of computer graphics. The paper proposes a simplified computerbased realization of J. H. Engel's wellknown algorithm, which makes it possible to determine the ninepoint quadric and its axes of symmetry. The proposed graphics algorithm can be considered an alternative to the algebraic solution of the stated problem. Keywords: Biquadratic curves, pencil of quadrics, pencil of conic sections, spatial configuration of Desargues, geometrically accurate construction, computer graphics. MSC: 51M15; 51M35, 51N20 [ Fulltextpdf (4876 KB)] 