Polyhedra inscribed in a quadric

Inscribed and Circumscribed Polyhedra for a Convex Body and Continuous Functions on a Sphere in Euclidean Space

Two related problems concerning continuous functions on a sphere Sn−1 ⊂ Rn are studied, together with the problem of finding a family of polyhedra in Rn one of which is inscribed in (respectively, circumscribed about) a given smooth convex body in Rn. In particular, it is proved that, in every convex body K ⊂ R3, one can inscribe an eight-vertex polyhedron obtained by “equiaugmentation” of a si...

The Polyhedra of Maximal Volume Inscribed in the Unit Sphere and of Minimal Volume Circumscribed about the Unit Sphere

In this paper, we consider two classes of polyhedra. One is the class of polyhedra of maximal volume with n vertices that are inscribed in the unit sphere of R. The other class is polyhedra of minimal volume with n vertices that are circumscribed about the unit sphere of R. We construct such polyhedra for n up to 30 by a computer aided search and discuss some of their properties.

Enumeration of polyominoes inscribed in a rectangle

A Property of Parallelograms Inscribed in Ellipses

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Quadric splines

Surface rendering or point location on a surface can easier be accomplished in an implicit rather than parametric representation This observation has been the key motivation for developing piecewise algebraic splines In particular Dahmen and Guo used triangular segments of quadrics to build tangent plane continuous surfaces interpolating the vertices of a trian gular net with prescribed normals...