We characterize all (n?2)-dimensional linear subspaces of Pn such that the induced projection, when restricted to rational normal curve, gives a Galois morphism. give an explicit description these spaces as disjoint union locally closed subvarieties in Grassmannian G(n?2,n).

Derivatives and normals of rational Bézier curves and surface patches are discussed. A nonuniformly scaled hodograph of a degree m × n tensor-product rational surface, which provides correct derivative direction but not magnitude, can be written as a degree (2m−2) × 2n or 2m× (2n−2) vector function in polynomial Bézier form. Likewise, the scaled normal direction is degree (3m−2)× (3n−2). Effici...

Observational data hint at a finite universe, with spherical manifolds such as the Poincaré dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincaré dodecahedral space S3/...

In this paper we propose a new kind of nonlinear and geometry driven subdivision scheme for curve interpolation. Instead of using linear combination of old vertexes, displacement vector for every new vertex is given by normal vectors at old vertexes. The normal vectors are computed adaptively for each time of subdivision, and the limit curve is G1 smooth with wide ranges of free parameters. Wit...