We study the tropical lines contained in smooth tropical surfaces in R3. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however, there exist smooth tropical surfaces of any degree with infinitely many tropical lines.

Wepresent a new variationalmethod formesh segmentation by fitting quadric surfaces. Each component of the resulting segmentation is represented by a general quadric surface (including plane as a special case). A novel energy function is defined to evaluate the quality of the segmentation, which combines both L2 and L2,1 metrics from a triangle to a quadric surface. The Lloyd iteration is used t...

In the present article, we provide examples of fake quadrics, i.e. complex surfaces of general type with the same numerical invariants as the quadric P × P which are quotients of the bidisc by an irreducible lattice of automorphisms. Moreover we list classes of arithmetic lattices over a real quadratic number field which define a fake quadric and give general results towards a classification of...

An important problem is that of finding a quadric surface which gives a “best” fit to m given data points. There are many application areas, for example metrology, computer graphics, pattern recognition, and in particular quadric surfaces are often to be found in manufactured parts. There are many criteria which can be used for fitting, but one of the simplest is so-called algebraic fitting, wh...

Techniques for the reconstruction of quadric surfaces (cones and cylinders) from disparity measurements obtained by a stereo vision system are presented. For the initial estimation of the geometrical parameters of cones, a regression based approach is adopted from Newman, Flynn, and Jain, CVGIP: Image Understanding, Vol. 58, pp. 235-249]. A new method based on surface normal estimation is devel...

We present a catalog of type-specific, direct quadric fitting methods: Given a selection of a point cloud or triangle mesh, and a desired quadric type (e.g. cone, ellipsoid, paraboloid, etc), our methods recover a best-fit surface of the given type to the given data. Type-specific quadric fitting methods are scattered throughout the literature; here we present a thorough, practical collection i...