(a) L R s (u; s) C i (u) (b) L R s (u; s) C i (u) Figure 9: A direct intersection curve tracing of a DSSI between a developable surface R s (u; s) and the Utah teapot, is used to derive the domain of C i (u) that is in shadow. Two views of the same scene are provides. a tight link between two diicult problems from the two elds of computer graphics and computer aided geometric design, namely SSI...

Abstract In this study, we define the generalized normal ruled surface of a curve in Euclidean 3-space E 3 . We study geometry such surfaces by calculating Gaussian and mean curvatures to determine when is flat or minimal (equivalently, helicoid). examine conditions for curves lying on be asymptotic curves, geodesics lines curvature. Finally, obtain Frenet vectors get some relations with helice...

The technique of scanning tunneling microscopy has been applied to topographic mapping of two optical surfaces: a ruled grating replica and a diamond-turned gold mirror. We have demonstrated the ability of the scanning tunneling microscope to measure surface topography of a ruled-grating replica over an area of 2 microm x 2 microm. Furthermore, surface structure on a diamond-turned gold mirror ...

Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in archite...

Introduction. In this paper a point correspondence is introduced which is proving to be very helpful in the study of a general non-ruled analytic surface in ordinary space. If on a surface S tangents to the curves of an asymptotic family are constructed at the points of two curves of 5 which are not members of the family and which intersect in a point y of S, two ruled surfaces are thereby form...

A four generation supersymmetric model is proposed, in which the Tevatron “top-quark” events are reinterpreted as the production of t′ which decays dominantly to bW. In this model, mt ≃ mW , and t → t̃χ̃01, with t̃ → cχ̃01. This decay chain, which rarely produces a hard isolated lepton, would have been missed in all previous top quark searches. A narrow region of the model parameter space exists wh...