In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...

Throughout this paper we will assume that q is even. We will be considering ovoids of PG(3, q) which contain a conic as a plane section by using different representations of the classical generalized quadrangle of order q. An oŠal / of PG(2, q) is a set of q­1 points of PG(2, q), with no three collinear. Let F be a line of PG(2, q) ; then F is incident with zero, one or two points of / and is a...

We present a short proof of Descartes Circle Theorem on the “curvaturecenters” of four mutually tangent circles. Key to the proof is associating an octahedral configuration of spheres to four mutually tangent circles. We also prove an analogue for spheres. It can be traced back to at least Descartes that four mutually tangent circles have curvatures (reciprocals of radii) satisfying the relatio...

M. F. Land and D. N. Lee (1994) suggested that steering around a bend is controlled through the estimation of curvature using the visual direction of a single road feature: the tangent point. The aim of this study was to evaluate, using a simulated environment, whether the high levels of tangent point fixation reported by some researchers are indeed related to steering control. In the first exp...

— A point P on a smooth hypersurface X of degree d in PN is called a star point if and only if the intersection of X with the embedded tangent space TP (X) is a cone with vertex P . This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in P3. We generalize results on the configuration space of total inflection points on plane curv...

A differential form vanishing on the tangent space at smooth points of a reduced embedded analytic germ is called conormal. For proving that a conormal one–form of a hypersurface vanishes at its singularities we state a Bertini–type theorem.

the deformation and stiffness characteristics of a cemented gravely sand was investigated using triaxial equipment. the triaxial tests were conducted in both dry and saturated undrained conditions. artificially cemented samples are prepared using gypsum plaster as the cementing agent. the plaster was mixed with the base soil at the weight percentages of 1.5, 3, 4.5 and 6. the applied confining ...

Given a finite set Σ of lines in the plane, we discuss necessary and sufficient conditions on when there is an ellipse E, with specified center (h, k) and angle of rotation α, which is tangent to each line in Σ. In all cases we assume that no three of the lines are parallel or have a common intersection point, else no such ellipse could exist. If such an ellipse exists, we say that (h, k) is α ...