In this study, we give a new curve pair that generalizes some of the famous pairs curves as Bertrand and constant torsion curves. This is defined with help vector obtained by intersection osculating planes such makes same angle $\gamma$ tangents We examine relations between torsions curvatures these mates. Also, have seen unit quaternion corresponding to rotation matrix Frenet vectors $q=\cos (...

The main motivation of this work is the problem of compute intersection curve between two surface. The surface/surface intersection, is a fundamental problem in computational geometry and geometric modelling of complex shapes. In general surface intersections, the most commonly used methods include subdivision and marching. Marching-based algorithms begin by finding a starting point on the inte...

We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the unused edge. When the initial edge is reached the path is considered completed. We also consider families of such paths which together cover every edge of the...

We generalize the classical Terracini’s Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the d-Veronese embedding of the projective 3-space. A.M.S. Math. Subject Classification (2000): 14N05.

Incidentally, the value of p obtained in (9) shows that the torsion, unlike the curvature, is independent of v. An arbitrary field of force (1) produces oo trajectories, of which oo pass through a given point in a given direction. These oo trajectories have, at the given point, a common osculating plane and a common torsion. The locus of centers of their osculating spheres is a straight line. T...