Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve ...

We show that the geometric Hermite interpolant can be easily calculated without solving a system of nonlinear equations. In addition we give geometric conditions for the existence and uniqueness of a solution to the interpolation problem. Finally we compare geometric Hermite interpolation with standard cubic Hermite interpolation. x1 Introduction Since parametric representations of curves are n...

The τ-boride Ni(23-x)Bi(x)B(6) [x = 2.44 (1)] adopts a ternary variant of the cubic Cr(23)C(6)-type structure, with Ni(8) cubes and Ni(12) cubocta-hedra arranged in a NaCl-type pattern. Two of the four independent metal sites (8c, 3m symmetry; 4a, mm symmetry) are occupied by a mixture of Ni and Bi atoms in a 0.106 (6):0.894 (6) and a 0.350 (7):0.650 (7) ratio, respectively.

Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth (G) constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in general be covered with G-connected Bézier patches of bi-degree 3 using the layout proposed in [ASC17]. This paper analyzes whether the pre-refinement of the in...

Let A∗ be a free monoid generated by a set A and let X ⊆ A∗ be a code with property P. The embedding of X into a complete code Y ⊆ A∗ with the same property P is called the completion of X . The method of completion of rational bi!x codes and codes with !nite decoding delays have been investigated by a number of authors. In this paper, we provide a general method of construction for completing ...

Abstract The present work introduces the problem of simultaneous bifurcation limit cycles and critical periods for a system polynomial differential equations in plane. simultaneity concept is defined, as well idea bi-weakness return map period function. Together with classical methods, we an approach which uses Lie bracket to address some cases. This used find cubic quartic Liénard systems, gen...

We investigate the Hasse principle for complete intersections cut out by a quadric and cubic hypersurface defined over the rational numbers.

For diagonal cubic surfaces, we study the behaviour of the height of the smallest rational point versus the Tamagawa type number introduced by E. Peyre.

We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.