This paper presents cubic spline interpolation based trajectory planning method which is aiming to achieve smooth biped robot walking trajectory. We first characterize the bipedal walking cycle and point out some major issues that need to be addressed to plan a continuous swing leg trajectory by using the concept of cubic polynomial and cubic spline interpolation. By applying these interpolatio...

Ž . Ž . The growth of cubic aluminum nitride AlN and cubic gallium nitride GaN is studied. The effects of ambient pressure and substrate temperature on the structure of the AlN and GaN films are systematically investigated. It is shown that the films are amorphous when the temperature and the pressure are too low. Cubic AlN is obtained at a temperature of 8008C and a pressure of 0.2 Torr. Cubic...

We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose vertex and edge sets are a subset of those of the primitive cubic lattice, the face-centred cubic lattice, or the body-centred cubic lattice.

Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K2ƒC2n, for some n ≥ 2, generalized Petersen graph G(10, 3), permutahedron, truncated cuboctahedron, or truncated icosidodecahedron. This complete classification of cubic, vertex-transitive partial cubes, a f...

In order to eliminate the weakness of large volumes data in 3D modeling process, a fast and efficient sampling method based on curvature analysis of cubic Bézier curve is presented. With the method, the characteristic points and curvature maximum value of cubic Bézier curve are used as the reference standard of the sampling interval and density. For cubic B-spline curves, the sampling data can ...

Results based on ab initio density functional calculations indicate that cubic diamond, boron nitride, and many other cubic structures including rocksalt share a general graphitization tendency in ultrathin films terminated by close-packed (111) surfaces. Whereas such compounds often show an energy preference for cubic rather than layered atomic arrangements in the bulk, the surface energy of l...

The rst part of this paper classi es all purely cubic function elds over a nite eld of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function eld of unit rank 1 and characteristic at least 5. The technique is based on Voronoi's algorithm for generating a chain of successive minima in a multipli...

We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its CH0-group. We prove that for odd dimensional cubic hypersurfaces or for cubic fourfolds, this is equivalent to the existence of a cohomological decomposition of the diagonal, and we translate geometrically this last condition. For cubic threef...

A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...