Spherical segment

Abstract: A spherical display and control device, that is preferably collapsible between a spherical configuration and a collapsed generally cylindrical ellipsoid configuration, comprising a flexible transparent spherical surface sprung attached to a central hinged modular cube assembly that contains digital displays on outward faces, and circuitry, battery units and electronic modules on inward surfaces, where said sphere surface contains surface position sensing layers and said central cube contains gyroscopic and inertial sensing devices to provide spherical rotation, and physical displacement data for the three dimensional control applications, where said displays preferably have curved polarizer lenses such that the overall device appears as a spherical display or are flat to form an overall Cuboid display or are combined with a flexible spherical display surface. The overall device being mechanically biased such that it is Bi-stable between the spherical and collapsed configuration via the action of pulling open and rotating the central cube halves.

Abstract: The device is intended for expanding profile pipes set in a well for patching off a troublesome zone, and also for straightening crumpled casings. The device comprises a housing having an expanding member mounted thereon in bearings on a journal exten-ding at an acute angle to the longitudinal axis of the housing. The expanding member is shaped as a spherical segment having its external surface defined by alterna-ting portions of a spherical surface and the lateral surfaces of cylinders whose geometric axes belong to a plane perpendicular to the axis of the journal.

Abstract: A golf ball has a plurality of dimples in its spherical outer surface and its spherical outer surface is divided into the faces of an icosahedron consisting of 20 regular spherical triangles, and the golf ball's spherical outer surface is further divided by great circle paths which obtained by extending spherical straight lines connecting the midpoint of each side of the sperical triangles of icosahedron to its opposite apex, then large spherical pentagons will be created on the polar regions of the golf ball's spherical outer surface. The center of large pentagon as a pole, which is a common apex of 5 regular spherical triangles of the spherical icosahedron, from the pole, spherical straight lines extend along the both sides of each of the 5 spherical triangles to the equator. (Same thing happens on the opposite pole.) The spherical outer surface is further divided by the spherical straight lines into small sections to arrange the dimples. Regarding to the dimples, arrange the largest circular dimples on the central region of each spherical triangle and also on each apex of the spherical triangles of the spherical icosahedron, and arrange the annular dimples which have the same center as the largest circular dimples on each apex of the spherical triangles, outside of them. In accordance with the dimple arrangement of the present invention, the drag coefficient of a golf ball in a low-speed area has reduced and the carry distance has increased. In addition, the center of each annular dimple will act as an authentic axis of rotation when the annular dimple becomes at a right angle with the direction of air stream and so keep the ball's rotation longer, that secure the flying stability and a longer carry distance.

Abstract: We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genus-zero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square image domain to cover the infinite plane, thereby providing a globally smooth surface parametrization. The 2D grid structure permits use of ordinary image wavelets, including higher-order wavelets with polynomial precision. The coarsest wavelets span the entire surface and thus encode the lowest frequencies of the shape. Finally, the compression and decompression algorithms operate on ordinary 2D arrays, and are thus ideally suited for hardware acceleration. In this paper, we detail two wavelet-based approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes.