Abstract: The present invention provides systems, methods, and computer readable media for manipulating and formatting data sets (e.g., 105, 106) described using different coordinate systems. One version of the invention provides a method for formatting data sets described using different coordinate systems into a single format (136). The method includes the steps of a) acquiring (310) a first coordinate system data set, b) formatting (320) the first coordinate system data set into non-Cartesian representation (NCR) format (136), and c) storing (330) the resulting formatted data sets in NCR format. The method can further include the step of acquiring a second coordinate system data set and formatting the second coordinate system data set in NCR format.

Abstract: A method and an apparatus capable of realizing at a high speed an elliptic curve cryptography in a finite field of characteristic 2, in which the elliptic curve is given by y2+xy=x3+ax2+b (b?0) and an elliptic curve cryptography method which can protect private key information against leaking from deviation information of processing time to thereby defend a cipher text against a timing attack and a differential power analysis attack are provided. To this end, an arithmetic process for executing scalar multiplication arithmetic d(x, y) a constant number of times per bit of the private key d is adopted. Further, for the scalar multiplication d(x, y), a random number k is generated upon transformation of the affine coordinates (x, y) to the projective coordinates for thereby effectuating the transformation (x, y)?[kx, ky, k] or alternatively (x, y)?[k2x, k3y, k]. Thus, object for the arithmetic is varied by the random number (k).

Abstract: A rectangular-to-polar-converter receives a complex input signal (having X0 and Y0 components) and determines an angle ? that represents the position of the complex signal in the complex plane. The rectangular-to polar-converter determines a coarse angle ?1 and a fine angle ?2, where ?=?1+?2. The coarse angle ?1 is obtained using a small arctangent table and a reciprocal table. These tables provide just enough precision such that the remaining fine angle ?2 is small enough to approximately equal its tangent value. Therefore the fine angle ?2 can be obtained without a look-up table, and the fine angle computations are consolidated into a few small multipliers, given a precision requirement. Applications of the rectangular-to-polar converter include symbol and carrier synchronization, including symbol synchronization for bursty transmissions of packet data systems. Other applications include any application requiring the rectangular-to-polar conversion of a complex input signal.

Abstract: A method for converting between source coordinates in a source coordinate system and target coordinates in a target coordinate system includes the step of defining a coordinate system conversion tree extending from a root coordinate system and branching to a plurality of other coordinate-systems including the source and target coordinate systems so that the source and target coordinate systems are connected to a common coordinate system other than the root coordinate system. Coordinate conversions are performed between the source and target coordinates along branches extending from the source coordinate system to the common coordinate system and to the target coordinate system without returning to the root coordinate system. Contextual data is associated with the coordinates to permit conversion to an adjacent coordinate system.

Abstract: Beginning with a successive commanded end-effector destination shift, the method of the invention, which includes a calculation corresponding to a special algorithm of inverse kinematics using the Jacobi Matrix in the control of a manipulator, effects an optimization of weighted criteria (energy criteria, acceleration criteria and reference-position criteria) in a real-time cycle while reliably maintaining all path limitations and resulting in an optimized acceleration behavior. The method of the invention can be used in interactive path guidance of a manipulator and/or as a modular component of a superordinate task, such as for force-control objectives.

Abstract: The present invention aims at providing a coordinate data converting method, which is adaptable to any coordinate data in different data formats, for converting coordinate data into predetermined coordinate data, and a device thereof. A conversion parameter master table (conversion PMT) is generated in a memory with a maintenance process (process ST1) in advance. In each conversion parameter table (conversion PT) of the conversion PMT, the data of 9 items such as a code format, data format, coordinate system, unit system, offset, flow direction, PCB size, data item, and special command specification are set in correspondence with diversified coordinate data of a CAD system, an NC system, etc. A suitable conversion PT is selected with a process S1; a conversion source file of CAD data, etc.

Abstract: An image data processing apparatus for adding a special effect to an input image data, which is provided with function data generating circuit for generating function data in accordance with positions of pixel data for each pixel data forming the image data, random number generating circuit for generating different random numbers for each pixel data, and output circuit for judging based on the function data and the random number data if the corresponding pixel data is valid data or invalid data, outputting the pixel data only when valid data.