Abstract: A hierarchical 3D graphics model can be viewed as a hierarchical graph of its nodes and their associated motions, with the mathematical type of motions graphically indicated. A user can click on a displayed motion to edit it. A motion API provides one or more of the following features: (1) spatial predicate functions; (2) functions for scaling motion intensity; (3) classes for shake, spin, and swing motions; (4) motion classes with a GUI interfaced for defining their duty cycle; (5) functions for defining and computing 0th through 2nd order derivatives of 3D position and orientation as function of time; (6) behaviors that constrain motions by boundaries in which the constraint is a reflection, clamp, andor onto constraint, or in which the boundary is a composite boundary. Motions can be defined by successive calls to an API and then be saved in a file.

Abstract: The invention, in one embodiment, is directed to a system and related methods of data analysis. According to one aspect, the invention processes a plurality of records, each of the records having an associated plurality of attributes, the plurality of records being divisible into at least two categories. More particularly, the invention provides a multidimensional array having intersecting first and second axes; assigns each of the attributes as a one dimensional vector aligned along the first axis, and each of the records as a one dimensional vector aligned along the second axis; displays a graphical indication of an occurrence and/or a value of each attribute for each record at an intersection of each record vector with each attribute vector; and manipulates the record vectors and/or the attribute vectors to produce a graphical pattern representative of the at least two categories.

Abstract: The invention, in one embodiment, processes a plurality of records, each of the records having an associated plurality of attributes, the plurality of records being divisible into at least two categories. More particularly, the invention assigns as a class of one dimensional vectors the records and/or the attributes; employs an maximum number K of uncorrelated vectors to be identified from the class of one-dimensional vectors; employs a threshold value; chooses a first vector from the class of one-dimensional vectors as a member of an uncorrelated vector set; and performs iteratively the steps of selecting an additional vector from the class of vectors, computing a correlation parameter using the first vector and the additional vector, comparing the correlation parameter to the threshold value, and adding the additional vector to the uncorrelated set of vectors if the correlation parameter is not greater than the threshold value.