Abstract: A system and method for dramatically reducing the number of vertices defining a polygon on a grid, without significantly changing its effective enclosed area is disclosed. A smoothing process is executed on any general purpose computer system to operate on one or more representations of one or more curves. Each of the curves has a set of a plurality of vertices. The smoothing process first selects a first vertex, a third vertex, and a second middle vertex, the first, second, and third vertices being sequential but not necessarily consecutive on the curve. Then the smoothing process determines the area of a triangle formed by the first, second, and third vertices. This triangular area is compared to a threshold area. If the area is less than the threshold, new vertices are selected along the curve and the process is repeated. However if the area of the triangle is greater than or equal to the threshold, the second (middle) vertex is marked as an important vertex before a new set of vertices is selected.

Abstract: Visually analyzing, selecting, manipulating, displaying, and exploring relationships among variables in data bases with a large number of variables is enables by visualization of pictorial presentations, usually scatter plots. Each scatter plot shows the relationship among some subset of variables in the database. The scatter plots are mutually coupled to one another so that any mathematical transformation of an independent variable in one plot causes changes in other plots with dependent variables according to the relationship between the changed independent variable and the dependent variable. The mutual coupling also applies to color selection and performing logical operations with color on the plots. The plots can access other subsidiary presentations by using specified access criteria. Subsidiary presentations also can access other presentations. All presentations are mutually coupled.

Abstract: A rule based system and method interacts with a user to provide the user a series of interim results. The system has a set of one or more operations. Each of these operations in turn has a set of one or more choices, called a choice set, associated with an operation. Rule based intelligence is applied to the operations set and/or one or more operation choice set by a set of rules associated with its respective operation and/or choice set. When one or more rules in a rule set are applied to the operation set, an offered operation set is created which is a subset of the operation set. Only the operations in the offered operation set are offered to the user. When one or more rules in a rule set are applied to a choice set, an offered choice set is created which is a subset of the choice set. Only those operation choices in the offered choice set are offered to the user.