To Approach Cylindrical Coordinates to Represent Multivariable Spatio-temporal Data

摘要

Data representing a moving object include the data of time, position, and attributes. The data of positions and attributes of a moving object, which change over time may be recorded asynchronously because of the difference of sampling methods. Mathematically, these data may be synchronized over time by space-time conversions to constitute the data tuples at various time moments. In this article, we proposed the concept of data plane to represent data according to each tuple at each time moment. Subsequently, we integrated the data planes into the dimensions of a cylindrical coordinate system to represent the movement of objects in a space-time cylinder (STCy). In a space-time cylinder, positions of moving objects are indicated on the data planes which are constituted by the cylinder axis employed as the cylindrical axis of the cylindrical coordinate system, and the polar vectors of the cylindrical coordinate system. Each data plane indicates the data of objects at a lime moment. The position of a moving object at a time moment is indicated by its coordinates on the data plane and the time moment by the angular coordinate of this plane. The attributes of moving objects are represented on data planes as the attribute bars parallel to the cylinder axis. The space-time path of a moving object surrounds the cylinder axis. Hence, the space-time cylinder is consistent with the representation of cyclic movements.