Abstract: The present invention is a computer system and method for determining the closest point on a shape (2 dimensional or 3 dimensional surface) to any general query point. The system has one or more central processing units (CPUs), one or more memories, and one or more geometric model portions stored in one or more of the memories. The geometric model portions have a plurality of line segments (polygons), each of the line segments (polygons) being between a first and a second endpoint (having a polygon boundary). The line segments and end points (polygons and polygon boundaries) are connected to form a shape (in 3 dimensions, a surface) with one or more parameters. Parameters can include geometric position, time, temperature, pressure, flow, color, texture, or any other descriptive value. A multiresolution process that creates one or more models of the shape (surface). The models having a hierarchy of resolutions.

Abstract: A hand-held device has access to a three-dimensional geometry database and a GPS receiver, and provides information on the one or more closest features to the device location in the three-dimensional geometry database. The system has data input devices, optionally digital cameras, and a data processor executing a location process. A multiresolution process creates one or more models of the three-dimensional geometry database. The models have a hierarchy of resolutions. The models have vertices, edges and polygons. The multiresolution process preferably associates data to the vertices, edges and polygons. A data processor executes a location process that determines a distance between the position of the hand-held device and corresponding one or more closest features on the hierarchy of resolutions of the database. The data processor produces display commands for displaying data and geometry relative to the one or more closest features.

Abstract: A computer implemented representation and a method for encoding and decoding sequences of changes of a manifold triangular mesh. The representation is composed of a base manifold triangular mesh and a succession of specialized mesh surgery operations that may be of a different type. The methods encode or decode any sequence of mark, move, cut, delete, close, fill, or add operations. The mark operation specifies a type of mark and a set of marked elements. The move operation determines a set of displaced vertices from a set of marked elements, and applies a set of vertex displacements to the set of displaced vertices. The cut operation cuts the changing mesh through a set of marked edges. The close operation is applied to one or more boundaries that are determined when the type of mark is a boundary type, and the one or more boundaries are determined by a marked elements variable.