Geometric algebra method for multidimensionally-unified GIS computation

Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach

Geometric Algebra Model for Geometry-oriented Topological Relation Computation

Classical topological relation expressions and computations are primarily based on abstract algebra. In this article, the representation and computation of geometry-oriented topological relations (GOTR) are developed. GOTR is the integration of geometry and topology. The geometries are represented by blades, which contain both algebraic expressions and construction structures of the geometries ...

A Filter Method with Unified Step Computation for Nonlinear Optimization

We present a filter linesearch method for solving general nonlinear and nonconvex optimization problems. The method is of the filter variety, but uses a robust (always feasible) subproblem based on an exact penalty function to compute a search direction. This contrasts traditional filter methods that use a (separate) restoration phase designed to reduce infeasibility until a feasible subproblem...

A Unified Spatial Model for Gis

GIS (Geographic Information Systems) are concerned with the manipulation and analysis of spatial data at a “Geographic” scale. Apart from issues of storage, database query and visualization, they must deal with several significantly different types of spatial information. These may be roughly classified as: discrete objects; networks; polygonal maps; and surfaces. Each of these has a specific s...

An improved formalism for quantum computation based on geometric algebra - case study: Grover's search algorithm

The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is desirable to represent it in the simplest and most intuitive formalism possible. We show firstly, that Clifford’s geometric algebra, provides a significantly simpler representation than the conventional bra-ket notation, and secondly, that the basis defined by the states of maximum an...