Abstract: Described are a method and system for describing a position of an entity in a three-dimensional coordinate system with respect to the reference model. The reference model is of a three-dimensional curved surface defined in the three-dimensional coordinate system. The three-dimensional curved surface is divided into a set of cells. Each cell is a subset of the three-dimensional curved surface and has a curved surface. A three-dimensional curvilinear coordinate system is defined for each cell in the set of cells. The three-dimensional curvilinear coordinate system for each cell has a curvilinear axis that extends along the curved surface of that cell.

Abstract: Described are a method and system for describing a position of an entity in a three-dimensional coordinate system with respect to the reference model. The reference model is of a three-dimensional curved surface defined in the three-dimensional coordinate system. The three-dimensional curved surface is divided into a set of cells. Each cell is a subset of the three-dimensional curved surface and has a curved surface. A three-dimensional curvilinear coordinate system is defined for each cellin the set of cells. The three-dimensional curvilinear coordinate system for each cell has a curvilinear axis that extends along the curved surface of that cell.

Abstract: Novel methods for converting coordinates for a position from a first coordinate system into coordinates in a second coordinate system are provided. Linear approximations of trigonometric functions are used to calculate values for the trigonometric functions when a position to be converted is within an acceptable bound of a previous position and more precise values of the trigonometric functions are used to perform the conversion when the position to be converted is not within an acceptable bound of a previous position. The present invention can be advantageously utilized to reduce the computation load in a distributed simulation environment, such as a federation of distributed interactive simulations.

Abstract: Novel methods for converting coordinates for a position from a first coordinate system into coordinates in a second coordinate system are provided. Linear approximations of trigonometric functions are used to calculate values for the trigonometric functions when a position to be converted is within an acceptable bound of a previous position and more precise values of the trigonometric functions are used to perform the conversion when the position to be converted is not within an acceptable bound of a previous position. The present invention can be advantageously utilized to reduce the computation load in a distributed simulation environment, such as a federation of distributed interactive simulations.

Abstract: Described are a method and system for describing a position of an entity in a three-dimensional coordinate system with respect to the reference model. The reference model is of a three-dimensional curved surface defined in the three-dimensional coordinate system. The three-dimensional curved surface is divided into a set of cells. Each cell is a subset of the three-dimensional curved surface and has a curved surface. A three-dimensional curvilinear coordinate system is defined for each cell in the set of cells. The three-dimensional curvilinear coordinate system for each cell has a curvilinear axis that extends along the curved surface of that cell.