Abstract: Two methods are provided for the automated derivation of Voronoi diagrams in 3D. The invention, implementable via various means such as a processing system, method, or data structure in a recording medium such as memory or as a self-contained electronic circuit, has wide ranging applicability to numerous fields such as big data analysis, computer graphics and animation, route planning, collision avoidance, computer vision, robotic vision, and etc. The first method of the invention details steps necessary to segment data according to a set of generators so as to produce a Voronoi partitioning of the data. The second method of the invention includes steps associated with the derivation of the mathematical specification of a 3D Voronoi diagram.

Abstract: A method is provided for the automated identification of real world objects. The invention, implementable via various means such as a processing system, method, or data structure in a recording medium such as memory or as a self-contained electronic circuit, has wide ranging applicability to numerous fields such as in a user interface for gaming systems, like Kinect, or immersive environments such as remote surgical operations, and other medical diagnostic applications. Similarly, our method can be utilized in artificial intelligence application for automated robotic identification of targets, such as drone assisted search and rescue missions, and the enablement of patent protection against unlawful replication on 3D printers.

Abstract: Three novel methods are provided which are valuable for the field of Delaunay tessellation derivation. The invention, implementable via various means such a digital processing system or an electronic circuit, has wide ranging applicability to numerous fields such as big data analysis, computer graphics and animation, mute planning, collision avoidance, computer vision, robotic vision, and etc. The first method of the invention details steps necessary to insert information into a data structuring in O(log n) while simultaneously retrieving sorted information relevant to the newly inserted information in O(1) time. The second method of the invention details and improvement to the Bowyer-Watson method that brings its runtime down to a tight O(n log n). The third method of the invention details steps necessary to compute the Delaunay tessellation of a set of line segment generators in k in O(n log n) time.

Abstract: Two methods are provided for the automated derivation of Voronoi diagrams in 3D. The invention, implementable via various means such as a processing system, method, or data structure in a recording medium such as memory or as a self-contained electronic circuit, has wide ranging applicability to numerous fields such as big data analysis, computer graphics and animation, route planning, collision avoidance, computer vision, robotic vision, and etc. The first method of the invention details steps necessary to segment data according to a set of generators so as to produce a Voronoi partitioning of the data. The second method of the invention includes steps associated with the derivation of the mathematical specification of a 3D Voronoi diagram.

Abstract: A method is provided for the automated identification of real world objects. The invention, implementable via various means such as a processing system, method, or data structure in a recording medium such as memory or as a self-contained electronic circuit, has wide ranging applicability to numerous fields such as in a user interface for gaming systems, like Kinect, or immersive environments such as remote surgical operations, and other medical diagnostic applications. Similarly, our method can be utilized in artificial intelligence application for automated robotic identification of targets, such as drone assisted search and rescue missions, and the enablement of patent protection against unlawful replication on 3D printers.