Adaptive Geometric Contouring for Vertex-Minimized Concave Hulls

The patent changes the fundamental parameters of contour generation by using a deterministic approach that evaluates multiple candidate edges at each vertex and selects the optimal edge based on geometric criteria. This transforms the approximate nature of conventional algorithms into a precise method that maintains region integrity while still achieving computational efficiency through systematic edge evaluation and selection.

The patent introduces dynamic edge selection where the contour edges are not fixed in advance but are determined adaptively during the algorithm execution. At each vertex, the algorithm dynamically evaluates multiple candidate edges and selects the best one based on geometric properties, allowing the contour to adapt to the actual shape features while maintaining efficiency.

The patent replaces the approximate mechanical sampling approach with a deterministic geometric system. Instead of using rough approximations that sacrifice data integrity, the system systematically evaluates geometric properties of candidate edges using precise mathematical criteria, substituting the approximate mechanical process with a rigorous geometric computation that preserves data integrity.

The patent incorporates feedback mechanisms where the algorithm continuously evaluates the geometric properties of candidate edges and uses this information to make informed selection decisions. The feedback from geometric evaluations (such as angle measurements, edge lengths, and region containment checks) guides the edge selection process to maintain both accuracy and efficiency.

The patent performs preliminary geometric evaluations of candidate edges before finalizing the contour. By pre-evaluating the geometric properties and selecting edges that satisfy specific criteria, the algorithm ensures that the resulting vertex-minimized contour maintains high accuracy. This preliminary action prevents the need for subsequent corrections and preserves contour fidelity.

The patent segments the contour generation process into distinct stages: identifying candidate edges, evaluating their geometric properties, selecting optimal edges, and constructing the final contour. This segmentation allows each stage to be optimized independently, ensuring that vertex minimization does not compromise overall contour accuracy while maintaining compression efficiency.