Apexderived

Apexderived is a term used in geometry and data analysis to describe a family of descriptors and transformation methods that originate from apex points of a geometric object or from apex regions in a dataset. The core idea is to derive secondary structures or features by focusing on apex vertices or apex-like regions and summarizing their local geometry.

In practice, an apex-derived descriptor is computed by first identifying apex points, typically vertices with maximal distance from a reference plane, peak curvature, or sharpness. The local neighborhood consisting of incident edges and faces is then analyzed to compute measures such as angles between incident edges, dihedral angles with neighboring faces, ratios of adjacent edge lengths, and curvature estimates. These measures are often normalized and aggregated to form a descriptor vector that characterizes the apex region.

Applications include mesh simplification, feature detection, and object recognition in 3D models, as well as analysis of point clouds where apex-derived features help distinguish sharp features from smooth regions. Variants of apexderived include apex-derived graphs, in which a graph is constructed around apex points, and apex-derived feature sets used as input to machine learning models.

Example: in a pyramidal mesh, an apex-derived descriptor for the apex vertex may include the set of incident face angles, the ratio of the two longest incident edges, and a curvature score summarizing the local surface.

See also: apex, derivative, geometric descriptor, feature extraction.