EllipsoidalReflectorSpotlights

EllipsoidalRef is a term used in geodesy and computer graphics to denote a reference framework and associated tools that describe and manipulate ellipsoidal shapes. An ellipsoidal reference frame models a three-dimensional ellipsoid with semi-axes a, b, and c and provides a set of coordinate systems and transformations for points on or near the surface. It is commonly used to approximate the shape of the Earth in Earth-centered, Earth-fixed coordinates, and to support conversions between geodetic coordinates (latitude, longitude, height) and Cartesian coordinates (X, Y, Z).

The mathematical model uses the ellipsoid equation x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. For Earth applications, a typical model is the WGS84 ellipsoid, with specific values for a and flattening f; standard references define the prime vertical radius of curvature and the meridional radius, and the formulas may include iterative methods to solve for latitude in the inverse problem. The framework emphasizes the distinction between geocentric (ECEF) and geodetic coordinates.

Implementations of EllipsoidalRef may include operations such as converting between coordinate systems, computing surface normals, sampling points on the ellipsoid, generating tangent planes, and evaluating distances from external points to the ellipsoidal surface. In graphics, ellipsoids are used for smooth shading and collision detection; in geodesy, they underpin mapping projections and GNSS data processing. Software tools adopting EllipsoidalRef concepts typically provide forward and inverse transformations, coordinate validation, and error handling related to ellipsoidal geometry.

Because Earth is not a perfect ellipsoid, real systems often use a reference ellipsoid plus a geoid or a grid-based model to account for local height variations. EllipsoidalRef concepts emphasize the distinction between geocentric and geodetic coordinates and the care needed when applying ellipsoidal geometry to measurements and visualizations.