NatHomC

NatHomC, short for Natural Homogeneous Coordinates, is a mathematical framework used in computer graphics and computational geometry to represent and manipulate geometric entities such as points, lines, and planes in a unified manner. It was introduced by Jean Ponce and others in the late 1990s as an alternative to traditional homogeneous coordinates, which are widely used in projective geometry.

In NatHomC, geometric entities are represented as vectors in a higher-dimensional space, where the additional dimensions encode the type of the entity (e.g., point, line, plane). This allows for a more intuitive and consistent representation of geometric relationships, as well as simplifying the implementation of geometric algorithms.

One of the key advantages of NatHomC is its ability to handle geometric entities of different types in a uniform manner. For example, the intersection of a line and a plane can be computed using the same operations as the intersection of two lines, without the need for case-specific handling. This makes NatHomC particularly well-suited for applications that involve complex geometric computations, such as computer-aided design, robotics, and computer vision.

NatHomC has been successfully applied in various domains, including the computation of geometric invariants, the estimation of geometric models from data, and the design of geometric algorithms. Its unified and consistent representation of geometric entities has made it a popular choice among researchers and practitioners in the field of computational geometry.