The Kyzis 3D Engine 2.0

Introduction The Kyzis 3D Engine 2.0 proposes a different conceptual approach to the representation and interaction of objects within a three-dimensional environment. Its fundamental principle is to move beyond considering dimensions solely as global axes uniformly imposed on an entire scene, and instead to assign their own dimensional reference frames to objects, their surfaces, and their various structures. In this approach, geometry becomes directly functional. A dimension can represent a direction required to construct, measure, traverse, or transform a shape. These directions constitute the object's potential dimensions. Their number is not necessarily absolute: it depends on the geometric complexity being considered and on the level of resolution chosen to describe the object. A surface can also possess its own dimensions of movement. In the case of a ball, for example, its surface is described by two finite, curved dimensions that allow it to be traversed. These dimensions follow the geometry of the ball and remain attached to its reference frame. Curvature therefore becomes an essential property: a flexible two-dimensional surface can locally change its orientation and thereby produce a variable three-dimensional geometry. This principle leads to a new way of approaching collisions. When two objects meet, their contact is considered an interaction between two surface reference frames. Relative velocity, angle of incidence, local orientation, direction of curvature, and texture properties all contribute to the creation of a local collision reference frame. The surface can then curve up to a limit determined by the interaction, after which it can restore its deformation, producing a push and potentially a rebound. The texture is therefore no longer considered merely a visual element. It becomes a geometric surface capable of possessing properties of flexibility, curvature, collision, and restitution. A contact point can develop into a contact region, deform according to the dimensions of the surfaces involved, and then disappear when the objects separate. The Kyzis 3D Engine 2.0 therefore seeks to connect several elements that are usually treated separately: geometry, reference frames, surfaces, movement, deformation, and collision. Each object retains its geometric identity, while its interactions are determined locally by the dimensions actually involved in the phenomenon. This proposal opens the way to an engine in which objects are no longer merely positioned within a three-dimensional environment: they carry their own dimensional structures and transform them throughout their interactions. This document presents the foundations of this architecture, from the definition of potential dimensions and dimensional reference frames to collision mechanics and the first equations intended to formalize the operation of the system.