Kyzis 3D Engine: A Geometry Based on Local Dimensions

Introduction A three-dimensional environment can be envisioned differently from a uniform space in which all objects are subject to the same fixed axes. A shape has its own geometry, its own surfaces and its own orientations. The Kyzis 3D engine starts from this principle: the geometry of each object defines its dimensional frame of reference. Dimensions are therefore not merely global axes used to position objects. They can be associated directly with their shape. A surface thus constitutes a two-dimensional space that can be curved, closed or deformed. Its local directions evolve with its geometry and with the point under consideration. A sphere provides a simple example. Its surface can be regarded as two dimensions folded around its volume. When an object moves across this surface, its motion can be determined relative to the local directions beneath it rather than solely relative to the general axes of the environment. The same principle becomes particularly interesting with complex shapes. A human body, for example, has arms, legs, a torso, a head and joints whose orientations differ. The bones can serve as reference structures for the movement of the limbs, while the surface of the body has its own dimensional continuity. A fly walking on a body naturally illustrates this approach. Moving from the forearm to the elbow, then to the arm and the shoulder, it follows a surface whose orientation changes continuously. Its frame of reference for movement can adapt to the local geometry it encounters. The notion of surface then becomes directly tied to movement and collision. Collision textures can also be associated with this geometry, making it possible to define the physical properties of different regions of a single surface. The geometric shape is not limited to a primitive such as a cube or a sphere: it can represent any structure, however irregular and complex it may be. The Kyzis 3D engine thus rests on a fundamental idea: Geometry defines the local dimensions of the object, and interactions appear when the dimensional frames of reference of several geometries come into relation. This approach opens the way to an engine in which surfaces, movements, joints and collisions are described from the objects' own geometry rather than from a single dimensional frame of reference imposed on the entire environment.