Adapting Game Engines to Curved Spaces

Abstract

Curved spaces are very un-intuitive to our eyes trained on Euclidean geometry. Games provide an interesting way to explore these strange worlds. Games are written with the help of modeling tools and game engines based on Euclidean geometry. This paper addresses the problem of adapting 3D game engines to the rules of curved spaces. We consider the conversion of Euclidean objects, geometric calculations, transformation pipeline, lighting and physical simulation. Finally, we identify where existing game engines should be modified.

Elliptic Quaternion and Elliptic linear Interpolation

“…Robot kinematics and computer games are covered extensively in Slerp notation. Especially in recent years, spherical interpolation and interpolations in Minkowski space and ellipsoid space have an important place in animation and modeling of robot movements in 3-dimensional computer games [12]. Also, interpolation between two rotations (slerp) is optimal.…”

“…But when interpolating between a number of rotations, the following issue appears: At the control points, the curve is not smooth. Smooth interpolation is used in computer animation to model motion solids, cameras, and lights [7,12]. The work done so far using quaternions has been interpolated on the Euclidean sphere, Lorentz and Hyperbolic spheres [4,11].…”

Elliptic Quaternion and Elliptic linear Interpolation

“…Especially in recent years, spherical interpolation and interpolations in Minkowski space and ellipsoid space have an important place in animation and modeling of robot movements in 3dimensional computer games [4]. Also, interpolation between two rotations (slerp) is optimal.…”