Non-geodesic

A non-geodesic refers to a path or trajectory that does not follow the shortest distance between two points within a given space, often in a curved or non-Euclidean geometry. Geodesics, the 'straightest' paths, minimize the distance between two points. A non-geodesic, in contrast, deviates from this optimal path, potentially due to external forces, the curvature of the space, or the method of travel. This concept is particularly relevant in fields like general relativity, where gravity bends spacetime, and in computer graphics where paths for light or objects might be non-geodesic to create realistic effects.

Non-geodesic meaning with examples

• In curved spacetime, a planet's orbit around a star is generally non-geodesic. Gravity warps the fabric of spacetime, so a straight path in three-dimensional space becomes curved, leading to a non-geodesic orbital path. The planet, in its movement, is following a trajectory dictated by the curvature of the geometry imposed by gravity.
• A ray of light travelling through a lens follows a non-geodesic path as it bends and refracts. The lens alters the light's original direction and therefore forces it away from the shortest path from the light source to a receiver. This deviation is central to the lens' function and enables optical effects.
• In a computer graphics rendering, a simulated object might move along a pre-defined, non-geodesic animation path rather than following a shortest distance. This would be to show a specific path. This non-geodesic trajectory allows for carefully controlled and visually compelling movements within the scene.
• An aircraft typically flies a non-geodesic path over the surface of the Earth when travelling long distances. Air currents, weather patterns, or restricted air spaces might require the airplane to take longer routes than a theoretical geodesic path would permit, optimizing fuel efficiency.