Geodesic

A geodesic represents the shortest path between two points on a curved surface. Unlike a straight line on a flat plane, a geodesic follows the curvature of the surface. It's a locally straight line, meaning that at any point along the path, the curvature is minimized. This concept is crucial in fields like physics (general relativity), computer graphics, and surveying for calculating distances and trajectories on non-Euclidean spaces. Essentially, it signifies the most 'direct' route within a given geometric constraint.

Geodesic meaning with examples

• In navigation, a geodesic helps airplanes follow the most fuel-efficient route over the Earth's curved surface, accounting for its spherical shape. The flight path is a geodesic.
• When rendering a sphere in a video game, the light travels as a geodesic on the surface to accurately simulate shadows and reflections on the spherical surface.
• Researchers used geodesics in general relativity to study how massive objects distort spacetime and affect the paths of light and other objects within its vicinity.
• Surveyors use geodesic calculations to minimize error when creating large-scale maps. This accounts for the Earth’s curvature over large areas, by calculating the shortest path.