G1G2Glättung

G1G2Glättung, also known as G1G2 smoothing, is a technique used in computer graphics and signal processing to smooth out transitions between two separate segments or curves. The name "G1G2" refers to the continuity conditions that are met. G1 continuity ensures that the tangent vectors of the two segments are continuous at their joining point, meaning there's no abrupt change in direction. G2 continuity goes a step further by ensuring that the curvature of the two segments is also continuous at the join, resulting in a smoother, more aesthetically pleasing transition without sharp kinks.

This method is particularly useful when constructing freeform curves and surfaces where a high degree of smoothness is desired for visual quality or for functional reasons, such as in automotive design or animation. Implementing G1G2Glättung typically involves adjusting the control points or parameters of the curves in the vicinity of the join to satisfy the required continuity conditions. Different mathematical approaches can be employed, often involving solving systems of equations derived from the continuity constraints. The goal is to achieve a visually seamless blend that feels natural and avoids jarring visual artifacts.