Arcvédvel

Arcvédvel is a term used in trajectory analysis and computer graphics to denote the rate at which an object traverses a curved path as a function of time. It serves as a practical measure for comparing how quickly different parameterizations move along the same geometric arc, and for guiding adaptive sampling and control in curved motion.

In formal terms, for a particle following a trajectory r(t) with arc length s(t) = ∫0^t ||r'(τ)|| dτ, the instantaneous arcvédvel is AV(t) = ds/dt = ||r'(t)||, i.e., the speed along the curve. In many contexts, arcvédvel is normalized by a reference speed v_ref to yield a dimensionless factor AV*(t) = AV(t) / v_ref. This normalization allows practitioners to assess whether a path is followed at the intended pace regardless of the curve’s parameterization.

Applications include robotics path planning, animation, and virtual reality, where arcvédvel informs adapter algorithms that subdivide curves, allocate processing resources, or synchronize motion with other events. By focusing on arc-length progress rather than time alone, arcvédvel helps produce motion that respects the geometry of the path while maintaining a predictable pace.

Origin and usage: arcvédvel is a relatively niche term within specialized literatures and is not universally adopted. It is described as a neologism combining arc (curved path) and velocity. In practice, it remains a conceptual tool rather than a universally standardized quantity, with limitations arising from reparameterization and inconsistent references to v_ref.