bogenlängenparametrisierte
Bogenlängenparametrisierte, often translated as arc length parameterization, is a method in differential geometry and calculus of curves where a curve is described by a parameter that directly represents the distance along the curve from a fixed starting point. This means that the parameter value at any point on the curve is equal to the length of the curve from the origin to that point.
To obtain an arc length parameterized curve, one typically starts with a standard parameterization, denoted as
Once the arc length function $s(t)$ is determined, it is invertible, allowing us to express the original
A key advantage of arc length parameterization is that the magnitude of the velocity vector, $||\mathbf{r}'(s)||$,