A parametric curve is the image of a continuous map 
from an interval 
. In the plane it is written 
, while in space it is written 
. The parameterization is regular where
the tangent vector 
is nonzero. Different parameterizations can trace the
same geometric curve with different speeds or orientations.
Parametric Curve
See also
Parameterization, Parametric Equations, Parametric Surface, Tangent VectorExplore with Wolfram|Alpha
References
do Carmo, M. P. Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, 1976.Cite this as:
Weisstein, Eric W. "Parametric Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParametricCurve.html