A Parametric Curve is a function from an interval I mapping to Rn. We consider 2D plane curves and 3D space curves. As the parameter t varies in the interval I, the point with position vector x(t) traces out the curve.

The trace of a parametric curve is the image of the function x, and we can find this by evaluating x at some points in the domain. A curve that does not cross itself is called simple.

The Arc-Length map is the integral of |x(t)| from t0 to t.

The Velocity Vector or Tangent Vector is dx/dt = x'. If |x'| > 0 then the parametric curve is regular and we can define the unit tangent vector T = x' / |x'|.

Plane Curve - A plane curve is a parametric curve whose trace lies in R2.

Space Curve - A space curve is a parametric curve whose trace lies in R3.

Parametric curves can also be expressed using polar coordinates.

	Erstellt von katie.barclay vor mehr als 11 Jahre

Bachelor Degree Applied Maths (Parametric Curves) Notiz am Parametric Curves, erstellt von katie.barclay am 19/06/2015.