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VectorCalculus

 SpaceCurve
 plot a space curve in ${R}^{2}$ or ${R}^{3}$

 Calling Sequence SpaceCurve(C, r)

Parameters

 C - Vector(algebraic); the free or position Vector representing a curve r - name=range; the range of the parameter of the curve

Description

 • The SpaceCurve(C, t=a..b) calling sequence plots a space curve in ${R}^{2}$ or ${R}^{3}$. The plot is displayed in Cartesian coordinates.
 • Alternatively, a curve can be defined using a position Vector and it can be visualized with PlotPositionVector.

Examples

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$

The commands to create the plots in the Plotting Guide are

 > $\mathrm{SpaceCurve}\left(⟨{ⅇ}^{-t}\mathrm{cos}\left(t\right),{ⅇ}^{-t}\mathrm{sin}\left(t\right)⟩,t=4..8\right)$
 > $\mathrm{SpaceCurve}\left(⟨\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),t⟩,t=1..9\right)$

Other example

 > $\mathrm{SetCoordinates}\left({\mathrm{polar}}_{r,t}\right)$
 ${{\mathrm{polar}}}_{{r}{,}{t}}$ (1)
 > $\mathrm{SpaceCurve}\left(\mathrm{PositionVector}\left(\left[1,t\right]\right),t=0..2\mathrm{Pi}\right)$