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ParametricPlot

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

ParametricPlot[{fx, fy}, {t, tmin, tmax}, opts...]

Adaptively samples the parametric curve (fx(t), fy(t)) over [tmin, tmax] and returns a Graphics[...] object (auto-displayed). The body may be any expression that evaluates to a 2-element {x,y} list (not just a literal {fx,fy}). Multiple curves: ParametricPlot[{{fx1,fy1}, ...}, {t,...}]. Two-iterator (filled region) form: ParametricPlot[body, {t,...}, {r,...}] samples a PlotPoints x PlotPoints grid and emits Polygon[] quads. Default AspectRatio -> 1 (both axes equally important). Options: PlotPoints (default 25), MaxRecursion (default 6), MaxPlotPoints, Mesh (All: dots for curves, grid lines for regions), PlotLegends (Automatic/"Expressions"/{labels...}: draws a legend), ColorFunction ("Rainbow" or f[t] / f[t,r]), ColorFunctionScaling (default True), RegionFunction (f[x,y] mask), PlotStyle, AspectRatio, Axes, PlotRange, PlotRangePadding, AxesLabel, AxesOrigin, Frame, FrameLabel, GridLines, Prolog, Epilog, PlotLabel, Background, ImageSize (all passed through to Graphics).

Examples (9)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (6)

In[1]:= ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2 Pi}]
Out[1]= -Graphics-

In[2]:= ParametricPlot[{Sin[2 t], Sin[3 t]}, {t, 0, 2 Pi}]
Out[2]= -Graphics-

In[3]:= ParametricPlot[{{Cos[t], Sin[t]}, {2 Cos[t], Sin[t]}}, {t, 0, 2 Pi}]
Out[3]= -Graphics-

In[4]:= ParametricPlot[2 {Cos[t], Sin[t]}, {t, 0, 2 Pi}]
Out[4]= -Graphics-

In[5]:= ParametricPlot[{r Cos[t], r Sin[t]}, {t, 0, 2 Pi}, {r, 1, 2}]
Out[5]= -Graphics-

In[6]:= ParametricPlot[r^2 {Sqrt[t] Cos[t], Sin[t]}, {t, 0, 3 Pi/2}, {r, 1, 2}]
Out[6]= -Graphics-

Options (3)

In[7]:= ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2 Pi}, ColorFunction -> (Hue[#] &)]
Out[7]= -Graphics-

In[8]:= ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2 Pi}, RegionFunction -> Function[{x, y}, x > 0]]
Out[8]= -Graphics-

In[9]:= ParametricPlot[{r Cos[t], r Sin[t]}, {t, 0, 2 Pi}, {r, 1, 2}, Mesh -> All]
Out[9]= -Graphics-

Algorithm

parametricplot.c — ParametricPlot[body, {t, tmin, tmax}, opts...]

                 — ParametricPlot[body, {t, tmin, tmax}, {r, rmin, rmax}, opts...]

HoldAll: the body and all iterator specs are unevaluated when received.

One-iterator form:

  body must evaluate to {x, y} for each t. Single body or
  {body1, body2,...} (list of bodies) for multi-curve.
  Adaptive 2D sampling with a Euclidean chord-deviation flatness test.
  Output: Graphics[{Line[...], ...}, opts].

Two-iterator form:

  body evaluates to {x, y} for each (t, r) pair.
  Samples a PlotPoints x PlotPoints grid and builds Polygon[] quads,
  like Plot3D but mapped back into the xy-plane.
  Output: Graphics[{Polygon[...], ...}, opts].

In both forms the body can be any expression that evaluates to a 2-element numeric list: a literal {fx, fy}, or a computed form such as r^2 * {Sqrt[t] Cos[t], Sin[t]}, as long as the result has head List and exactly two finite-real elements.

Implementation notes

Attributes: HoldAll, Protected.

References

See also: HoldAll