A cardioid
r = 1 + cos θ over the default full turn.
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<notatio-polar-plot expr="1 + Cos(theta)" />Polar Plot
A curve r(θ) on a polar grid (Wolfram's PolarPlot), rendered by <notatio-polar-plot>. The expression is compiled to a native function and sampled at n angles across trange; a pole (a non-finite radius) breaks the curve into subpaths rather than joining two branches with a spurious chord. A negative radius points the opposite way, as in Wolfram.
The plot area is square and centred, so angles are never sheared: a circle stays a circle regardless of the element's width.
Function curves
A four-petal rose
filled shades the enclosed region under the stroked curve. The petals that fall on a negative radius sweep out the opposite quadrants.
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<notatio-polar-plot expr="Cos(2 * theta)" filled label="r = cos 2θ" />An Archimedean spiral
trange takes θ well past a single turn; n raises the angular sampling to keep the outer windings smooth.
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<notatio-polar-plot expr="theta" trange="0,18.85" n="600" />A limaçon, without the grid
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<notatio-polar-plot expr="1 + 2 * Cos(theta)" axes="false" />List polar plots
data plots explicit points (Wolfram's ListPolarPlot) — either [θ, r] pairs, or bare radii spread evenly over trange.
Explicit (θ, r) pairs
closed joins the last point back to the first.
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<notatio-polar-plot data="[[0,1],[1.57,2],[3.14,1],[4.71,2]]" closed />Bare radii over a turn
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<notatio-polar-plot data="[1,1.5,2,1.5,1,1.5,2,1.5,1]" />Roadmap
- Angular tick labels (0, π/6, …) on the spokes.
- Several curves on one grid, à la
Plot's multi-expression form. Manipulate-style parameter sliders (params), matchingPlot/Plot3D.