<notatio-polar-plot>

Parse a JSON attribute defensively -- an empty/invalid value reads as undefined. */ function parseJson(value: string): unknown { const text = value.trim(); if (!text) return undefined; try { return JSON.parse(text); } catch { return undefined; } }

const log = debug("polarplot");

const isNumber = (v: unknown): v is number => typeof v === "number" && Number.isFinite(v);

/** [[θ, r], ...] (or a bare [r, ...], indexed by sample) for ListPolarPlot. */ function toPolarPoints(data: unknown, t0: number, t1: number): PolarPoint[] | undefined { if (!Array.isArray(data) || data.length === 0) return undefined; if (data.every((p) => Array.isArray(p) && p.length >= 2 && p.every(isNumber))) return (data as number[][]).map(([theta, r]) => ({ theta, r })); if (data.every(isNumber)) { const n = data.length; return (data as number[]).map((r, i) => ({ theta: n > 1 ? t0 + ((t1 - t0) * i) / (n - 1) : t0, r, })); } return undefined; }

/** <notatio-polar-plot expr="1 + \cos(\theta)" trange="0,6.283"> -- a curve r(θ) on a polar grid (Wolfram's PolarPlot). expr is sampled at n angles across trange; poles (non-finite r) break the curve rather than joining branches. data gives ListPolarPlot: a JSON list of [θ, r] pairs, or bare radii spread evenly over trange.

Stories in the playground·packages/notatio-lit/src/notatio-polar-plot.ts· in Vue: <PolarPlot>

Attributes

Attribute	Type	Default	Notes
expr	string	""	The radius r(θ), in notatio.
tvar	string	""	The angle variable; defaults to the expression's first unknown, else theta.
trange	string	"0,6.283185307179586"	The angular sweep, as lo,hi in radians.
n	number	240	Sample count across the sweep.
max	number	0	Clamp the radial axis; 0 fits the samples.
axes	string	"true"	"false" hides the polar grid.
closed	string	"false"	Anything but "false" joins the last point back to the first.
filled	string	"false"	Anything but "false" shades the region the curve encloses.
markers	string	""	"false" hides the point markers on an explicit data list.
label	string	""	Caption drawn above the figure.
data	string	""	An explicit point list — [[θ,r],…] or bare radii — plotted instead of expr.