quick-vertex

Plot feasible regions of two-variable linear programs in Typst,
drawn with CeTZ. One call gives you the
shaded region, the boundary lines, the vertices, the objective's level lines and
gradient, and a vertex table with the optimum highlighted.

It is built for teaching (secondary school / early undergraduate), and it handles
the cases a synthetic example set usually forgets: unbounded regions, multiple
optima, unbounded objectives, empty regions, strict inequalities and any quadrant.

Usage

#import "@preview/quick-vertex:0.1.1": feasible-region

#feasible-region(
  ((1, 1, 4, "<="), (1, 3, 6, "<=")),
  objective: (3, 4),
  sense: "max",
  labels: ($x + y = 4$, $x + 3y = 6$),
)
// → Optimum (max): Z = 13 at C(3, 1)

This is exactly the first image in the gallery above.

Each constraint is a 4-tuple (a, b, c, op) meaning a·x + b·y op c, where
op is one of "<=", ">=", "<", ">". The objective is Z = c1·x + c2·y,
given as (c1, c2).

Parameters

Parameter	Default	Meaning
constraints	(required)	Array of (a, b, c, op). op ∈ "<=", ">=", "<", ">". An optional 5th element sets that line's color: (a, b, c, op, color).
objective	none	(c1, c2) of Z = c1·x + c2·y. Omit to just draw the region. An optional 3rd element sets the objective color: (c1, c2, color).
sense	"max"	Optimization sense: "max" or "min".
gradient	true	Draw the ∇Z vector at the optimum.
table	true	Show the vertex table; if false, a compact vertex legend.
first-quadrant	true	Add x ≥ 0, y ≥ 0 implicitly. See the note below.
labels	none	Line equations (content), in the order of constraints.
lang	"en"	Language of the rendered labels: "en" or "es".
region-color	blue	Fill / hatch / border color of the feasible region.
size	(6, 4.5)	Canvas size, in CeTZ units — with equal-aspect: true, an upper bound: the drawn extent shrinks in whichever dimension isn't the tightest fit.
margin	1.15	Padding factor around the region.
equal-aspect	true	Both axes use the same units-per-length scale (textbook square-grid convention; both axes also share one tick step). false stretches each axis independently to fill size exactly, with its own tick step — ∇Z stays perpendicular to the level lines either way.

⚠️ first-quadrant is true by default, so x ≥ 0 and y ≥ 0 are added
automatically (the usual assumption in school problems). Pass
first-quadrant: false to draw only the constraints you write — for example
when the region lives in another quadrant.

Note on two "senses". The 4th tuple element is the inequality operator
("<=", …). The sense parameter is the optimization sense ("max"/"min").
They are unrelated.

Colors

Every boundary line gets a distinct color automatically — a curated palette
first, then generated hues — so colors never repeat, no matter how many
constraints you add. Override any of them explicitly:

#feasible-region(
  (
    (1, 1, 4, "<=", red),          // this line in red
    (1, 3, 6, "<="),               // auto color
  ),
  objective: (3, 4, olive),        // objective, optimum and ∇Z in olive
  region-color: rgb("#2b8a3e"),    // the feasible region in green
)

What it handles

Case	Behavior
Bounded region	Filled + hatched polygon.
Unbounded region	Filled correctly; arrows on the open sides + an "unbounded" note.
Unique optimum	Highlighted vertex, optimal level line, ∇Z, table with the optimal row marked.
Multiple optima	Detects the tie between adjacent vertices; highlights the segment (or ray) and labels it.
Unbounded objective	Detects that no finite max/min exists and says so, instead of inventing a vertex.
Empty region	Labels "Infeasible region".
Strict inequalities (<, >)	Correct region + dashed boundary.
Any quadrant	first-quadrant: false works (frame, axes and ticks with negatives).

Localization

Rendered labels default to English. Pass lang: "es" for Spanish. Adding a
language is a matter of copying one block in the _i18n dictionary in lib.typ
and translating it — contributions welcome.

How it works

The shading is obtained by clipping the visible frame against each half-plane
(Sutherland–Hodgman), so open regions fill correctly whether bounded or not. A
recession-cone sample decides whether the region is unbounded, extends the frame
towards where it escapes, and detects when the objective has no finite optimum.

Compatibility

• Typst >= 0.14.0
• CeTZ 0.5.2

Known limitations

See ROADMAP.md. In short: a couple of cosmetic issues (a vertex
label can still land on an axis tick; zero-area regions) and two rare semantic
edge cases (a strict inequality binding the optimum; more than two vertices
tied in Z). None affect ordinary textbook problems.

License

MIT.