Universe

A comprehensive Euclidean geometry package for Typst, inspired by the LaTeX tkz-euclide package.

Note: This package is a port of the LaTeX tkz-euclide package. We are deeply grateful to Alain Matthes for creating the original tkz-euclide package, without which this Typst port would have been impossible. This package is will try to implement the complete set of features of the tkz-euclide package, we are not there yet.

Development Note: This package was coded entirely by Claude Code Opus 4.5 and Codex. Nevertheless, I have spent lots of time and energy in the following feedback look : prompting, reviewing, testing and designing. Any mistakes or bugs are my own.

⚠️ Early Development Status

This package is by no means definitive. Improvements and features are planned and will be implemented over time. The API may change as the package evolves.

This package is being developed. Expect:

  • Bug fixes and improvements
  • New features and triangle centers
  • API refinements
  • Performance optimizations

Dependencies

Changelog

0.1.0

  • Initial public release
  • Core Euclidean constructions, transformations, intersections
  • Drawing utilities with unified ctz-draw
  • Conics, parabola helpers, and inversion features
  • Manual PDF and gallery examples

Click on an image to see the source code.

Triangle Centers
Triangle Centers 		Nine-Point Circle
Nine-Point Circle 		Regular Pentagon
Regular Pentagon
Inscribed Angle
Inscribed Angle 		Apollonius Circle
Apollonius Circle 		Orthocenter
Orthocenter
Equilateral Triangle
Equilateral Triangle 		Perpendicular Bisectors
Perpendicular Bisectors 		Thales' Theorem
Thales' Theorem
Inversion
Inversion 		Inversion Packing
Inversion Packing 		Inversion Ladder
Inversion Ladder

Documentation

📖 Complete Manual (PDF) - Comprehensive documentation with examples and gallery

The manual includes:

  • Detailed API reference for all functions
  • Step-by-step examples and tutorials
  • Gallery of advanced geometric constructions
  • Complete feature overview

Deploy Checklist

  1. Switch docs to local imports and compile:
./scripts/use-local-docs.sh
typst compile docs/manual.typ docs/manual.pdf
  1. Rebuild gallery images locally:
for f in gallery/*.typ; do
  typst compile "$f" "${f%.typ}.png"
done
  1. Switch docs/tests back to preview imports for publishing:
./scripts/use-preview-package.sh
find gallery -name "*.typ" -type f -exec sed -i 's|@local/ctz-euclide:0.1.0|@preview/ctz-euclide:0.1.0|g' {} \;

Contributions Welcome

Contributions, bug reports, feature requests, and feedback are warmly welcomed! Please feel free to:

  • Open issues on the repository
  • Submit pull requests
  • Share examples and use cases
  • Report bugs or suggest improvements

Quick Start

#import "@preview/ctz-euclide:0.1.0": *

#ctz-canvas({
  import cetz.draw: *

  ctz-init()
  ctz-style(point: (shape: "cross", size: 0.1, stroke: black + 1.5pt))

  // Define points
  ctz-def-points(A: (0, 0), B: (4, 0), C: (2, 3))

  // Draw triangle
  ctz-draw-line("A", "B", "C", "A", stroke: black)

  // Mark points and add labels
  ctz-draw-points("A", "B", "C")
  ctz-draw-labels("A", "B", "C",
    A: "below left", B: "below right", C: "above")

  // Mark an angle
  ctz-draw-angle("A", "B", "C", label: $alpha$, radius: 0.5)
})

Naming notes:

  • All public functions are prefixed with ctz- to avoid conflicts.
  • Point creation and drawing use ctz-def-points and ctz-draw-points.
  • Other constructors use ctz-def-*, and drawing utilities use ctz-draw-*.

Features

  • Point Constructions: Define points by coordinates, transformations, intersections
  • Transformations: Rotation, reflection, translation, scaling, projection
  • Intersections: Line-line, line-circle, circle-circle
  • Triangle Centers: Centroid, circumcenter, incenter, orthocenter, and many more
  • Special Triangles: Medial, orthic, intouch triangles, Thales’ triangle
  • Drawing: Points, lines, angles, circles, arcs
  • Inversion: Invert points and objects about a circle
  • Conics: Ellipses and parabolas, including focus/directrix and focus/parameter forms
  • Parabolas: Directrix helpers, tangents, and projectile trajectories
  • Projections: Point projections and descriptive-geometry helpers
  • Unified Drawing: ctz-draw() works with any object type (points, lines, circles, polygons)
  • Object Duplication: ctz-duplicate() duplicates any geometric object
  • Angle Marking: With customizable labels and positioning
  • Point Styles: Multiple marker types (cross, dot, circle, plus, etc.)

Basic Features

Point Definition

// Define points
ctz-def-points(A: (0, 0), B: (3, 0), C: (1.5, 2.5))

Transformations

// Rotation
ctz-def-rotation("B", "A", "O", 60)  // Rotate A around O by 60°

// Reflection
ctz-def-reflect("C", "A", "P", "Q")  // Reflect A across line PQ

// Translation
ctz-def-translate("D", "A", (2, 3))  // Translate A by vector (2, 3)

Intersections

// Line-line intersection
ctz-def-ll("E", ("A", "B"), ("C", "D"))

// Line-circle intersection
ctz-def-lc(("F", "G"), ("A", "B"), ("O", "P"))

// Circle-circle intersection
ctz-def-cc(("H", "I"), ("O1", "P1"), ("O2", "P2"))

Triangle Centers

// Centroid
ctz-def-centroid("G", "A", "B", "C")

// Circumcenter
ctz-def-circumcenter("O", "A", "B", "C")

// Incenter
ctz-def-incenter("I", "A", "B", "C")

// Orthocenter
ctz-def-orthocenter("H", "A", "B", "C")

Drawing

// Draw points
ctz-draw-points("A", "B", "C")

// Add labels
ctz-draw-labels("A", "B", "C",
  A: "below left", B: "below right", C: "above")

// Mark angles
ctz-draw-angle("B", "A", "C", label: $alpha$, radius: 0.6)

Paths and Arrows

// TikZ-like per-segment tips
ctz-draw-path("A--B->C|-|D", stroke: black)

Supported connectors: --, ->, <-, <->, |-|, |->, <-|. By default, points (small dots) and labels (below) are drawn. Override with {...} in the path: "A{below}--B{below}->C{above}|-|D{below}". You can customize point appearance with point-style and point-color, or disable with points: false.

Segment Measurements

ctz-draw-measure-segment("A", "B", label: $5$, offset: 0.3, side: "left")

Advanced Features

The package includes many advanced features:

  • Extended triangle centers (Euler, Lemoine, Nagel, Gergonne, Spieker, Feuerbach, etc.)
  • Special triangle constructions (medial, orthic, intouch, excentral, tangential)
  • Thales’ Triangle: ctz-def-thales-triangle() creates right triangles inscribed in circles
  • Circle operations (tangents, radical axis, Apollonius circles)
  • Point constructions (midpoint, golden ratio, barycentric coordinates)
  • Geometric transformations (symmetry, inversion)
  • Polymorphic Transformations: ctz-def-rotation() works on all object types (points, lines, circles, polygons)
  • Drawing utilities (polygons, segments, arcs, sectors)
  • Marking utilities (segment marks, right angles, angle fills)

See the complete documentation for details on all features.

Acknowledgments

This package is a port of the LaTeX tkz-euclide package created by Alain Matthes. The original tkz-euclide package has been an invaluable resource for geometric constructions in LaTeX, and this port aims to bring similar functionality to the Typst ecosystem.

License

MIT License - see LICENSE file for details.

Changelog

[0.1.0] - 2026-01-21

Initial Release

  • Core geometric constructions (points, lines, circles)
  • Point transformations (rotation, reflection, translation, scaling)
  • Intersection algorithms (line-line, line-circle, circle-circle)
  • Basic triangle centers (centroid, circumcenter, incenter, orthocenter)
  • Extended triangle centers (Euler, Lemoine, Nagel, Gergonne, Spieker, etc.)
  • Special triangle constructions
  • Angle marking with customizable labels
  • Multiple point styles
  • Drawing utilities
  • Built on CeTZ v0.4.2