moonlight-triangulation

Part of Moonlight, the sheaf-theoretic computation layer beneath Melusine and Pale Meridian.

moonlight-triangulation carries Delaunay and constrained Delaunay triangulations as a lawful finite-set algebra under canonical observation: a mesh represents its site set, a join returns a valid Delaunay representative, and the result is a triangulation again — so the operations close, compose, and fold. Operations return typed obstructions where the finite arena cannot represent a result.

Delaunay triangulation, constrained Delaunay (CDT), exact rational planar regions and labelled overlay, intrinsic valuations, polygonal Minkowski morphology, the Voronoi dual, natural-neighbour interpolation, Ruppert refinement, walk point location, convex hull, exact Shewchuk predicates, and versioned binary serialization.

Persistence rose

Open the animation directly. · Open the static vector poster. · Read the exhibit guide.

Operations

Interpret cell sets as incidence categories. · Compute persistent alpha topology.

Foreign bindings

The C ABI and its Python, TypeScript, and Rust consumers are documented in the foreign-bindings guide. It owns construction, ABI versioning, lifecycle, obstruction semantics, and consumer examples.

Algebraic contract

union is idempotent; commutativity and associativity hold after canonicalize. Structural Eq is resident equality; use siteRelation for support comparison.

Set-operation types

union :: JoinSemilattice annotation
      => Triangulation 'Unconstrained annotation () () ()
      -> Triangulation 'Unconstrained annotation () () ()
      -> Either BuildError (Triangulation 'Unconstrained annotation () () ())

unions :: JoinSemilattice annotation
       => [Triangulation 'Unconstrained annotation () () ()]
       -> Either BuildError (Triangulation 'Unconstrained annotation () () ())

siteRelation
      :: Triangulation leftMode leftAnnotation leftDirected leftUndirected leftFace
      -> Triangulation rightMode rightAnnotation rightDirected rightUndirected rightFace
      -> SiteRelation

intersection
      :: Triangulation 'Unconstrained () () () ()
      -> Triangulation 'Unconstrained () () () ()
      -> Either BuildError (Triangulation 'Unconstrained () () () ())

intersectionWith
      :: (leftAnnotation -> rightAnnotation -> annotation)
      -> Triangulation 'Unconstrained leftAnnotation () () ()
      -> Triangulation 'Unconstrained rightAnnotation () () ()
      -> Either BuildError (Triangulation 'Unconstrained annotation () () ())

difference
      :: Triangulation 'Unconstrained leftAnnotation () () ()
      -> Triangulation 'Unconstrained rightAnnotation () () ()
      -> Either BuildError (Triangulation 'Unconstrained leftAnnotation () () ())

symmetricDifference
      :: Triangulation 'Unconstrained annotation () () ()
      -> Triangulation 'Unconstrained annotation () () ()
      -> Either BuildError (Triangulation 'Unconstrained annotation () () ())

Publication schedules and scale behavior.

Use

Use the main facade with explicit Vector inputs. Construction and set algebra retain their typed obstruction in Either:

build-depends:
  base >= 4.19 && < 5,
  moonlight-triangulation >= 1.4 && < 1.5,
  vector >= 0.13 && < 0.14

SetAlgebra.hs is the smallest compile-checked workflow. The example index adds constrained interiors, alpha-boundary descent, exact overlay and valuations, and polygonal morphology.

Architecture

The resident DCEL is immutable structure-of-arrays over paged copy-on-write storage; local mutation is sealed in ST. Half-edge twins are index complements. Exact predicates use bounded machine-word evaluation and fall through to aligned Integer arithmetic when required.

Consumer libraries

The Cabal manifest owns component visibility and dependencies; this is its consumer-facing projection. External packages normally use the main library and add only the public sublibraries whose modules they import. The finite DCEL and construction kernel remain private behind the main facade.

Build and validate package components locally.