Geometry.SetOperations

Set Operations of Polytopes. You can read about implementation details of this algorithm in a dedicated Blog Post.

Small example:

test :: SetOperation -> Double -> PolyT3D
test op t = fromVolume $ merge op boxA boxB
    where
    boxA = cube
    boxB = toVolume $ Poly3 (papply tr <$> ps) is
    Poly3 ps is = cubePoly3
    tr = translation (V3 (sin (t*0.3) * 0.3) 0.2 0.3)
       <> aboutX (t*20 @@ deg)
       <> aboutY (t*3  @@ deg)

Rendered:

Base Functionality

data Volume b v n

Volume, currently represented as a list of Facets and a BSP Tree.

emptyVolume :: Volume b v n

Empty volume.

toVolume :: (FromPolytopeRep p b v n, Clip b v n, Functor v, Num n) => p v n -> Volume b v n

Convert an arbitrary polytope boundary representation into a Volume.

fromVolume :: ToPolytopeRep p b v n => Volume b v n -> p v n

Recover a boundary representation of a Volume.

data SetOperation

Four basic set operations:

Constructors

Union

Intersection

Difference

SymmetricDifference

merge :: Merge b v n => SetOperation -> Volume b v n -> Volume b v n -> Volume b v n

Merge two Volumes under a specified Set Operation.

merges :: Merge b v n => SetOperation -> [Volume b v n] -> Volume b v n

Merges list of Volumes under a specified Set Operation. Empty list equals empty set.

Selected Merge Operations

union :: Merge b v n => Volume b v n -> Volume b v n -> Volume b v n

Union of two volumes. Convenience synonym for `merge Union`

unions :: Merge b v n => [Volume b v n] -> Volume b v n

Union of list of volumes.

intersection :: Merge b v n => Volume b v n -> Volume b v n -> Volume b v n

Intersection of two volumes.

intersections :: Merge b v n => [Volume b v n] -> Volume b v n

Intersection of list of volumes.

difference :: Merge b v n => Volume b v n -> Volume b v n -> Volume b v n

Difference between two volumes.

differences :: Merge b v n => Volume b v n -> [Volume b v n] -> Volume b v n

Subtract list of volumes from a given volume.

Conversion from/to BReps

class FromPolytopeRep p b v n

Convert from polytope to a list of Facets.

Minimal complete definition

fromPolytopeRep

Instances

(MakePlane v n, Eq (v n), Foldable v, Applicative v, R3 v, Num n, Ord n, EqZero n) => FromPolytopeRep Poly3 (FB3 v n) v n

Methods

fromPolytopeRep :: Poly3 v n -> [Facet (FB3 v n) v n]

class ToPolytopeRep p b v n

Convert from list of Facets to a polytope boundary representation.

Minimal complete definition

toPolytopeRep

Instances

ToPolytopeRep PolyT3 (FB3 v n) v n

Methods

toPolytopeRep :: [Facet (FB3 v n) v n] -> PolyT3 v n

data Poly3 v n

Indexed 3-BRep as a list of convex polygons. Continent as a way to introduce new base shapes into the constructive geometry context.

Constructors

Poly3 (Vector (Point v n)) [[Int]]

Instances

(MakePlane v n, Eq (v n), Foldable v, Applicative v, R3 v, Num n, Ord n, EqZero n) => FromPolytopeRep Poly3 (FB3 v n) v n

Methods

fromPolytopeRep :: Poly3 v n -> [Facet (FB3 v n) v n]

newtype PolyT3 v n

Simple direct 3-BRep as a list of triangles. Useful as an output after performing specified set operations of the base shapes for rendering.

Constructors

PolyT3 [[Point v n]]

Instances

ToPolytopeRep PolyT3 (FB3 v n) v n

Methods

toPolytopeRep :: [Facet (FB3 v n) v n] -> PolyT3 v n

Primitives

cubePoly3 :: Poly3D

Cube represented as a denormalized list of polygons.

cube :: Volume3D

Cube volume.

Specializations/Synonyms

toVolume3D :: Poly3D -> Volume3D

Convert a simple 3-BRep polyhedron to a Volume.

fromVolume3D :: Volume3D -> PolyT3D

Reconstruct a triangulated 3-BRep from a Volume.