Safe Haskell	None
Language	Haskell2010

Data.Geometry.Properties

Synopsis

Documentation

type family Dimension t :: Nat Source

A type family for types that are associated with a dimension. The dimension is the dimension of the geometry they are embedded in.

Instances

type Dimension (Boundary g) = Dimension g Source
type Dimension (Image r) = 2 Source
type Dimension (IpeSymbol r) = 2 Source
type Dimension (MiniPage r) = 2 Source
type Dimension (TextLabel r) = 2 Source
type Dimension (PathSegment r) = 2 Source
type Dimension (Path r) = 2 Source
type Dimension (IpeObject r) = 2 Source
type Dimension (Group r) = 2 Source
type Dimension (Point d r) = d Source
type Dimension (Interval a r) = 1 Source
type Dimension (Line d r) = d Source
type Dimension (HalfLine d r) = d Source
type Dimension (Triangle p r) = 2 Source
type Dimension (Box d p r) = d Source
type Dimension (SubLine d p r) = d Source
type Dimension (LineSegment d p r) = d Source
type Dimension (PolyLine d p r) = d Source
type Dimension (Polygon t p r) = 2 Source	Polygons are per definition 2 dimensional
type Dimension (Ball d p r) = d Source

type family NumType t :: * Source

A type family for types that have an associated numeric type.

Instances

type NumType (Boundary g) = NumType g Source
type NumType (Image r) = r Source
type NumType (IpeSymbol r) = r Source
type NumType (MiniPage r) = r Source
type NumType (TextLabel r) = r Source
type NumType (PathSegment r) = r Source
type NumType (Path r) = r Source
type NumType (IpeObject r) = r Source
type NumType (Group r) = r Source
type NumType (Point d r) = r Source
type NumType (Transformation d r) = r Source
type NumType (Interval a r) = r Source
type NumType (Line d r) = r Source
type NumType (HalfLine d r) = r Source
type NumType (Triangle p r) = r Source
type NumType (Box d p r) = r Source
type NumType (SubLine d p r) = r Source
type NumType (LineSegment d p r) = r Source
type NumType (PolyLine d p r) = r Source
type NumType (Polygon t p r) = r Source
type NumType (Ball d p r) = r Source

data NoIntersection Source

A simple data type expressing that there are no intersections

Constructors

NoIntersection

Instances

Eq NoIntersection Source
Ord NoIntersection Source
Read NoIntersection Source
Show NoIntersection Source

type Intersection g h = CoRec Identity (IntersectionOf g h) Source

The result of interesecting two geometries is a CoRec,

type family IntersectionOf g h :: [*] Source

The type family specifying the list of possible result types of an intersection.

Instances

type IntersectionOf (Range a) (Range a) = (:) * NoIntersection ((:) * (Range a) ([] *)) Source
type IntersectionOf (Line 2 r) (Boundary (Rectangle p r)) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (Point 2 r, Point 2 r) ((:) * (LineSegment 2 () r) ([] *)))) Source
type IntersectionOf (Interval a r) (Interval a r) = (:) * NoIntersection ((:) * (Interval a r) ([] *)) Source
type IntersectionOf (Line 2 r) (Line 2 r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (Line 2 r) ([] *))) Source	The intersection of two lines is either: NoIntersection, a point or a line.
type IntersectionOf (Line 2 r) (Rectangle p r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 () r) ([] *))) Source
type IntersectionOf (Line 2 r) (Circle p r) = (:) * NoIntersection ((:) * (Touching (Point 2 r)) ((:) * (Point 2 r, Point 2 r) ([] *))) Source	No intersection, one touching point, or two points
type IntersectionOf (HalfLine 2 r) (HalfLine 2 r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 () r) ((:) * (HalfLine 2 r) ([] *)))) Source
type IntersectionOf (HalfLine 2 r) (Line 2 r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (HalfLine 2 r) ([] *))) Source
type IntersectionOf (Line 2 r) (Slab o a r) = (:) * NoIntersection ((:) * (Line 2 r) ((:) * (LineSegment 2 a r) ([] *))) Source
type IntersectionOf (HalfLine 2 r) (LineSegment 2 p r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 () r) ([] *))) Source
type IntersectionOf (LineSegment 2 p r) (Line 2 r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 p r) ([] *))) Source
type IntersectionOf (LineSegment 2 p r) (Circle q r) = (:) * NoIntersection ((:) * (Touching (Point 2 r)) ((:) * (Point 2 r) ((:) * (Point 2 r, Point 2 r) ([] *)))) Source	A line segment may not intersect a circle, touch it, or intersect it properly in one or two points.
type IntersectionOf (Box d p r) (Box d q r) = (:) * NoIntersection ((:) * (Box d () r) ([] *)) Source
type IntersectionOf (SubLine 2 p r) (SubLine 2 q r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (SubLine 2 p r) ([] *))) Source
type IntersectionOf (SubLine 2 p r) (Slab o a r) = (:) * NoIntersection ((:) * (SubLine 2 a r) ((:) * (LineSegment 2 a r) ([] *))) Source
type IntersectionOf (LineSegment 2 p r) (LineSegment 2 p r) = (:) * NoIntersection ((:) * (Point 2 r) ((:) * (LineSegment 2 p r) ([] *))) Source
type IntersectionOf (Slab o a r) (Slab o a r) = (:) * NoIntersection ((:) * (Slab o a r) ([] *)) Source
type IntersectionOf (Slab Horizontal a r) (Slab Vertical a r) = (:) * (Rectangle (a, a) r) ([] *) Source

coRec :: a ∈ as => a -> CoRec Identity as Source

Helper to produce a corec

class IsIntersectableWith g h where Source

Minimal complete definition

intersect, nonEmptyIntersection

Methods

intersect :: g -> h -> Intersection g h Source

intersects :: g -> h -> Bool Source

g intersects h = The intersection of g and h is non-empty.

The default implementation computes the intersection of g and h, and uses nonEmptyIntersection to determine if the intersection is non-empty.

nonEmptyIntersection :: proxy g -> proxy h -> Intersection g h -> Bool Source

Helper to implement intersects.

Instances

Ord a => IsIntersectableWith (Range a) (Range a) Source
Ord r => IsIntersectableWith (Interval a r) (Interval a r) Source
(Eq r, Fractional r) => IsIntersectableWith (Line 2 r) (Line 2 r) Source
(Ord r, Floating r) => IsIntersectableWith (Line 2 r) (Circle p r) Source
(Num r, Ord r) => IsIntersectableWith (Rectangle p r) (Rectangle p r) Source
(Fractional r, Ord r, HasBoundingLines o) => IsIntersectableWith (Line 2 r) (Slab o a r) Source
(Ord r, Fractional r) => IsIntersectableWith (LineSegment 2 p r) (Line 2 r) Source
(Ord r, Floating r) => IsIntersectableWith (LineSegment 2 p r) (Circle q r) Source
(Ord r, Fractional r) => IsIntersectableWith (SubLine 2 p r) (SubLine 2 p r) Source
(Fractional r, Ord r, HasBoundingLines o) => IsIntersectableWith (SubLine 2 a r) (Slab o a r) Source
(Ord r, Fractional r) => IsIntersectableWith (LineSegment 2 p r) (LineSegment 2 p r) Source
Ord r => IsIntersectableWith (Slab o a r) (Slab o a r) Source
IsIntersectableWith (Slab Horizontal a r) (Slab Vertical a r) Source

type AlwaysTrueIntersection g h = RecApplicative (IntersectionOf g h) Source

When using IntersectionOf we may need some constraints that are always true anyway.

defaultNonEmptyIntersection :: forall g h proxy. (NoIntersection ∈ IntersectionOf g h, RecApplicative (IntersectionOf g h)) => proxy g -> proxy h -> Intersection g h -> Bool Source

Returns True iff the resultt is a NoIntersection

type family Union g h :: * Source

class IsUnionableWith g h where Source

Methods

union :: g -> h -> Union g h Source