Diagrams.BoundingBox

Bounding boxes are not very compositional (e.g. it is not possible to do anything sensible with them under rotation), so they are not used in the diagrams core. However, they do have their uses; this module provides definitions and functions for working with them.

Bounding boxes

data BoundingBox v n

A bounding box is an axis-aligned region determined by two points indicating its "lower" and "upper" corners. It can also represent an empty bounding box - the points are wrapped in Maybe.

Instances

Functor v => Functor (BoundingBox v)

Methods

fmap :: (a -> b) -> BoundingBox v a -> BoundingBox v b

(<$) :: a -> BoundingBox v b -> BoundingBox v a

Eq (v n) => Eq (BoundingBox v n)

Methods

(==) :: BoundingBox v n -> BoundingBox v n -> Bool

(/=) :: BoundingBox v n -> BoundingBox v n -> Bool

Read (v n) => Read (BoundingBox v n)

Methods

readsPrec :: Int -> ReadS (BoundingBox v n)

readList :: ReadS [BoundingBox v n]

readPrec :: ReadPrec (BoundingBox v n)

readListPrec :: ReadPrec [BoundingBox v n]

Show (v n) => Show (BoundingBox v n)

Methods

showsPrec :: Int -> BoundingBox v n -> ShowS

show :: BoundingBox v n -> String

showList :: [BoundingBox v n] -> ShowS

(Additive v, Ord n) => Semigroup (BoundingBox v n)

Methods

(<>) :: BoundingBox v n -> BoundingBox v n -> BoundingBox v n

sconcat :: NonEmpty (BoundingBox v n) -> BoundingBox v n

stimes :: Integral b => b -> BoundingBox v n -> BoundingBox v n

(Additive v, Ord n) => Monoid (BoundingBox v n)

Methods

mempty :: BoundingBox v n

mappend :: BoundingBox v n -> BoundingBox v n -> BoundingBox v n

mconcat :: [BoundingBox v n] -> BoundingBox v n

(Metric v, Traversable v, OrderedField n) => Enveloped (BoundingBox v n)

Methods

getEnvelope :: BoundingBox v n -> Envelope (V (BoundingBox v n)) (N (BoundingBox v n))

TypeableFloat n => Traced (BoundingBox V3 n)

Methods

getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n))

RealFloat n => Traced (BoundingBox V2 n)

Methods

getTrace :: BoundingBox V2 n -> Trace (V (BoundingBox V2 n)) (N (BoundingBox V2 n))

(Additive v, Num n) => HasOrigin (BoundingBox v n)

Methods

moveOriginTo :: Point (V (BoundingBox v n)) (N (BoundingBox v n)) -> BoundingBox v n -> BoundingBox v n

AsEmpty (BoundingBox v n)

Methods

_Empty :: Prism' (BoundingBox v n) ()

(Metric v, Traversable v, OrderedField n) => Alignable (BoundingBox v n)

Methods

alignBy' :: (InSpace v n (BoundingBox v n), Fractional n, HasOrigin (BoundingBox v n)) => (v n -> BoundingBox v n -> Point v n) -> v n -> n -> BoundingBox v n -> BoundingBox v n

defaultBoundary :: (((* -> *) ~ V (BoundingBox v n)) v, (* ~ N (BoundingBox v n)) n) => v n -> BoundingBox v n -> Point v n

alignBy :: (InSpace v n (BoundingBox v n), Fractional n, HasOrigin (BoundingBox v n)) => v n -> n -> BoundingBox v n -> BoundingBox v n

(Additive v, Foldable v, Ord n) => HasQuery (BoundingBox v n) Any

Methods

getQuery :: BoundingBox v n -> Query (V (BoundingBox v n)) (N (BoundingBox v n)) Any

(Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n')

Only valid if the second point is not smaller than the first.

Methods

each :: Traversal (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n')

type V (BoundingBox v n)

type V (BoundingBox v n) = v

type N (BoundingBox v n)

type N (BoundingBox v n) = n

Constructing bounding boxes

emptyBox :: BoundingBox v n

An empty bounding box. This is the same thing as mempty, but it doesn't require the same type constraints that the Monoid instance does.

fromCorners :: (Additive v, Foldable v, Ord n) => Point v n -> Point v n -> BoundingBox v n

Create a bounding box from a point that is component-wise (<=) than the other. If this is not the case, then mempty is returned.

fromPoint :: Point v n -> BoundingBox v n

Create a degenerate bounding "box" containing only a single point.

fromPoints :: (Additive v, Ord n) => [Point v n] -> BoundingBox v n

Create the smallest bounding box containing all the given points.

boundingBox :: (InSpace v n a, HasBasis v, Enveloped a) => a -> BoundingBox v n

Create a bounding box for any enveloped object (such as a diagram or path).

Queries on bounding boxes

isEmptyBox :: BoundingBox v n -> Bool

Queries whether the BoundingBox is empty.

getCorners :: BoundingBox v n -> Maybe (Point v n, Point v n)

Gets the lower and upper corners that define the bounding box.

getAllCorners :: (Additive v, Traversable v) => BoundingBox v n -> [Point v n]

Computes all of the corners of the bounding box.

boxExtents :: (Additive v, Num n) => BoundingBox v n -> v n

Get the size of the bounding box - the vector from the (component-wise) lesser point to the greater point.

boxCenter :: (Additive v, Fractional n) => BoundingBox v n -> Maybe (Point v n)

Get the center point in a bounding box.

mCenterPoint :: (InSpace v n a, HasBasis v, Enveloped a) => a -> Maybe (Point v n)

Get the center of a the bounding box of an enveloped object, return Nothing for object with empty envelope.

centerPoint :: (InSpace v n a, HasBasis v, Enveloped a) => a -> Point v n

Get the center of a the bounding box of an enveloped object, return the origin for object with empty envelope.

boxTransform :: (Additive v, Fractional n) => BoundingBox v n -> BoundingBox v n -> Maybe (Transformation v n)

Create a transformation mapping points from one bounding box to the other. Returns Nothing if either of the boxes are empty.

boxFit :: (InSpace v n a, HasBasis v, Enveloped a, Transformable a, Monoid a) => BoundingBox v n -> a -> a

Transforms an enveloped thing to fit within a BoundingBox. If the bounding box is empty, then the result is also mempty.

contains :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> Point v n -> Bool

Check whether a point is contained in a bounding box (including its edges).

contains' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> Point v n -> Bool

Check whether a point is strictly contained in a bounding box.

inside :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool

Test whether the first bounding box is contained inside the second.

inside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool

Test whether the first bounding box is strictly contained inside the second.

outside :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool

Test whether the first bounding box lies outside the second (although they may intersect in their boundaries).

outside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool

Test whether the first bounding box lies strictly outside the second (they do not intersect at all).

boxGrid :: (Traversable v, Additive v, Num n, Enum n) => n -> BoundingBox v n -> [Point v n]

boxGrid f box returns a grid of regularly spaced points inside the box, such that there are (1/f) points along each dimension. For example, for a 3D box with corners at (0,0,0) and (2,2,2), boxGrid 0.1 would yield a grid of approximately 1000 points (it might actually be 11^3 instead of 10^3) spaced 0.2 units apart.

Operations on bounding boxes

union :: (Additive v, Ord n) => BoundingBox v n -> BoundingBox v n -> BoundingBox v n

Form the smallest bounding box containing the given two bound union. This function is just an alias for mappend.

intersection :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> BoundingBox v n

Form the largest bounding box contained within this given two bounding boxes, or Nothing if the two bounding boxes do not overlap at all.