OpenSolid.BoundingBox2d

A BoundingBox2d is a rectangular box in 2D defined by its minimum and maximum X and Y values. It is possible to generate bounding boxes for most geometric objects; for example, Triangle2d.boundingBox takes a Triangle2d and returns a BoundingBox2d that contains that triangle. There are several use cases where it is more efficient to deal with the bounding box of an object than the object itself, such as:

Intersection checking: If (for example) the bounding boxes of a line segment and a triangle do not overlap, then the line segment and triangle cannot possibly intersect each other. Expensive intersection checking therefore only has to be performed for line segments and triangles whose bounding boxes do overlap.
2D rendering: When rendering a 2D scene, any object whose bounding box does not overlap the viewing area must itself be completely outside the viewing area, and therefore does not have to be drawn. This provides a simple form of culling.

Bounding boxes can be constructed by passing a record with minX, maxX, minY and maxY fields to the BoundingBox2d constructor, for example

exampleBox =
    BoundingBox2d
        { minX = 3
        , maxX = 8
        , minY = 2
        , maxY = 6
        }

If you construct a BoundingBox2d this way, you must ensure that the given values are properly ordered: minX <= maxX, minY <= maxY. Alternately, you can construct bounding boxes using functions such as Point2d.hull where the input order does not matter.

Constructors

singleton : Point2d -> BoundingBox2d

Construct a zero-width bounding box containing a single point.

point =
    Point2d ( 2, 3 )


BoundingBox2d.singleton point
--> BoundingBox2d
-->     { minX = 2
-->     , maxX = 2
-->     , minY = 3
-->     , maxY = 3
-->     }

containing : List Point2d -> Maybe BoundingBox2d

Construct a bounding box containing all points in the given list. If the list is empty, returns Nothing.

points =
    [ Point2d ( 2, 3 )
    , Point2d ( -1, 5 )
    , Point2d ( 6, 4 )
    ]


BoundingBox2d.containing points
--> Just
-->     (BoundingBox2d
-->         { minX = -1
-->         , maxX = 6
-->         , minY = 3
-->         , maxY = 5
-->         }
-->     )


BoundingBox2d.containing []
--> Nothing

If you have exactly two points, you can use Point2d.hull instead (which returns a BoundingBox2d instead of a Maybe BoundingBox2d).

Accessors

extrema :

BoundingBox2d

-> { minX : Float

, maxX : Float

, minY : Float

, maxY : Float

}

Get the minimum and maximum X and Y values of a bounding box in a single record.

BoundingBox2d.extrema exampleBox
--> { minX = 3
--> , maxX = 8
--> , minY = 2
--> , maxY = 6
--> }

Can be useful when combined with record destructuring, for example

{ minX, maxX, minY, maxY } =
    BoundingBox2d.extrema exampleBox
--> minX = 3
--> maxX = 8
--> minY = 2
--> maxY = 6

minX : BoundingBox2d -> Float

Get the minimum X value of a bounding box.

BoundingBox2d.minX exampleBox
--> 3

maxX : BoundingBox2d -> Float

Get the maximum X value of a bounding box.

BoundingBox2d.maxX exampleBox
--> 8

minY : BoundingBox2d -> Float

Get the minimum Y value of a bounding box.

BoundingBox2d.minY exampleBox
--> 2

maxY : BoundingBox2d -> Float

Get the maximum Y value of a bounding box.

BoundingBox2d.maxY exampleBox
--> 6

dimensions : BoundingBox2d -> ( Float, Float )

Get the X and Y dimensions (width and height) of a bounding box.

( width, height ) =
    BoundingBox2d.dimensions exampleBox
--> width = 5
--> height = 4

midX : BoundingBox2d -> Float

Get the median X value of a bounding box.

BoundingBox2d.midX exampleBox
--> 5.5

midY : BoundingBox2d -> Float

Get the median Y value of a bounding box.

BoundingBox2d.midY exampleBox
--> 4

centroid : BoundingBox2d -> Point2d

Get the point at the center of a bounding box.

BoundingBox2d.centroid exampleBox
--> Point2d ( 5.5, 4 )

Checks

contains : Point2d -> BoundingBox2d -> Bool

Check if a bounding box contains a particular point.

BoundingBox2d.contains (Point2d ( 4, 3 )) exampleBox
--> True


BoundingBox2d.contains Point2d.origin exampleBox
--> False

overlaps : BoundingBox2d -> BoundingBox2d -> Bool

Test if one bounding box overlaps (touches) another.

firstBox =
    BoundingBox2d
        { minX = 0
        , maxX = 3
        , minY = 0
        , maxY = 2
        }


secondBox =
    BoundingBox2d
        { minX = 0
        , maxX = 3
        , minY = 1
        , maxY = 4
        }


thirdBox =
    BoundingBox2d
        { minX = 0
        , maxX = 3
        , minY = 4
        , maxY = 5
        }


BoundingBox2d.overlaps firstBox secondBox
--> True


BoundingBox2d.overlaps firstBox thirdBox
--> False

isContainedIn : BoundingBox2d -> BoundingBox2d -> Bool

Test if the second given bounding box is fully contained within the first (is a subset of it).

outerBox =
    BoundingBox2d
        { minX = 0
        , maxX = 10
        , minY = 0
        , maxY = 10
        }


innerBox =
    BoundingBox2d
        { minX = 1
        , maxX = 5
        , minY = 3
        , maxY = 9
        }


overlappingBox =
    BoundingBox2d
        { minX = 1
        , maxX = 5
        , minY = 3
        , maxY = 12
        }


BoundingBox2d.isContainedIn outerBox innerBox
--> True


BoundingBox2d.isContainedIn outerBox overlappingBox
--> False

Boolean operations

hull : BoundingBox2d -> BoundingBox2d -> BoundingBox2d

Build a bounding box that contains both given bounding boxes.

firstBox =
    BoundingBox2d
        { minX = 1
        , maxX = 4
        , minY = 2
        , maxY = 3
        }


secondBox =
    BoundingBox2d
        { minX = -2
        , maxX = 2
        , minY = 4
        , maxY = 5
        }


BoundingBox2d.hull firstBox secondBox
--> BoundingBox2d
-->     { minX = -2
-->     , maxX = 4
-->     , minY = 2
-->     , maxY = 5
-->     }

intersection : BoundingBox2d -> BoundingBox2d -> Maybe BoundingBox2d

Attempt to build a bounding box that contains all points common to both given bounding boxes. If the given boxes do not overlap, returns Nothing.

firstBox =
    BoundingBox2d
        { minX = 1
        , maxX = 4
        , minY = 2
        , maxY = 3
        }


secondBox =
    BoundingBox2d
        { minX = 2
        , maxX = 5
        , minY = 1
        , maxY = 4
        }


thirdBox =
    BoundingBox2d
        { minX = 1
        , maxX = 4
        , minY = 4
        , maxY = 5
        }


BoundingBox2d.intersection firstBox secondBox
--> Just
-->     (BoundingBox2d
-->         { minX = 2
-->         , maxX = 4
-->         , minY = 2
-->         , maxY = 3
-->         }
-->     )


BoundingBox2d.intersection firstBox thirdBox
--> Nothing

opensolid/geometry/1.0.0

OpenSolid.BoundingBox2d

Constructors

Accessors

Checks

Boolean operations

Modules