OpenSolid.BoundingBox3d

A BoundingBox3d is a rectangular box in 3D defined by its minimum and maximum X, Y and Z values. It is possible to generate bounding boxes for most geometric objects; Triangle3d.boundingBox takes a Triangle3d and returns a BoundingBox3d 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.
3D rendering: When rendering a 3D scene, any object whose bounding box is not visible must itself be not visible, 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, maxY, minZ and maxZ fields to the BoundingBox3d constructor, for example

exampleBox =
    BoundingBox3d
        { minX = -2
        , maxX = 2
        , minY = 2
        , maxY = 5
        , minZ = 3
        , maxZ = 4
        }

If you construct a BoundingBox3d this way, you must ensure that the given values are properly ordered: minX <= maxX, minY <= maxY, minZ <= maxZ. Alternately, you can construct bounding boxes using functions such as Point3d.hull where the input order does not matter.

Constructors

singleton : Point3d -> BoundingBox3d

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

point =
    Point3d ( 2, 1, 3 )


BoundingBox3d.singleton point
--> BoundingBox3d
-->     { minX = 2
-->     , maxX = 2
-->     , minY = 1
-->     , maxY = 1
-->     , minZ = 3
-->     , maxZ = 3
-->     }

containing : List Point3d -> Maybe BoundingBox3d

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

points =
    [ Point3d ( 2, 1, 3 )
    , Point3d ( -1, 5, -2 )
    , Point3d ( 6, 4, 2 )
    ]


BoundingBox3d.containing points
--> Just
-->     (BoundingBox3d
-->         { minX = -1
-->         , maxX = 6
-->         , minY = 1
-->         , maxY = 5
-->         , minZ = -2
-->         , maxZ = 3
-->         }
-->     )


BoundingBox3d.containing []
--> Nothing

If you have exactly two points, you can use Point3d.hull instead (which returns a BoundingBox3d instead of a Maybe BoundingBox3d).

Accessors

extrema :

BoundingBox3d

-> { minX : Float

, maxX : Float

, minY : Float

, maxY : Float

, minZ : Float

, maxZ : Float

}

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

BoundingBox3d.extrema exampleBox
--> { minX = -2
--> , maxX = 2
--> , minY = 2
--> , maxY = 5
--> , minZ = 3
--> , maxZ = 4
--> }

Can be useful when combined with record destructuring, for example

{ minX, maxX, minY, maxY, minZ, maxZ } =
    BoundingBox3d.extrema exampleBox
--> minX = -2
--> maxX = 2
--> minY = 2
--> maxY = 5
--> minZ = 3
--> maxZ = 4

minX : BoundingBox3d -> Float

Get the minimum X value of a bounding box.

BoundingBox3d.minX exampleBox
--> -2

maxX : BoundingBox3d -> Float

Get the maximum X value of a bounding box.

BoundingBox3d.maxX exampleBox
--> 2

minY : BoundingBox3d -> Float

Get the minimum Y value of a bounding box.

BoundingBox3d.minY exampleBox
--> 2

maxY : BoundingBox3d -> Float

Get the maximum Y value of a bounding box.

BoundingBox3d.maxY exampleBox
--> 5

minZ : BoundingBox3d -> Float

Get the minimum Z value of a bounding box.

BoundingBox3d.minZ exampleBox
--> 3

maxZ : BoundingBox3d -> Float

Get the maximum Z value of a bounding box.

BoundingBox3d.maxZ exampleBox
--> 4

dimensions : BoundingBox3d -> ( Float, Float, Float )

Get the X, Y and Z dimensions (widths) of a bounding box.

BoundingBox3d.dimensions exampleBox
--> ( 4, 3, 1 )

midX : BoundingBox3d -> Float

Get the median X value of a bounding box.

BoundingBox3d.midX exampleBox
--> 0

midY : BoundingBox3d -> Float

Get the median Y value of a bounding box.

BoundingBox3d.midY exampleBox
--> 3.5

midZ : BoundingBox3d -> Float

Get the median Z value of a bounding box.

BoundingBox3d.midZ exampleBox
--> 3.5

centroid : BoundingBox3d -> Point3d

Get the point at the center of a bounding box.

BoundingBox3d.centroid exampleBox
--> Point3d ( 0, 3.5, 3.5 )

Checks

contains : Point3d -> BoundingBox3d -> Bool

Check if a bounding box contains a particular point.

firstPoint =
    Point3d ( 1, 4, 3 )


secondPoint =
    Point3d ( 3, 4, 5 )


BoundingBox3d.contains firstPoint exampleBox
--> True


BoundingBox3d.contains secondPoint exampleBox
--> False

overlaps : BoundingBox3d -> BoundingBox3d -> Bool

Test if one bounding box overlaps (touches) another.

firstBox =
    BoundingBox3d
        { minX = 0
        , maxX = 3
        , minY = 0
        , maxY = 2
        , minZ = 0
        , maxZ = 1
        }


secondBox =
    BoundingBox3d
        { minX = 0
        , maxX = 3
        , minY = 1
        , maxY = 4
        , minZ = -1
        , maxZ = 2
        }


thirdBox =
    BoundingBox3d
        { minX = 0
        , maxX = 3
        , minY = 4
        , maxY = 5
        , minZ = -1
        , maxZ = 2
        }


BoundingBox3d.overlaps firstBox secondBox
--> True


BoundingBox3d.overlaps firstBox thirdBox
--> False

isContainedIn : BoundingBox3d -> BoundingBox3d -> Bool

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

outerBox =
    BoundingBox3d
        { minX = 0
        , maxX = 10
        , minY = 0
        , maxY = 10
        , minZ = 0
        , maxZ = 10
        }


innerBox =
    BoundingBox3d
        { minX = 1
        , maxX = 5
        , minY = 3
        , maxY = 9
        , minZ = 7
        , maxZ = 8
        }


overlappingBox =
    BoundingBox3d
        { minX = 1
        , maxX = 5
        , minY = 3
        , maxY = 12
        , minZ = 7
        , maxZ = 8
        }


BoundingBox3d.isContainedIn outerBox innerBox
--> True


BoundingBox3d.isContainedIn outerBox overlappingBox
--> False

Boolean operations

hull : BoundingBox3d -> BoundingBox3d -> BoundingBox3d

Build a bounding box that contains both given bounding boxes.

firstBox =
    BoundingBox3d
        { minX = 1
        , maxX = 4
        , minY = 2
        , maxY = 3
        , minZ = 0
        , maxZ = 5
        }


secondBox =
    BoundingBox3d
        { minX = -2
        , maxX = 2
        , minY = 4
        , maxY = 5
        , minZ = -1
        , maxZ = 0
        }


BoundingBox3d.hull firstBox secondBox
--> BoundingBox3d
-->     { minX = -2
-->     , maxX = 4
-->     , minY = 2
-->     , maxY = 5
-->     , minZ = -1
-->     , maxZ = 5
-->     }

intersection : BoundingBox3d -> BoundingBox3d -> Maybe BoundingBox3d

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 =
    BoundingBox3d
        { minX = 1
        , maxX = 4
        , minY = 2
        , maxY = 3
        , minZ = 5
        , maxZ = 8
        }


secondBox =
    BoundingBox3d
        { minX = 2
        , maxX = 5
        , minY = 1
        , maxY = 4
        , minZ = 6
        , maxZ = 7
        }


thirdBox =
    BoundingBox3d
        { minX = 1
        , maxX = 4
        , minY = 4
        , maxY = 5
        , minZ = 5
        , maxZ = 8
        }


BoundingBox3d.intersection firstBox secondBox
--> Just
-->     (BoundingBox3d
-->         { minX = 2
-->         , maxX = 4
-->         , minY = 2
-->         , maxY = 3
-->         , minZ = 6
-->         , maxZ = 7
-->         }
-->     )


BoundingBox3d.intersection firstBox thirdBox
--> Nothing

opensolid/geometry/1.0.1

OpenSolid.BoundingBox3d

Constructors

Accessors

Checks

Boolean operations

Modules