A Plane3d
is an infinite flat plane in 3D. It is defined by an origin
point and normal direction and is useful for several operations including:
Geometry.Types.Plane3d
xy : Plane3d
The global XY plane, centered at the origin with a normal in the positive Z direction.
Plane3d.xy
--> Plane3d.through Point3d.origin Direction3d.z
yz : Plane3d
The global YZ plane, centered at the origin with a normal in the positive X direction.
Plane3d.yz
--> Plane3d.through Point3d.origin Direction3d.x
zx : Plane3d
The global ZX plane, centered at the origin with a normal in the positive Y direction.
Plane3d.zx
--> through Point3d.origin Direction3d.y
through : Point3d -> Direction3d -> Plane3d
Construct a plane through the given point, with the given normal direction.
xyPlane =
Plane3d.through Point3d.origin Direction3d.z
withNormalDirection : Direction3d -> Point3d -> Plane3d
Construct a plane with the given normal direction, through the given point.
Flipped version of through
.
plane =
Plane3d.withNormalDirection Direction3d.y
(Point3d.fromCoordinates ( 2, 1, 3 ))
throughPoints : Point3d -> Point3d -> Point3d -> Maybe Plane3d
Attempt to construct a plane passing through the three given points. The
origin point of the resulting plane will be equal to the first given point, and
the normal direction will be such that the three given points are in
counterclockwise order around it according to the right-hand rule. If the three
given points are collinear, returns Nothing
.
Plane3d.throughPoints
(Point3d.fromCoordinates ( 2, 0, 0 ))
(Point3d.fromCoordinates ( 3, 0, 0 ))
(Point3d.fromCoordinates ( 4, 1, 1 ))
--> Just
--> (Plane3d.through
--> (Point3d.fromCoordinates ( 2, 0, 0 ))
--> (Direction3d.fromAzimuthAndElevation
--> (degrees -90)
--> (degrees 45)
--> )
--> )
Plane3d.throughPoints
(Point3d.fromCoordinates ( 2, 0, 0 ))
(Point3d.fromCoordinates ( 3, 0, 0 ))
(Point3d.fromCoordinates ( 4, 0, 0 ))
--> Nothing
originPoint : Plane3d -> Point3d
Get the origin point of a plane.
Plane3d.originPoint Plane3d.xy
--> Point3d.origin
normalDirection : Plane3d -> Direction3d
Get the normal direction of a plane.
Plane3d.normalDirection Plane3d.xy
--> Direction3d.z
normalAxis : Plane3d -> Axis3d
Construct an axis from the origin point and normal direction of a plane.
Plane3d.normalAxis Plane3d.zx
--> Axis3d.y
offsetBy : Basics.Float -> Plane3d -> Plane3d
Shift a plane in its own normal direction by the given (signed) distance.
Plane3d.offsetBy 1.0 Plane3d.zx
--> Plane3d.withNormalDirection Direction3d.y
--> (Point3d.fromCoordinates ( 0, 1, 0 ))
Plane3d.offsetBy -2.0 Plane3d.xy
--> Plane3d.withNormalDirection Direction3d.z
--> (Point3d.fromCoordinates ( 0, 0, -2 ))
reverseNormal : Plane3d -> Plane3d
Reverse a plane's normal direction while leaving its origin point unchanged.
Plane3d.reverseNormal Plane3d.xy
--> Plane3d.through Point3d.origin
--> Direction3d.negativeZ
rotateAround : Axis3d -> Basics.Float -> Plane3d -> Plane3d
Rotate a plane around an axis by a given angle.
Plane3d.rotateAround Axis3d.y (degrees 90) Plane3d.xy
--> Plane3d.yz
translateBy : Vector3d -> Plane3d -> Plane3d
Translate a plane by a given displacement. Applies the given displacement to the plane's origin point and leaves its normal direction unchanged.
plane =
Plane3d.withNormalDirection Direction3d.z
(Point3d.fromCoordinates ( 1, 1, 1 ))
displacement =
Vector3d.fromComponents ( 1, 2, 3 )
Plane3d.translateBy displacement plane
--> Plane3d.withNormalDirection Direction3d.z
--> (Point3d.fromCoordinates ( 2, 3, 4 ))
translateIn : Direction3d -> Basics.Float -> Plane3d -> Plane3d
Translate a plane in a given direction by a given distance;
Plane3d.translateIn direction distance
is equivalent to
Plane3d.translateBy
(Vector3d.withLength distance direction)
moveTo : Point3d -> Plane3d -> Plane3d
Move a plane so that it has the given origin point but unchanged normal direction.
newOrigin =
Point3d.fromCoordinates ( 1, 2, 3 )
Plane3d.moveTo newOrigin Plane3d.xy
--> Plane3d.through newOrigin Direction3d.z
mirrorAcross : Plane3d -> Plane3d -> Plane3d
Mirror one plane across another. The plane to mirror across is given first and the plane to mirror is given second.
plane =
Plane3d.withNormalDirection Direction3d.z
(Point3d.fromCoordinates ( 1, 2, 3 ))
Plane3d.mirrorAcross Plane3d.xy plane
--> Plane3d.withNormalDirection Direction3d.negativeZ
--> (Point3d.fromCoordinates ( 1, 2, -3 ))
relativeTo : Geometry.Types.Frame3d -> Plane3d -> Plane3d
Take a plane defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame.
referenceFrame =
Frame3d.atPoint
(Point3d.fromCoordinates ( 1, 1, 1 ))
plane =
Plane3d.withNormalDirection Direction3d.z
(Point3d.fromCoordinates ( 0, 0, 2 ))
Plane3d.relativeTo referenceFrame plane
--> Plane3d.withNormalDirection Direction3d.z
--> (Point3d.fromCoordinates ( -1, -1, 1 ))
placeIn : Geometry.Types.Frame3d -> Plane3d -> Plane3d
Take a plane defined in local coordinates relative to a given reference frame, and return that plane expressed in global coordinates.
referenceFrame =
Frame3d.atPoint
(Point3d.fromCoordinates ( 1, 1, 1 ))
plane =
Plane3d.withNormalDirection Direction3d.z
(Point3d.fromCoordinates ( 1, 2, 3 ))
Plane3d.placeIn referenceFrame plane
--> Plane3d.withNormalDirection Direction3d.z
--> (Point3d.fromCoordinates ( 2, 3, 4 ))