A Triangle2d
represents a triangle in 2D space, and is defined by its
three vertices. This module contains triangle-related functionality such as:
Geometry.Types.Triangle2d units coordinates
fromVertices : ( Point2d units coordinates, Point2d units coordinates, Point2d units coordinates ) -> Triangle2d units coordinates
Construct a triangle from its three vertices:
exampleTriangle =
Triangle2d.fromVertices
( Point2d.meters 1 1
, Point2d.meters 2 1
, Point2d.meters 1 3
)
from : Point2d units coordinates -> Point2d units coordinates -> Point2d units coordinates -> Triangle2d units coordinates
Construct a triangle from the first point, to the second, to the third:
exampleTriangle =
Triangle2d.from
(Point2d.meters 1 1)
(Point2d.meters 2 1)
(Point2d.meters 1 3)
Useful with map3
functions such as Json.Decode.map3
.
vertices : Triangle2d units coordinates -> ( Point2d units coordinates, Point2d units coordinates, Point2d units coordinates )
Get the vertices of a triangle.
( p1, p2, p3 ) =
Triangle2d.vertices exampleTriangle
edges : Triangle2d units coordinates -> ( LineSegment2d units coordinates, LineSegment2d units coordinates, LineSegment2d units coordinates )
Get the edges of a triangle: from the first vertex to the second, from the second to the third, and from the third back to the first.
( e1, e2, e3 ) =
Triangle2d.edges exampleTriangle
--> e1 =
--> LineSegment2d.from
--> (Point2d.meters 1 1)
--> (Point2d.meters 2 1)
-->
--> e2 =
--> LineSegment2d.from
--> (Point2d.meters 2 1)
--> (Point2d.meters 1 3)
-->
--> e3 =
--> LineSegment2d.from
--> (Point2d.meters 1 3)
--> (Point2d.meters 1 1)
centroid : Triangle2d units coordinates -> Point2d units coordinates
Get the centroid (center of mass) of a triangle.
Triangle2d.centroid exampleTriangle
--> Point2d.meters 1.3333 1.6667
area : Triangle2d units coordinates -> Quantity Basics.Float (Quantity.Squared units)
Get the area of a triangle. The result will always be positive regardless of whether the triangle's vertices are in clockwise or counterclockwise order.
counterclockwiseArea : Triangle2d units coordinates -> Quantity Basics.Float (Quantity.Squared units)
Get the signed area of a triangle, returning a positive value if the triangle's vertices are in counterclockwise order and a negative value otherwise.
Triangle2d.counterclockwiseArea exampleTriangle
--> Area.squareMeters 1.0
clockwiseArea : Triangle2d units coordinates -> Quantity Basics.Float (Quantity.Squared units)
Get the signed area of a triangle, returning a positive value if the triangle's vertices are in clockwise order and a negative value otherwise.
Triangle2d.clockwiseArea exampleTriangle
--> Area.squareMeters -1.0
boundingBox : Triangle2d units coordinates -> BoundingBox2d units coordinates
Get the minimal bounding box containing a given triangle.
Triangle2d.boundingBox exampleTriangle
--> BoundingBox2d.from
--> (Point2d.meters 1 1)
--> (Point2d.meters 2 3)
circumcircle : Triangle2d units coordinates -> Maybe (Circle2d units coordinates)
Attempt to find the circumcircle of a triangle, a circle that passes through each of the triangle's vertices;
Triangle2d.circumcircle triangle
is equivalent to
let
( p1, p2, p3 ) =
Triangle2d.vertices triangle
in
Circle2d.throughPoints p1 p2 p3
If the triangle is degenerate (its three vertices are collinear), returns
Nothing
.
contains : Point2d units coordinates -> Triangle2d units coordinates -> Basics.Bool
Check whether a given point is inside a given triangle. It does not matter whether the triangle's vertices are in clockwise or counterclockwise order.
These transformations generally behave just like the ones in the Point2d
module.
scaleAbout : Point2d units coordinates -> Basics.Float -> Triangle2d units coordinates -> Triangle2d units coordinates
Scale a triangle about a given point by a given scale. Note that scaling by a negative value will result in the 'winding direction' of the triangle being flipped - if the triangle's vertices were in counterclockwise order before the negative scaling, they will be in clockwise order afterwards and vice versa.
rotateAround : Point2d units coordinates -> Angle -> Triangle2d units coordinates -> Triangle2d units coordinates
Rotate a triangle around a given point by a given angle.
translateBy : Vector2d units coordinates -> Triangle2d units coordinates -> Triangle2d units coordinates
Translate a triangle by a given displacement.
translateIn : Direction2d coordinates -> Quantity Basics.Float units -> Triangle2d units coordinates -> Triangle2d units coordinates
Translate a triangle in a given direction by a given distance.
mirrorAcross : Axis2d units coordinates -> Triangle2d units coordinates -> Triangle2d units coordinates
Mirror a triangle across a given axis. Note that mirroring a triangle will result in its 'winding direction' being flipped - if the triangle's vertices were in counterclockwise order before mirroring, they will be in clockwise order afterwards and vice versa.
mapVertices : (Point2d unitsA coordinatesA -> Point2d unitsB coordinatesB) -> Triangle2d unitsA coordinatesA -> Triangle2d unitsB coordinatesB
Transform each vertex of a triangle by a given function and create a new
triangle from the resulting points. Most other transformation functions can be
defined in terms of mapVertices
; for example,
Triangle2d.mirrorAcross axis
is equivalent to
Triangle2d.mapVertices (Point2d.mirrorAcross axis)
at : Quantity Basics.Float (Quantity.Rate units2 units1) -> Triangle2d units1 coordinates -> Triangle2d units2 coordinates
Convert a triangle from one units type to another, by providing a conversion factor given as a rate of change of destination units with respect to source units.
at_ : Quantity Basics.Float (Quantity.Rate units1 units2) -> Triangle2d units1 coordinates -> Triangle2d units2 coordinates
Convert a triangle from one units type to another, by providing an 'inverse' conversion factor given as a rate of change of source units with respect to destination units.
relativeTo : Frame2d units globalCoordinates { defines : localCoordinates } -> Triangle2d units globalCoordinates -> Triangle2d units localCoordinates
Take a triangle defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame.
placeIn : Frame2d units globalCoordinates { defines : localCoordinates } -> Triangle2d units localCoordinates -> Triangle2d units globalCoordinates
Take a triangle considered to be defined in local coordinates relative to a given reference frame, and return that triangle expressed in global coordinates.