Construct a triangle from its three vertices:

exampleTriangle =
    Triangle2d.fromVertices
        ( Point2d.fromCoordinates ( 1, 1 )
        , Point2d.fromCoordinates ( 2, 1 )
        , Point2d.fromCoordinates ( 1, 3 )
        )

Get the vertices of a triangle.

( p1, p2, p3 ) =
    Triangle2d.vertices exampleTriangle




--> p1 = Point2d.fromCoordinates ( 1, 1 )
--> p2 = Point2d.fromCoordinates ( 2, 1 )
--> p3 = Point2d.fromCoordinates ( 1, 3 )

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.fromEndpoints
-->         ( Point2d.fromCoordinates ( 1, 1 )
-->         , Point2d.fromCoordinates ( 2, 1 )
-->         )
-->
--> e2 =
-->     LineSegment2d.fromEndpoints
-->         ( Point2d.fromCoordinates ( 2, 1 )
-->         , Point2d.fromCoordinates ( 1, 3 )
-->         )
-->
--> e3 =
-->     LineSegment2d.fromEndpoints
-->         ( Point2d.fromCoordinates ( 1, 3 )
-->         , Point2d.fromCoordinates ( 1, 1 )
-->         )

Get the centroid (center of mass) of a triangle.

Triangle2d.centroid exampleTriangle
--> Point2d.fromCoordinates ( 1.3333, 1.6667 )

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.

Triangle2d.area exampleTriangle
--> 1.0

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
--> 1.0

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
--> -1.0

Get the minimal bounding box containing a given triangle.

Triangle2d.boundingBox exampleTriangle
--> BoundingBox2d.fromExtrema
-->     { minX = 1
-->     , maxX = 2
-->     , minY = 1
-->     , maxY = 3
-->     }

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

( p1, p2, p3 ) =
    Triangle2d.vertices triangle


Circle2d.throughPoints p1 p2 p3

If the triangle is degenerate (its three vertices are collinear), returns Nothing.

Check whether a given point is inside a given triangle.

interiorPoint =
    Point2d.fromCoordinates ( 1.5, 1.5 )


Triangle2d.contains interiorPoint exampleTriangle
--> True


Triangle2d.contains Point2d.origin exampleTriangle
--> False

It does not matter whether the triangle's vertices are in clockwise or counterclockwise order.

Scale a triangle about a given point by a given scale.

Triangle2d.scaleAbout Point2d.origin 2 exampleTriangle
--> Triangle2d.fromVertices
-->     ( Point2d.fromCoordinates ( 2, 2 )
-->     , Point2d.fromCoordinates ( 4, 2 )
-->     , Point2d.fromCoordinates ( 2, 6 )
-->     )

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.

Rotate a triangle around a given point by a given angle (in radians).

exampleTriangle
    |> Triangle2d.rotateAround Point2d.origin
        (degrees 90)
--> Triangle2d.fromVertices
-->     ( Point2d.fromCoordinates ( -1, 1 )
-->     , Point2d.fromCoordinates ( -1, 2 )
-->     , Point2d.fromCoordinates ( -3, 1 )
-->     )

Translate a triangle by a given displacement.

displacement =
    Vector2d.fromComponents ( 2, -3 )


Triangle2d.translateBy displacement exampleTriangle
--> Triangle2d.fromVertices
-->     ( Point2d.fromCoordinates ( 3, -2 )
-->     , Point2d.fromCoordinates ( 4, -2 )
-->     , Point2d.fromCoordinates ( 3, 0 )
-->     )

Translate a triangle in a given direction by a given distance;

Triangle2d.translateIn direction distance

is equivalent to

Triangle2d.translateBy
    (Vector2d.withLength distance direction)

Mirror a triangle across a given axis.

Triangle2d.mirrorAcross Axis2d.y exampleTriangle
--> Triangle2d.fromVertices
-->     ( Point2d.fromCoordinates ( -1, 1 )
-->     , Point2d.fromCoordinates ( -2, 1 )
-->     , Point2d.fromCoordinates ( -1, 3 )
-->     )

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.

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)

Take a triangle defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame.

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 1, 2 ))


Triangle2d.relativeTo localFrame exampleTriangle
--> Triangle2d.fromVertices
-->     ( Point2d.fromCoordinates ( 0, -1 )
-->     , Point2d.fromCoordinates ( 1, -1 )
-->     , Point2d.fromCoordinates ( 0, 1 )
-->     )

Take a triangle considered to be defined in local coordinates relative to a given reference frame, and return that triangle expressed in global coordinates.

localFrame =
    Frame2d.atPoint (Point2d.fromCoordinates ( 1, 2 ))


Triangle2d.placeIn localFrame exampleTriangle
--> Triangle2d.fromVertices
-->     ( Point2d.fromCoordinates ( 2, 3 )
-->     , Point2d.fromCoordinates ( 3, 3 )
-->     , Point2d.fromCoordinates ( 2, 5 )
-->     )