Construct a triangle from its three vertices:

exampleTriangle =
    Triangle3d.fromVertices
        ( Point3d.meters 1 0 0
        , Point3d.meters 2 0 0
        , Point3d.meters 2 1 3
        )

Construct a triangle from the first point, to the second, to the third:

exampleTriangle =
    Triangle3d.from
        (Point3d.meters 1 0 0)
        (Point3d.meters 2 0 0)
        (Point3d.meters 2 1 3)

Useful with map3 functions such as Json.Decode.map3.

Construct a 3D triangle lying on a sketch plane by providing a 2D triangle specified in XY coordinates within the sketch plane.

Triangle3d.on SketchPlane3d.xz <|
    Triangle2d.from
        (Point2d.meters 1 1)
        (Point2d.meters 2 1)
        (Point2d.meters 1 3)
--> Triangle3d.from
-->     (Point3d.meters 1 0 1)
-->     (Point3d.meters 2 0 1)
-->     (Point3d.meters 1 0 3)

Get the vertices of a triangle.

( p1, p2, p3 ) =
    Triangle3d.vertices exampleTriangle


--> p1 = Point3d.meters 1 0 0
--> p2 = Point3d.meters 2 0 0
--> p3 = Point3d.meters 2 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 ) =
    Triangle3d.edges exampleTriangle


--> e1 =
-->     LineSegment3d.from
-->         (Point3d.meters 1 0 0)
-->         (Point3d.meters 2 0 0)
-->
--> e2 =
-->     LineSegment3d.from
-->         (Point3d.meters 2 0 0)
-->         (Point3d.meters 2 1 3)
-->
--> e3 =
-->     LineSegment3d.from
-->         (Point3d.meters 2 1 3)
-->         (Point3d.meters 1 0 0)

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

Triangle3d.centroid exampleTriangle
--> Point3d.meters 1.6667 0.6667 1

Get the area of a triangle. This value is always positive.

Triangle3d.area exampleTriangle
--> Area.squareMeters 1.5811

Attempt to find the normal direction to a triangle. The resulting direction will be oriented such that the triangle vertices are in counterclockwise order around it according to the right-hand rule. If the triangle is degenerate (its three vertices are collinear), returns Nothing.

Triangle3d.normalDirection exampleTriangle
--> Just (Direction3d.yz (Angle.degrees 161.57))

Get the minimal bounding box containing a given triangle.

Triangle3d.boundingBox exampleTriangle
--> BoundingBox3d.fromExtrema
-->     { minX = Length.meters 1
-->     , maxX = Length.meters 2
-->     , minY = Length.meters 0
-->     , maxY = Length.meters 1
-->     , minZ = Length.meters 0
-->     , maxZ = Length.meters 3
-->     }

Attempt to find the circumcircle of a triangle, a circle that passes through each of the triangle's vertices;

Triangle3d.circumcircle triangle

is equivalent to

let
    ( p1, p2, p3 ) =
        Triangle3d.vertices triangle
in
Circle3d.throughPoints p1 p2 p3

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

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.

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.

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

Rotate a triangle around a given axis by a given angle.

Translate a triangle by a given displacement.

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

Mirror a triangle across a given plane.

Find the orthographic projection of a triangle onto a plane.

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,

Triangle3d.projectOnto plane

is equivalent to

Triangle3d.mapVertices (Point3d.projectOnto plane)

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

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

Project a triangle into a given sketch plane. Conceptually, this finds the orthographic projection of the triangle onto the plane and then expresses the projected triangle in 2D sketch coordinates.