elm-geometry

elm-geometry is an Elm package for working with 2D and 3D geometry. It provides a wide variety of geometric data types such as points, vectors, arcs, spline curves and coordinate frames, along with functions for transforming and combining them in many different ways. You can:

• Rotate points around axes in 3D
• Mirror triangles across 3D planes
• Project 3D geometry into 2D sketch planes
• Measure distances and angles between different objects
• Convert objects between different coordinate systems
• Compose complex 2D/3D transformations
• ...and much more!

A wide variety of data types are supported:

• Point2d, Point3d, Vector2d, Vector3d, Direction2d, Direction3d

  

• Axis2d, Axis3d, Plane3d

  

• Frame2d, Frame3d, SketchPlane3d

  

• BoundingBox2d, BoundingBox3d

  

• LineSegment2d, LineSegment3d, Triangle2d, Triangle3d

  

• Polyline2d, Polyline3d, Polygon2d

  

• Circle2d, Circle3d, Arc2d, Arc3d

  

• Ellipse2d, EllipticalArc2d

  

• QuadraticSpline2d, QuadraticSpline3d, CubicSpline2d, CubicSpline3d

  

A large range of geometric functionality is included, such as various forms of constructors...

Point3d.fromCoordinates ( 1, 4, 5 )

Direction2d.fromAngle (degrees 30)

Point3d.midpoint p1 p2

Vector2d.withLength 3 Direction2d.y

Triangle2d.fromVertices ( p1, p2, p3 )

-- fit a plane through three points
Plane3d.throughPoints p1 p2 p3

Axis3d.through Point3d.origin Direction3d.z

Arc2d.from p1 p2 (degrees 90)

QuadraticSpline3d.with
    { startPoint = p1
    , controlPoint = p2
    , endPoint = p3
    }

CubicSpline2d.fromEndpoints
    { startPoint = p1
    , startDerivative = v1
    , endPoint = p2
    , endDerivative = v2
    }

...point/vector arithmetic...

Vector3d.sum v1 v2

-- the vector from the point p1 to the point p2
Vector2d.from p1 p2

Vector3d.crossProduct v1 v2

Vector2d.length vector

-- distance of a point from the origin point (0, 0)
point |> Point2d.distanceFrom Point2d.origin

...2D/3D transformations...

Vector2d.rotateBy (degrees 45) vector

Point2d.rotateAround Point2d.origin (degrees 45) point

Point3d.mirrorAcross Plane3d.xy point

Vector3d.projectionIn Direction3d.z vector

Triangle3d.rotateAround Axis3d.x (degrees 45) triangle

lineSegment
    |> LineSegment3d.mirrorAcross Plane3d.yz
    |> LineSegment3d.projectOnto Plane3d.xy

Plane3d.offsetBy 3 Plane3d.xy

...and conversions between coordinate systems:

rotatedFrame =
    Frame2d.xy |> Frame2d.rotateBy (degrees 30)

-- convert from global coordinates to local coordinates
-- (relative to the given coordinate frame)
Vector2d.relativeTo rotatedFrame vector

-- convert from local coordinates (relative to the given
-- coordinate frame) to global coordinates
Point2d.placeIn rotatedFrame point

-- convert from global 3D coordinates to local 2D
-- coordinates in the given sketch plane
point2d =
    Point3d.projectInto SketchPlane3d.yz point3d

-- convert from local 2D coordinates in the given
-- sketch plane back to global 3D coordinates
point3d =
    Point3d.on SketchPlane3d.yz point2d

Installation

Assuming you have installed Elm and started a new project, you can install elm-geometry by running

elm install ianmackenzie/elm-geometry

in a command prompt inside your project directory.

Documentation

Full API documentation is available for each module. Most modules are associated with a particular data type (for example, the Point3d module contains functions for creating and manipulating Point3d values).

Usage details

Following the Elm package design guidelines, most elm-geometry modules are designed to be imported exposing only the corresponding types, and using the module name as a prefix for everything else:

import Point3d exposing (Point3d)
import Axis3d exposing (Axis3d)

rotatedPoint : Point3d
rotatedPoint =
    Point3d.rotateAround Axis3d.x (degrees 30) originalPoint

Questions? Comments?

Please open a new issue if you run into a bug, if any documentation is missing/incorrect/confusing, or if there's a new feature that you would find useful. For general questions about using elm-geometry, the best place is probably the #geometry channel on the friendly Elm Slack:

You can also try:

• Sending me (@ianmackenzie) a message on Slack - even if you don't have any particular questions right now, it would be great to know what you're hoping to do with the package!
• Posting to the Elm Discourse forums
• Or if you happen to be in the New York area, come on out to the Elm NYC meetup =)

You can also find me on Twitter (@ianemackenzie), where I occasionally post elm-geometry-related stuff like demos or new releases. Have fun, and don't be afraid to ask for help!