Cone3d

A Cone3d consists of a conical outer surface, a circular base and a tip; it is defined by its center point on the base, axial direction, radius and overall length. This module contains functionality for:

Constructing cones in various ways
Scaling, rotating and translating cones
Extracting cone properties like base point and volume

type alias Cone3d units coordinates =

Cone3d units coordinates

Constructors

along :

Axis3d units coordinates

-> { base : Quantity Float units

, tip : Quantity Float units

, radius : Quantity Float units

}

-> Cone3d units coordinates

Construct a cone that lies along the given axis, with the center of the base and tip points given as (signed) distances along that axis:

exampleCone =
    Cone3d.along Axis3d.x
        { base = Length.meters -1
        , tip = Length.meters 3
        , radius = Length.meters 1
        }


Cone3d.basePoint exampleCone
--> Point3d.meters -1 0 0


Cone3d.tipPoint exampleCone
--> Point3d.meters 3 0 0


Cone3d.length exampleCone
--> Length.meters 4

Note that tip may be less than base, but then the axial direction of the returned cone will be the opposite of the axial direction of the given axis.

startingAt :

Point3d units coordinates

-> Direction3d coordinates

-> { radius : Quantity Float units

, length : Quantity Float units

}

-> Cone3d units coordinates

Construct a cone given the center point on the base, axial direction towards the tip, radius and length. Negative values for radius or length will be treated as positive (the absolute values will be used).

from :

Point3d units coordinates

-> Point3d units coordinates

-> Quantity Float units

-> Maybe (Cone3d units coordinates)

Attempt to construct a cone from the given center point on the base, tip point and radius. If the base and tip points are coincident (the same point), returns Nothing.

Properties

axis : Cone3d units coordinates -> Axis3d units coordinates

Get the central axis of a cone. The origin point of the axis will be at the center point of the base, and the direction of the axis will be from the cone's base point towards its tip.

axialDirection : Cone3d units coordinates -> Direction3d coordinates

Get the axial direction of a cone.

radius : Cone3d units coordinates -> Quantity Float units

Get the base radius of a cone.

diameter : Cone3d units coordinates -> Quantity Float units

Get the base diameter of a cone (twice its radius).

length : Cone3d units coordinates -> Quantity Float units

Get the overall length of a cone.

basePoint : Cone3d units coordinates -> Point3d units coordinates

Get the base point of a cone. This is the center point of the circle that forms the base of the cone.

tipPoint : Cone3d units coordinates -> Point3d units coordinates

Get the tip point of a cone.

base : Cone3d units coordinates -> Circle3d units coordinates

Get the circle at the base of a cone. The axial direction of this circle will be the reverse of the axial direction of the cone itself (the circle axial direction will point backwards/outwards).

basePlane : Cone3d units coordinates -> Plane3d units coordinates

Get the plane at the base of a cone. The normal direction of this plane will be the same as the axial direction of the cone itself.

volume : Cone3d units coordinates -> Quantity Float (Cubed units)

Get the volume of a cone.

boundingBox : Cone3d units coordinates -> BoundingBox3d units coordinates

Get the minimal bounding box containing a given cone.

Queries

contains : Point3d units coordinates -> Cone3d units coordinates -> Bool

Check if a cone contains a given point.

Transformations

Transformations generally behave just like the ones in the Point3d module.

scaleAbout :

Point3d units coordinates

-> Float

-> Cone3d units coordinates

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

rotateAround :

Axis3d units coordinates

-> Angle

-> Cone3d units coordinates

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

translateBy :

Vector3d units coordinates

-> Cone3d units coordinates

Translate a cone by a given displacement.

translateIn :

Direction3d coordinates

-> Quantity Float units

-> Cone3d units coordinates

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

mirrorAcross :

Plane3d units coordinates

-> Cone3d units coordinates

Mirror a cone across a given plane.

Unit conversions

at :

Quantity Float (Rate units2 units1)

-> Cone3d units1 coordinates

-> Cone3d units2 coordinates

Convert a cone 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 Float (Rate units1 units2)

-> Cone3d units1 coordinates

-> Cone3d units2 coordinates

Convert a cone 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.

Coordinate conversions

placeIn :

Frame3d units globalCoordinates { defines : localCoordinates }

-> Cone3d units localCoordinates

-> Cone3d units globalCoordinates

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

relativeTo :

Frame3d units globalCoordinates { defines : localCoordinates }

-> Cone3d units globalCoordinates

-> Cone3d units localCoordinates

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

ianmackenzie/elm-geometry/3.5.0

Cone3d

Constructors

Properties

Queries

Transformations

Unit conversions

Coordinate conversions

Modules