Direction2D (Math.Geometry)

Direction2D Module

Namespace: Math.Geometry
Assembly: Math.Geometry.dll

Functions and values

Function or value	Description
`angleFrom d1 d2` Full Usage: `angleFrom d1 d2` Parameters: d1 : `Direction2D<'Coordinates>` d2 : `Direction2D<'Coordinates>` Returns: `Angle`	Find the counterclockwise angle from the first direction to the second. The result will be in the range -180 to 180 degrees d1 : `Direction2D<'Coordinates>` d2 : `Direction2D<'Coordinates>` Returns: `Angle`
`componentIn d2 d1` Full Usage: `componentIn d2 d1` Parameters: d2 : `Direction2D<'Coordinates>` d1 : `Direction2D<'Coordinates>` Returns: `float`	Find the component of one direction in another direction. This is equal to the cosine of the angle between the directions, or equivalently the dot product of the two directions converted to unit vectors. This is more general and flexible than using `xComponent` or `yComponent`, both of which can be expressed in terms of `componentIn`; for example, `Direction2d.xComponent direction` is equivalent to `Direction2d.componentIn Direction2d.x direction`. d2 : `Direction2D<'Coordinates>` d1 : `Direction2D<'Coordinates>` Returns: `float`
`components d` Full Usage: `components d` Parameters: d : `Direction2D<'Coordinates>` Returns: `float * float`	Get the X and Y component of the direction in a tuple. d : `Direction2D<'Coordinates>` Returns: `float * float`
`degrees d` Full Usage: `degrees d` Parameters: d : `float` Returns: `Direction2D<'Coordinates>`	d : `float` Returns: `Direction2D<'Coordinates>`
`equalWithin angle rhs lhs` Full Usage: `equalWithin angle rhs lhs` Parameters: angle : `Angle` rhs : `Direction2D<'Coordinates>` lhs : `Direction2D<'Coordinates>` Returns: `bool`	Compare two directions within an angular tolerance. Returns true if the absolute value of the angle between the two given directions is less than the given tolerance. angle : `Angle` rhs : `Direction2D<'Coordinates>` lhs : `Direction2D<'Coordinates>` Returns: `bool`
`from first second` Full Usage: `from first second` Parameters: first : `Point2D<'Units, 'Coordinates>` second : `Point2D<'Units, 'Coordinates>` Returns: `Direction2D<'Coordinates> option`	first : `Point2D<'Units, 'Coordinates>` second : `Point2D<'Units, 'Coordinates>` Returns: `Direction2D<'Coordinates> option`
`fromAngle angle` Full Usage: `fromAngle angle` Parameters: angle : `Angle` Returns: `Direction2D<'Coordinates>`	angle : `Angle` Returns: `Direction2D<'Coordinates>`
`fromComponents (x, y)` Full Usage: `fromComponents (x, y)` Parameters: x : `float` y : `float` Returns: `Direction2D<'Coordinates> option`	x : `float` y : `float` Returns: `Direction2D<'Coordinates> option`
`mirrorAcross axis d` Full Usage: `mirrorAcross axis d` Parameters: axis : `Axis2D<'Units, 'Corodiantes>` d : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`	Mirror a direction across a particular axis. Note that only the direction of the axis affects the result, since directions are position-independent. axis : `Axis2D<'Units, 'Corodiantes>` d : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`
`negativeX` Full Usage: `negativeX` Returns: `Direction2D<'Coordinates>`	Returns: `Direction2D<'Coordinates>`
`negativeY` Full Usage: `negativeY` Returns: `Direction2D<'Coordinates>`	Returns: `Direction2D<'Coordinates>`
`orthonormalize xVector xyVector` Full Usage: `orthonormalize xVector xyVector` Parameters: xVector : `Vector2D<'Units, 'Coordinates>` xyVector : `Vector2D<'Units, 'Coordinatres>` Returns: `(Direction2D<'Coordinates> * Direction2D<'Coordinates>) option`	Attempt to form a pair of perpendicular directions from the two given vectors by performing [Gram-Schmidt normalization](https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process): * The first returned direction will be equal to the direction of the first given vector * The second returned direction will be as close as possible to the second given vector while being perpendicular to the first returned direction xVector : `Vector2D<'Units, 'Coordinates>` xyVector : `Vector2D<'Units, 'Coordinatres>` Returns: `(Direction2D<'Coordinates> * Direction2D<'Coordinates>) option`
`perpendicularTo d` Full Usage: `perpendicularTo d` Parameters: d : `Direction2D<'Coordaintes>` Returns: `Direction2D<'Coordaintes>`	Construct a direction perpendicular to the given direction, by rotating the given direction 90 degrees counterclockwise. This is the same `Direction2D.rotateBy (Angle.degrees 90)` but is more efficient. Alias for `rotateCounterclockwise`. d : `Direction2D<'Coordaintes>` Returns: `Direction2D<'Coordaintes>`
`placeIn reference direction` Full Usage: `placeIn reference direction` Parameters: reference : `Frame2D<'Units, 'GlobalCoordinates, 'LocalCoordinates>` direction : `Direction2D<'LocalCoordinates>` Returns: `Direction2D<'GlobalCoordinates>`	Take a direction defined in local coordinates relative to a given reference frame, and return that direction expressed in global coordinates. reference : `Frame2D<'Units, 'GlobalCoordinates, 'LocalCoordinates>` direction : `Direction2D<'LocalCoordinates>` Returns: `Direction2D<'GlobalCoordinates>`
`positiveX` Full Usage: `positiveX` Returns: `Direction2D<'Coordinates>`	Returns: `Direction2D<'Coordinates>`
`positiveY` Full Usage: `positiveY` Returns: `Direction2D<'Coordinates>`	Returns: `Direction2D<'Coordinates>`
`radians r` Full Usage: `radians r` Parameters: r : `float` Returns: `Direction2D<'Coordinates>`	r : `float` Returns: `Direction2D<'Coordinates>`
`relativeTo frame d` Full Usage: `relativeTo frame d` Parameters: frame : `Frame2D<'Units, 'GlobalCoordaintes, 'LocalCoordinates>` d : `Direction2D<'GlobalCoordinates>` Returns: `Direction2D<'LocalCoordaintes>`	Take a direction defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame. frame : `Frame2D<'Units, 'GlobalCoordaintes, 'LocalCoordinates>` d : `Direction2D<'GlobalCoordinates>` Returns: `Direction2D<'LocalCoordaintes>`
`reverse direction` Full Usage: `reverse direction` Parameters: direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`	direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`
`rotateBy angle direction` Full Usage: `rotateBy angle direction` Parameters: angle : `Angle` direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`	Rotate a direction counterclockwise by a given angle. angle : `Angle` direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`
`rotateClockwise direction` Full Usage: `rotateClockwise direction` Parameters: direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`	direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`
`rotateCounterclockwise direction` Full Usage: `rotateCounterclockwise direction` Parameters: direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`	direction : `Direction2D<'Coordinates>` Returns: `Direction2D<'Coordinates>`
`toAngle d` Full Usage: `toAngle d` Parameters: d : `Direction2D<'Coordinates>` Returns: `Angle`	Convert a direction to a polar angle (the counterclockwise angle from the positive X direction). The result will be in the range -180 to 180 degrees. d : `Direction2D<'Coordinates>` Returns: `Angle`
`toTuple d` Full Usage: `toTuple d` Parameters: d : `Direction2D<'Coordinates>` Returns: `float * float`	{-\| Get the X and Y components of a direction as a tuple (X, Y). d : `Direction2D<'Coordinates>` Returns: `float * float`
`toVector d` Full Usage: `toVector d` Parameters: d : `Direction2D<'Coordiantes>` Returns: `Vector2D<Unitless, 'Coordinates>`	Convert a direction to a unitless vector of length 1. d : `Direction2D<'Coordiantes>` Returns: `Vector2D<Unitless, 'Coordinates>`
`x` Full Usage: `x` Returns: `Direction2D<'Coordinates>`	Returns: `Direction2D<'Coordinates>`
`xComponent d` Full Usage: `xComponent d` Parameters: d : `Direction2D<'Coordinates>` Returns: `float`	Get the X component of the direction. d : `Direction2D<'Coordinates>` Returns: `float`
`xy x y` Full Usage: `xy x y` Parameters: x : `float` y : `float` Returns: `Direction2D<'Coordinates> option`	Get a direction vector from the x and y components. This function takes care of normalizing the x and y components into the unit direction vector. This function also checks for the edge case where the x and y components are both zero. In that case, the function returns `None`. x : `float` y : `float` Returns: `Direction2D<'Coordinates> option`
`xyQuantity x y` Full Usage: `xyQuantity x y` Parameters: x : `Quantity<'Units>` y : `Quantity<'Units>` Returns: `Direction2D<'Coordinates> option`	Get a direction vector from the x and y length components. This function takes care of normalizing the x and y components into the unit direction vector. This function also checks for the edge case where the x and y components are both zero. In that case, the function returns `None`. x : `Quantity<'Units>` y : `Quantity<'Units>` Returns: `Direction2D<'Coordinates> option`
`xyUnsafe x y` Full Usage: `xyUnsafe x y` Parameters: x : `float` y : `float` Returns: `Direction2D<'Coordinates>`	Create a direction vector from the x and y components. This function doesn't perform either zero magnitude checks nor does it normalize the input vectors. This function should only be used with input constants or when you are sure that you aren't going to create a direction with an invalid state. x : `float` y : `float` Returns: `Direction2D<'Coordinates>`
`y` Full Usage: `y` Returns: `Direction2D<'Coordinates>`	Returns: `Direction2D<'Coordinates>`
`yComponent d` Full Usage: `yComponent d` Parameters: d : `Direction2D<'Coordinates>` Returns: `float`	Get the Y component of the direction. d : `Direction2D<'Coordinates>` Returns: `float`