Libraries.Compute.Quaternion Documentation

Quaternion is a class representing a quaternion, which are useful for 3D computer graphics.

Example Code

use Libraries.Compute.Quaternion

Quaternion quaternion

quaternion:Set(1, 2, 3, 4)

number length = quaternion:Length()

output "The length of the quaternion is " + length

Inherits from: Libraries.Language.Object

Summary

Actions Summary Table

ActionsDescription
Add(number x, number y, number z, number w)This action adds the passed values representing a quaternion to this quaternion.
Add(Libraries.Compute.Quaternion quaternion)This action adds the passed quaternion to this quaternion.
Compare(Libraries.Language.Object object)This action compares two object hash codes and returns a CompareResult.
Conjugate()This action conjugates the quaternion.
Copy()This action creates and returns a copy of the quaternion.
DotProduct(number x, number y, number z, number w)This action finds the dot product between this quaternion and the quaternion with the passed x, y, z, and w values.
DotProduct(Libraries.Compute.Quaternion other)This action finds the dot product between this quaternion and the passed quaternion.
DotProduct(number x1, number y1, number z1, number w1, number x2, number y2, number z2, number w2)This action finds the dot product between the two quaternions with the passed x, y, z, and w values.
Equals(Libraries.Language.Object object)This action determines if two objects are equal based on their hash code values.
Exponent(number alpha)This action raises the quaternion to the passed number.
GetAngle()This action gets the angle in degrees of the rotation of the quaternion.
GetAngleAround(Libraries.Compute.Vector3 axis)This action gets the angle in degrees of the rotation around the specified axis.
GetAngleAround(number axisX, number axisY, number axisZ)This action gets the angle in degrees of the rotation around the specified axis.
GetAngleAroundRadians(number axisX, number axisY, number axisZ)This action gets the angle in radians of the rotation around the specified axis.
GetAngleAroundRadians(Libraries.Compute.Vector3 axis)This action gets the angle in radians of the rotation around the specified axis.
GetAngleRadians()This action gets the angle in radians of the rotation of the quaternion.
GetAxisAngle(Libraries.Compute.Vector3 axis)This action gets the axis angle representation of the rotation in degrees of the quaternion.
GetAxisAngleRadians(Libraries.Compute.Vector3 axis)This action gets the axis angle representation of the rotation in radians of the quaternion.
GetGimbalPole()This action gets the pole of the gimbal lock if there is one.
GetHashCode()This action gets the hash code for an object.
GetPitch()This action gets the pitch euler angle in degrees, which is the rotation around the x-axis.
GetPitchRadians()This action gets the pitch euler angle in radians, which is the rotation around the x-axis.
GetRoll()This action gets the roll euler angle in degrees, which is the rotation around the z-axis.
GetRollRadians()This action gets the roll euler angle in radians, which is the rotation around the z-axis.
GetSwingTwist(Libraries.Compute.Vector3 axis, Libraries.Compute.Quaternion swing, Libraries.Compute.Quaternion twist)This action gets the swing rotation and the twist rotation for the specified axis.
GetSwingTwist(number axisX, number axisY, number axisZ, Libraries.Compute.Quaternion swing, Libraries.Compute.Quaternion twist)This action gets the swing rotation and the twist rotation for the specified axis.
GetW()This action gets the w value of the quaternion
GetX()This action gets the x value of the quaternion
GetY()This action gets the y value of the quaternion
GetYaw()This action gets the yaw euler angle in degrees, which is the rotation around the y-axis.
GetYawRadians()This action gets the yaw euler angle in radians, which is the rotation around the y-axis.
GetZ()This action gets the z value of the quaternion
IsIdentity()This action determines whether the quaternion is the identity quaternion.
IsIdentity(number tolerance)This action determines whether the quaternion is the identity quaternion to within the passed tolerance.
Length(number x, number y, number z, number w)This action returns the length of the quaternion with the passed x, y, z, and w values.
Length()This action returns the length of the quaternion.
LengthSquared()This action returns the square of the length of the quaternion.
LengthSquared(number x, number y, number z, number w)This action returns the square of the length of the quaternion with the passed x, y, z, and w values.
Multiply(number scalar)This action multiplies the quaternion by the passed scalar value
Multiply(number x, number y, number z, number w)This action multiplies the quaternion by the passed values representing a quaternion.
Multiply(Libraries.Compute.Quaternion other)This action multiplies the quaternion by the passed quaternion.
Normalize()This action normalizes the quaternion so that its length is between 0 and 1.
Set(number x, number y, number z, number w)This action sets the quaternion's values to the passed values.
Set(Libraries.Compute.Vector3 axis, number angle)This action sets the quaternion from the given axis and the angle around the axis.
Set(Libraries.Compute.Quaternion quaternion)This action sets the quaternion using the x, y, z, and w values from the passed quaternion.
SetEulerAngles(number yaw, number pitch, number roll)This action sets the quaternion to the given euler angles in degrees
SetEulerAnglesRadians(number yaw, number pitch, number roll)This action sets the quaternion to the given euler angles in radians
SetFromAxes(boolean normalizeAxes, number xAxisX, number xAxisY, number xAxisZ, number yAxisX, number yAxisY, number yAxisZ, number zAxisX, number zAxisY, number zAxisZ)This action sets the quaternion from the given x, y, and z axes which all have to be orthogonal.
SetFromAxes(number xAxisX, number xAxisY, number xAxisZ, number yAxisX, number yAxisY, number yAxisZ, number zAxisX, number zAxisY, number zAxisZ)This action sets the quaternion from the given x, y, and z axes which all have to be orthogonal.
SetFromAxis(number x, number y, number z, number degrees)This action sets the quaternion from the given axis and angle around that axis.
SetFromAxis(Libraries.Compute.Vector3 axis, number degrees)This action sets the quaternion from the given axis and angle around that axis.
SetFromAxisRadians(number x, number y, number z, number radians)This action sets the quaternion from the given axis and angle around that axis.
SetFromAxisRadians(Libraries.Compute.Vector3 axis, number radians)This action sets the quaternion from the given axis and angle around that axis.
SetFromCross(Libraries.Compute.Vector3 vector1, Libraries.Compute.Vector3 vector2)This action sets the quaternion to be the rotation between the two passed vectors
SetFromCross(number x1, number y1, number z1, number x2, number y2, number z2)This action sets the quaternion to be the rotation between the two passed vectors
SetFromMatrix(Libraries.Compute.Matrix3 matrix)This action sets the quaternion using the passed matrix.
SetFromMatrix(Libraries.Compute.Matrix4 matrix)This action sets the quaternion using the passed matrix.
SetFromMatrix(boolean normalizeAxes, Libraries.Compute.Matrix3 matrix)This action sets the quaternion using the passed matrix.
SetFromMatrix(boolean normalizeAxes, Libraries.Compute.Matrix4 matrix)This action sets the quaternion using the passed matrix.
SetToIdentity()This action sets the quaternion to the identity quaternion.
SphericalLinearInterpolation(Libraries.Containers.Array<Libraries.Compute.Quaternion> quaternions, Libraries.Containers.Array<number> weights)This action performs a spherical linear interpolation on multiple quaternions and stores the result in the calling quaternion.
SphericalLinearInterpolation(Libraries.Compute.Quaternion endQuaternion, number alpha)This action performs a spherical linear interpolation between this quaternion and the passed quaternion by the passed alpha value.
SphericalLinearInterpolation(Libraries.Containers.Array<Libraries.Compute.Quaternion> quaternions)This action performs a spherical linear interpolation on multiple quaternions and stores the result in the calling quaternion.
ToMatrix()This action builds a 4x4 matrix (a Matrix4 object) with the rotation matrix represented by this quaternion.
Transform(Libraries.Compute.Vector3 vector)This action transforms the passed vector using the quaternion.

Actions Documentation

Add(number x, number y, number z, number w)

This action adds the passed values representing a quaternion to this quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)
    
    quaternion:Add(5, 6, 7, 8)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The sum is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The sum of the quaternions

Add(Libraries.Compute.Quaternion quaternion)

This action adds the passed quaternion to this quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion leftHandSide
    Quaternion rightHandSide

    leftHandSide:Set(1, 2, 3, 4)
    rightHandSide:Set(5, 6, 7, 8)
    
    leftHandSide:Add(rightHandSide)

    number x = leftHandSide:GetX()
    number y = leftHandSide:GetY()
    number z = leftHandSide:GetZ()
    number w = leftHandSide:GetW()

    output "The sum is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The sum of the quaternions

Compare(Libraries.Language.Object object)

This action compares two object hash codes and returns a CompareResult. The compare result is either larger if this hash code is larger than the object passed as a parameter, smaller, or equal.

Example Code

use Libraries.Language.Support.CompareResult
        Object o
        Object t
        CompareResult result = o:Compare(t)

Parameters

Return

Libraries.Language.Support.CompareResult: The Compare result, Smaller, Equal, or Larger.

Conjugate()

This action conjugates the quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Conjugate()

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Return

Libraries.Compute.Quaternion: The conjugate of the quaternion

Copy()

This action creates and returns a copy of the quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    quaternion:Set(1, 2, 3, 4)

    Quaternion copy
    
    copy = quaternion:Copy()

    number x = copy:GetX()
    number y = copy:GetY()
    number z = copy:GetZ()
    number w = copy:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Return

Libraries.Compute.Quaternion: a new quaternion that is a copy of this quaternion

DotProduct(number x, number y, number z, number w)

This action finds the dot product between this quaternion and the quaternion with the passed x, y, z, and w values.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number dotProduct = quaternion:DotProduct(5, 6, 7, 8)

    output "The dot product is " + dotProduct

Parameters

Return

number: The dot product of the two quaternions

DotProduct(Libraries.Compute.Quaternion other)

This action finds the dot product between this quaternion and the passed quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    Quaternion other

    quaternion:Set(1, 2, 3, 4)
    other:Set(5, 6, 7, 8)

    number dotProduct = quaternion:DotProduct(other)

    output "The dot product is " + dotProduct

Parameters

Return

number: The dot product of the two quaternions

DotProduct(number x1, number y1, number z1, number w1, number x2, number y2, number z2, number w2)

This action finds the dot product between the two quaternions with the passed x, y, z, and w values.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    number dotProduct = quaternion:DotProduct(1, 2, 3, 4, 5, 6, 7, 8)

    output "The dot product is " + dotProduct

Parameters

Return

number: The dot product of the two quaternions

Equals(Libraries.Language.Object object)

This action determines if two objects are equal based on their hash code values.

Example Code

use Libraries.Language.Object
        use Libraries.Language.Types.Text
        Object o
        Text t
        boolean result = o:Equals(t)

Parameters

Return

boolean: True if the hash codes are equal and false if they are not equal.

Exponent(number alpha)

This action raises the quaternion to the passed number.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Exponent(3)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion raised to alpha

GetAngle()

This action gets the angle in degrees of the rotation of the quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number degrees = quaternion:GetAngle()

    output "The angle in degrees is " + degrees

Return

number: The angle in degrees of the rotation

GetAngleAround(Libraries.Compute.Vector3 axis)

This action gets the angle in degrees of the rotation around the specified axis. The axis must be normalized.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion

    Vector3 axis
    axis:Set(5, 4, 3)
    axis:Normalize()

    quaternion:Set(1, 2, 3, 4)

    number rotation = quaternion:GetAngleAround(axis)

    output "The rotation around is " + rotation

Parameters

Return

number: The angle in degrees of the rotation around the passed axis

GetAngleAround(number axisX, number axisY, number axisZ)

This action gets the angle in degrees of the rotation around the specified axis. The axis must be normalized.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number rotation = quaternion:GetAngleAround(1, 0, 0)

    output "The rotation around is " + rotation

Parameters

Return

number: The angle in degrees of the rotation around the passed axis

GetAngleAroundRadians(number axisX, number axisY, number axisZ)

This action gets the angle in radians of the rotation around the specified axis. The axis must be normalized.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number rotation = quaternion:GetAngleAroundRadians(1, 0, 0)

    output "The rotation around is " + rotation

Parameters

Return

number: The angle in radians of the rotation around the passed axis

GetAngleAroundRadians(Libraries.Compute.Vector3 axis)

This action gets the angle in radians of the rotation around the specified axis. The axis must be normalized.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion

    Vector3 axis
    axis:Set(5, 4, 3)
    axis:Normalize()

    quaternion:Set(1, 2, 3, 4)

    number rotation = quaternion:GetAngleAroundRadians(axis)

    output "The rotation around is " + rotation

Parameters

Return

number: The angle in radians of the rotation around the passed axis

GetAngleRadians()

This action gets the angle in radians of the rotation of the quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number radians = quaternion:GetAngleRadians()

    output "The angle in radians is " + radians

Return

number: The angle in radians of the rotation

GetAxisAngle(Libraries.Compute.Vector3 axis)

This action gets the axis angle representation of the rotation in degrees of the quaternion. The passed axis will be given the axis of the rotation and the action will return the rotation angle in degrees. The passed vector is altered by this action. The existing values of the vector are ignored.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion
    Vector3 axis

    quaternion:Set(1, 2, 3, 4)

    number degrees = quaternion:GetAxisAngle(axis)

    number x = axis:GetX()
    number y = axis:GetY()
    number z = axis:GetZ()

    output "The rotation axis is [" + x + ", " + y + ", " + z + "]"
    output "The rotation angle is " + degrees + " degrees"

Parameters

Return

number: The angle in degrees

GetAxisAngleRadians(Libraries.Compute.Vector3 axis)

This action gets the axis angle representation of the rotation in radians of the quaternion. The passed axis will be given the axis of the rotation and the action will return the rotation angle in radians. The passed vector is altered by this action. The existing values of the vector are ignored.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion
    Vector3 axis

    quaternion:Set(1, 2, 3, 4)

    number radians = quaternion:GetAxisAngleRadians(axis)

    number x = axis:GetX()
    number y = axis:GetY()
    number z = axis:GetZ()

    output "The rotation axis is [" + x + ", " + y + ", " + z + "]"
    output "The rotation angle is " + radians + " radians"

Parameters

Return

number: The angle in radians

GetGimbalPole()

This action gets the pole of the gimbal lock if there is one.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number pole = quaternion:GetGimbalPole()

    if pole = 1
        output "The gimbal pole is the north pole."
    elseif pole = -1
        output "The gimbal pole is the south pole."
    else
        output "There is no gimbal pole."
    end

Return

integer: : 1 for the north pole, -1 for the south pole, 0 if there is no gimbal lock

GetHashCode()

This action gets the hash code for an object.

Example Code

Object o
        integer hash = o:GetHashCode()

Return

integer: The integer hash code of the object.

GetPitch()

This action gets the pitch euler angle in degrees, which is the rotation around the x-axis. The quaternion must be normalized before calling this action.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number pitch = quaternion:GetPitch()

    output "The pitch in degrees is " + pitch

Return

number: The rotation around the x-axis in degrees

GetPitchRadians()

This action gets the pitch euler angle in radians, which is the rotation around the x-axis. The quaternion must be normalized before calling this action.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number pitch = quaternion:GetPitchRadians()

    output "The pitch in radians is " + pitch

Return

number: The rotation around the x-axis in radians

GetRoll()

This action gets the roll euler angle in degrees, which is the rotation around the z-axis. The quaternion must be normalized before calling this action.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number roll = quaternion:GetRoll()

    output "The roll in degrees is " + roll

Return

number: The rotation around the z-axis in degrees

GetRollRadians()

This action gets the roll euler angle in radians, which is the rotation around the z-axis. The quaternion must be normalized before calling this action.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number roll = quaternion:GetRollRadians()

    output "The roll in radians is " + roll

Return

number: The rotation around the z-axis in radians

GetSwingTwist(Libraries.Compute.Vector3 axis, Libraries.Compute.Quaternion swing, Libraries.Compute.Quaternion twist)

This action gets the swing rotation and the twist rotation for the specified axis. The twist rotation is the rotation around the specified axis. The swing rotation is the rotation of the specified axis itself, which is the rotation around an axis perpendicular to that axis. The passed axis should be normalized.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion
    Quaternion swing
    Quaternion twist

    Vector3 axis
    axis:Set(4, 7, 3)
    axis:Normalize()

    quaternion:Set(1, 2, 3, 4)

    quaternion:GetSwingTwist(axis, swing, twist)

    number swingX = swing:GetX()
    number swingY = swing:GetY()
    number swingZ = swing:GetZ()
    number swingW = swing:GetW()

    number twistX = twist:GetX()
    number twistY = twist:GetY()
    number twistZ = twist:GetZ()
    number twistW = twist:GetW()

    output "The swing is [" + swingX + ", " + swingY + ", " + swingZ + ", " + swingW + "]"
    output "The twist is [" + twistX + ", " + twistY + ", " + twistZ + ", " + twistW + "]"

Parameters

GetSwingTwist(number axisX, number axisY, number axisZ, Libraries.Compute.Quaternion swing, Libraries.Compute.Quaternion twist)

This action gets the swing rotation and the twist rotation for the specified axis. The twist rotation is the rotation around the specified axis. The swing rotation is the rotation of the specified axis itself, which is the rotation around an axis perpendicular to that axis. The passed axis should be normalized.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    Quaternion swing
    Quaternion twist

    quaternion:Set(1, 2, 3, 4)

    quaternion:GetSwingTwist(0, 0, 1, swing, twist)

    number swingX = swing:GetX()
    number swingY = swing:GetY()
    number swingZ = swing:GetZ()
    number swingW = swing:GetW()

    number twistX = twist:GetX()
    number twistY = twist:GetY()
    number twistZ = twist:GetZ()
    number twistW = twist:GetW()

    output "The swing is [" + swingX + ", " + swingY + ", " + swingZ + ", " + swingW + "]"
    output "The twist is [" + twistX + ", " + twistY + ", " + twistZ + ", " + twistW + "]"

Parameters

GetW()

This action gets the w value of the quaternion

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number w = quaternion:GetW()

    output "The w value of the quaternion is " + w

Return

number: The w value of the quaternion

GetX()

This action gets the x value of the quaternion

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number x = quaternion:GetX()

    output "The x value of the quaternion is " + x

Return

number: The x value of the quaternion

GetY()

This action gets the y value of the quaternion

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number y = quaternion:GetY()

    output "The y value of the quaternion is " + y

Return

number: The y value of the quaternion

GetYaw()

This action gets the yaw euler angle in degrees, which is the rotation around the y-axis. The quaternion must be normalized before calling this action.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number yaw = quaternion:GetYaw()

    output "The yaw in degrees is " + yaw

Return

number: The rotation around the y-axis in degrees

GetYawRadians()

This action gets the yaw euler angle in radians, which is the rotation around the y-axis. The quaternion must be normalized before calling this action.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number yaw = quaternion:GetYawRadians()

    output "The yaw in radians is " + yaw

Return

number: The rotation around the y-axis in radians

GetZ()

This action gets the z value of the quaternion

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number z = quaternion:GetZ()

    output "The z value of the quaternion is " + z

Return

number: The z value of the quaternion

IsIdentity()

This action determines whether the quaternion is the identity quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    if quaternion:IsIdentity()
        output "The quaternion is the identity quaternion"
    else
        output "The quaternion is not the identity quaternion"
    end

Return

boolean: true if the quaternion is the identity quaternion, false otherwise

IsIdentity(number tolerance)

This action determines whether the quaternion is the identity quaternion to within the passed tolerance.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    if quaternion:IsIdentity(0.001)
        output "The quaternion is the identity quaternion"
    else
        output "The quaternion is not the identity quaternion"
    end

Parameters

Return

boolean: true if the quaternion is the identity quaternion to within the passed tolerance, false otherwise

Length(number x, number y, number z, number w)

This action returns the length of the quaternion with the passed x, y, z, and w values.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    number length = quaternion:Length(1, 2, 3, 4)
    
    output "The length of the quaternion is " + length

Parameters

Return

number: The length of the quaternion

Length()

This action returns the length of the quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number length = quaternion:Length()
    
    output "The length of the quaternion is " + length

Return

number: The length of the quaternion

LengthSquared()

This action returns the square of the length of the quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    quaternion:Set(1, 2, 3, 4)
    
    number lengthSquared = quaternion:LengthSquared()

    output "The length squared is " + lengthSquared

Return

number: The square of the length of the quaternion

LengthSquared(number x, number y, number z, number w)

This action returns the square of the length of the quaternion with the passed x, y, z, and w values.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    number lengthSquared = quaternion:LengthSquared(1, 2, 3, 4)

    output "The length squared is " + lengthSquared

Parameters

Return

number: The square of the length of the quaternion

Multiply(number scalar)

This action multiplies the quaternion by the passed scalar value

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    quaternion:Set(1, 2, 3, 4)

    quaternion:Multiply(2)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after being multiplied by the scalar

Multiply(number x, number y, number z, number w)

This action multiplies the quaternion by the passed values representing a quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)
    
    quaternion:Multiply(5, 6, 7, 8)
    
    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The product is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The product of the two quaternions

Multiply(Libraries.Compute.Quaternion other)

This action multiplies the quaternion by the passed quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion multiplicand
    Quaternion multiplier

    multiplicand:Set(1, 2, 3, 4)
    multiplier:Set(5, 6, 7, 8)
    
    multiplicand:Multiply(multiplier)

    number x = multiplicand:GetX()
    number y = multiplicand:GetY()
    number z = multiplicand:GetZ()
    number w = multiplicand:GetW()
    
    output "The product is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The product of the two quaternions

Normalize()

This action normalizes the quaternion so that its length is between 0 and 1.

Example Code

use Libraries.Compute.Quaternion
    
    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    quaternion:Normalize()

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The new quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Return

Libraries.Compute.Quaternion: The normalized quaternion

Set(number x, number y, number z, number w)

This action sets the quaternion's values to the passed values.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:Set(1, 2, 3, 4)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

Set(Libraries.Compute.Vector3 axis, number angle)

This action sets the quaternion from the given axis and the angle around the axis.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion

    Vector3 axis
    axis:Set(1, 0, 0)

    quaternion:Set(axis, 45)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

Set(Libraries.Compute.Quaternion quaternion)

This action sets the quaternion using the x, y, z, and w values from the passed quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    Quaternion setQuaternion

    setQuaternion:Set(1, 2, 3, 4)

    quaternion:Set(setQuaternion)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetEulerAngles(number yaw, number pitch, number roll)

This action sets the quaternion to the given euler angles in degrees

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion

    quaternion:SetEulerAngles(45, 30, 60)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetEulerAnglesRadians(number yaw, number pitch, number roll)

This action sets the quaternion to the given euler angles in radians

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Math

    Math math

    Quaternion quaternion

    quaternion:SetEulerAnglesRadians(math:pi / 4, math:pi / 6, math:pi / 3)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()
    
    output "The quaternion is: [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromAxes(boolean normalizeAxes, number xAxisX, number xAxisY, number xAxisZ, number yAxisX, number yAxisY, number yAxisZ, number zAxisX, number zAxisY, number zAxisZ)

This action sets the quaternion from the given x, y, and z axes which all have to be orthogonal.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    quaternion:SetFromAxes(true, 4, 0, 5, 0, 4, 5, 0, 0, 4)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromAxes(number xAxisX, number xAxisY, number xAxisZ, number yAxisX, number yAxisY, number yAxisZ, number zAxisX, number zAxisY, number zAxisZ)

This action sets the quaternion from the given x, y, and z axes which all have to be orthogonal.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    quaternion:SetFromAxes(0.625, 0, 0.781, 0, 0.625, 0.781, 0, 0, 1)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromAxis(number x, number y, number z, number degrees)

This action sets the quaternion from the given axis and angle around that axis.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    quaternion:SetFromAxis(1, 0, 0, 45)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromAxis(Libraries.Compute.Vector3 axis, number degrees)

This action sets the quaternion from the given axis and angle around that axis.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion

    Vector3 axis
    axis:Set(1, 0, 0)
    
    quaternion:SetFromAxis(axis, 45)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromAxisRadians(number x, number y, number z, number radians)

This action sets the quaternion from the given axis and angle around that axis.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Math
    
    Math math

    Quaternion quaternion
    
    quaternion:SetFromAxisRadians(1, 0, 0, math:pi / 4)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromAxisRadians(Libraries.Compute.Vector3 axis, number radians)

This action sets the quaternion from the given axis and angle around that axis.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3
    use Libraries.Compute.Math

    Math math

    Quaternion quaternion

    Vector3 axis
    axis:Set(1, 0, 0)
    
    quaternion:SetFromAxisRadians(axis, math:pi / 4)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromCross(Libraries.Compute.Vector3 vector1, Libraries.Compute.Vector3 vector2)

This action sets the quaternion to be the rotation between the two passed vectors

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion

    Vector3 first
    Vector3 second

    first:Set(2, 3, 4)
    second:Set(4, 3, 6)
    
    quaternion:SetFromCross(first, second)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromCross(number x1, number y1, number z1, number x2, number y2, number z2)

This action sets the quaternion to be the rotation between the two passed vectors

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    quaternion:SetFromCross(2, 3, 4, 4, 3, 6)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromMatrix(Libraries.Compute.Matrix3 matrix)

This action sets the quaternion using the passed matrix.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Matrix3
    
    Quaternion quaternion

    Matrix3 matrix
    matrix:Set(4, 0, 5, 0, 4, 5, 0, 0, 4)

    quaternion:SetFromMatrix(matrix)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromMatrix(Libraries.Compute.Matrix4 matrix)

This action sets the quaternion using the passed matrix.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Matrix4
    
    Quaternion quaternion

    Matrix4 matrix
    matrix:Set(4, 0, 5, 0, 0, 4, 5, 0, 0, 0, 4, 0, 0, 0, 0, 4)

    quaternion:SetFromMatrix(matrix)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromMatrix(boolean normalizeAxes, Libraries.Compute.Matrix3 matrix)

This action sets the quaternion using the passed matrix.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Matrix3
    
    Quaternion quaternion

    Matrix3 matrix
    matrix:Set(4, 0, 5, 0, 4, 5, 0, 0, 4)

    quaternion:SetFromMatrix(true, matrix)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetFromMatrix(boolean normalizeAxes, Libraries.Compute.Matrix4 matrix)

This action sets the quaternion using the passed matrix.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Matrix4
    
    Quaternion quaternion

    Matrix4 matrix
    matrix:Set(4, 0, 5, 0, 0, 4, 5, 0, 0, 0, 4, 0, 0, 0, 0, 4)

    quaternion:SetFromMatrix(true, matrix)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion after setting

SetToIdentity()

This action sets the quaternion to the identity quaternion.

Example Code

use Libraries.Compute.Quaternion

    Quaternion quaternion
    
    quaternion:SetToIdentity()

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The identity quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Return

Libraries.Compute.Quaternion: The quaternion as the identity quaternion

SphericalLinearInterpolation(Libraries.Containers.Array<Libraries.Compute.Quaternion> quaternions, Libraries.Containers.Array<number> weights)

This action performs a spherical linear interpolation on multiple quaternions and stores the result in the calling quaternion.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Containers.Array

    Array<Quaternion> quaternions
    Array<number> weights

    Quaternion quaternion1
    quaternion1:Set(1, 2, 3, 4)

    Quaternion quaternion2
    quaternion2:Set(5, 6, 7, 8)

    Quaternion quaternion3
    quaternion3:Set(9, 10, 11, 12)

    Quaternion quaternion4
    quaternion4:Set(13, 14, 15, 16)

    quaternions:Add(quaternion2)
    quaternions:Add(quaternion3)
    quaternions:Add(quaternion4)

    weights:Add(0.5)
    weights:Add(0.5)
    weights:Add(0.5)

    quaternion1:SphericalLinearInterpolation(quaternions, weights)

    number x = quaternion1:GetX()
    number y = quaternion1:GetY()
    number z = quaternion1:GetZ()
    number w = quaternion1:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion with the result of all the spherical linear interpolations

SphericalLinearInterpolation(Libraries.Compute.Quaternion endQuaternion, number alpha)

This action performs a spherical linear interpolation between this quaternion and the passed quaternion by the passed alpha value.

Example Code

use Libraries.Compute.Quaternion
    
    Quaternion quaternion
    Quaternion endQuaternion

    quaternion:Set(1, 2, 3, 4)
    endQuaternion:Set(5, 4, 6, 2)

    quaternion:SphericalLinearInterpolation(endQuaternion, 0.5)

    number x = quaternion:GetX()
    number y = quaternion:GetY()
    number z = quaternion:GetZ()
    number w = quaternion:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The spherical linear interpolation between the two quaternions

SphericalLinearInterpolation(Libraries.Containers.Array<Libraries.Compute.Quaternion> quaternions)

This action performs a spherical linear interpolation on multiple quaternions and stores the result in the calling quaternion.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Containers.Array

    Array<Quaternion> quaternions

    Quaternion quaternion1
    quaternion1:Set(1, 2, 3, 4)

    Quaternion quaternion2
    quaternion2:Set(5, 6, 7, 8)

    Quaternion quaternion3
    quaternion3:Set(9, 10, 11, 12)

    Quaternion quaternion4
    quaternion4:Set(13, 14, 15, 16)

    quaternions:Add(quaternion2)
    quaternions:Add(quaternion3)
    quaternions:Add(quaternion4)

    quaternion1:SphericalLinearInterpolation(quaternions)

    number x = quaternion1:GetX()
    number y = quaternion1:GetY()
    number z = quaternion1:GetZ()
    number w = quaternion1:GetW()

    output "The quaternion is [" + x + ", " + y + ", " + z + ", " + w + "]"

Parameters

Return

Libraries.Compute.Quaternion: The quaternion with the result of all the spherical linear interpolations

ToMatrix()

This action builds a 4x4 matrix (a Matrix4 object) with the rotation matrix represented by this quaternion.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Matrix4

    Quaternion quaternion
    Matrix4 matrix

    quaternion:Set(1, 2, 3, 4)

    matrix = quaternion:ToMatrix()

    number row0column0 = matrix:row0column0
    number row0column1 = matrix:row0column1
    number row0column2 = matrix:row0column2
    number row0column3 = matrix:row0column3
    number row1column0 = matrix:row1column0
    number row1column1 = matrix:row1column1
    number row1column2 = matrix:row1column2
    number row1column3 = matrix:row1column3
    number row2column0 = matrix:row2column0
    number row2column1 = matrix:row2column1
    number row2column2 = matrix:row2column2
    number row2column3 = matrix:row2column3
    number row3column0 = matrix:row3column0
    number row3column1 = matrix:row3column1
    number row3column2 = matrix:row3column2
    number row3column3 = matrix:row3column3

    output "The matrix is:"
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + ", " + row0column3 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + ", " + row1column3 + "|"
    output "|" + row2column0 + ", " + row2column1 + ", " + row2column2 + ", " + row2column3 + "|"
    output "|" + row3column0 + ", " + row3column1 + ", " + row3column2 + ", " + row3column3 + "|"

Return

Libraries.Compute.Matrix4: The matrix built from this quaternion

Transform(Libraries.Compute.Vector3 vector)

This action transforms the passed vector using the quaternion.

Example Code

use Libraries.Compute.Quaternion
    use Libraries.Compute.Vector3

    Quaternion quaternion
    Vector3 vector

    quaternion:Set(1, 2, 3, 4)
    vector:Set(3, 4, 7)

    quaternion:Transform(vector)

    number x = vector:GetX()
    number y = vector:GetY()
    number z = vector:GetZ()

    output "The transformed vector is [" + x + ", " + y + ", " + z + "]"

Parameters

Return

Libraries.Compute.Vector3: The transformed vector