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Auki::Ark::MathHelpers

Collection of helper functions.

Public Types​

Name
enum classPoseAxis { Right = 0, Up = 1, Forward = 2}
Defines common directions.

Public Functions​

Name
floatXY2Deg(float x, float y)
Returns angle for point with coordinates X and Y in degrees.
floatNominalYRotation(Matrix4x4 m)
Returns Y rotation of a specific Matrix4x4 in degrees.
voidLogMatrix(Matrix4x4 m, string label)
Logs a Matrix4x4 in the Unity console.
stringPoseConstructorString(Pose p)
Converts a Pose to string format.
stringMatrixConstructorString(Matrix4x4 m, string name)
Converts a Matrix4x4 to string format.
floatAngleIn(Quaternion q)
Gives sum of rotation around all axes of a quaternion in degrees.
floatAngleBetween(Quaternion q1, Quaternion q2)
Gives angle between 2 quaternion rotations in degrees.
Quaternion float amountOfRectificationInDegreesClosestRotationWithSameAngleToUp(Quaternion toImitate, Quaternion toRectify)
Matrix4x4PoseLocalToWorldMatrix(Pose pose)
Constructs a local to world matrix for a pose.
Matrix4x4PoseWorldToLocalMatrix(Pose pose)
Constructs a world to local matrix for a pose.
Matrix4x4Pose1ToPose2Matrix(Pose p1, Pose p2)
Converts a pose 1 to pose 2 transform matrix.
Matrix4x4 float upErrorComputeCalibrationMatrixWhileRestrictingRotationToYAxis(Pose officialPose, Pose observedPose, bool observedPoseIsAlreadyRectified =false)
Vector3ExtractScaleFromMatrix(Matrix4x4 matrix)
Extracts scale in Vector3 format from a matrix.
Matrix4x4TransformParentToLocalMatrix(Transform t)
Constructs a transformation matrix that converts from parent to local coordinate system.
Matrix4x4TransformLocalToParentMatrix(Transform t)
Constructs a transformation matrix that converts from local to parent coordinate system.
voidSetTransformByMatrix(Transform transform, Matrix4x4 matrix, bool skipLocalScale =true)
Given a matrix m sets a transform t's rotation and position and scale so that t's local coordinate transformation (from node to parent) is m.
voidLeftMultiplyTransform(Transform transform, Matrix4x4 matrix, bool skipLocalScale =true)
Multiplies input transform by a specified transformation matrix (i.e. T*M).
Pose float rectificationAmountSnapPoseAxisTo(Pose pose, PoseAxis axis, Vector3 direction)
Vector3SelectAxis(Pose pose, PoseAxis axis)
Given a Pose and PoseAxis, returns the corresponding axis of the pose.
Pose float PoseAxis Vector3 verticalDirectionSnapPoseToNearestVertical(Pose pose)
QuaternionRestrictQuaternionToY(Quaternion q)
Keeps rotation only around the Y-axis.

Public Attributes​

Name
QuaternionrectifiedRotation
Returns a pose that has as close as possible angle to up as the 'toImitate' pose and also the absolute amount of rotation correction that was needed to achieve it.
Matrix4x4calibrationMatrix
0. takes the observed pose of an object and the official pose, in some other coordinate system
PoserectifiedPose
Returns a new pose that has a specific axis pointing in a given direction and the absolute amount of rotation correction needed to achieve this.
Pose floatamountOfRectificationInDegrees
Pose float PoseAxisaxis

Public Types Documentation​

enum PoseAxis​

EnumeratorValueDescription
Right0Right direction.
Up1Up direction.
Forward2Forward direction.

Defines common directions.

Public Functions Documentation​

function XY2Deg​

static float XY2Deg(
    float x,
    float y
)

Returns angle for point with coordinates X and Y in degrees.

Parameters:

  • x X coordinate
  • y Y coordinate

Return: Angle in degrees

function NominalYRotation​

static float NominalYRotation(
    Matrix4x4 m
)

Returns Y rotation of a specific Matrix4x4 in degrees.

Parameters:

  • m Input matrix

Return: Angle in degrees

function LogMatrix​

static void LogMatrix(
    Matrix4x4 m,
    string label
)

Logs a Matrix4x4 in the Unity console.

Parameters:

  • m Matrix to print
  • label Label before data

function PoseConstructorString​

static string PoseConstructorString(
    Pose p
)

Converts a Pose to string format.

Parameters:

  • p Input pose

Return: String representation of input pose

function MatrixConstructorString​

static string MatrixConstructorString(
    Matrix4x4 m,
    string name
)

Converts a Matrix4x4 to string format.

Parameters:

  • m Input matrix
  • name Name of matrix in string

Return: String representation of input matrix

function AngleIn​

static float AngleIn(
    Quaternion q
)

Gives sum of rotation around all axes of a quaternion in degrees.

Parameters:

  • q Input rotation quaternion

Return: Angle in degrees

function AngleBetween​

static float AngleBetween(
    Quaternion q1,
    Quaternion q2
)

Gives angle between 2 quaternion rotations in degrees.

Parameters:

  • q1 Rotation quaternion 1
  • q2 Rotation quaternion 2

Return: Angle in degrees

function ClosestRotationWithSameAngleToUp​

static Quaternion float amountOfRectificationInDegrees ClosestRotationWithSameAngleToUp(
    Quaternion toImitate,
    Quaternion toRectify
)

function PoseLocalToWorldMatrix​

static Matrix4x4 PoseLocalToWorldMatrix(
    Pose pose
)

Constructs a local to world matrix for a pose.

Parameters:

  • pose Input pose

Return: Local to world matrix for input pose

function PoseWorldToLocalMatrix​

static Matrix4x4 PoseWorldToLocalMatrix(
    Pose pose
)

Constructs a world to local matrix for a pose.

Parameters:

  • pose Input pose

Return: World to local matrix for input pose

function Pose1ToPose2Matrix​

static Matrix4x4 Pose1ToPose2Matrix(
    Pose p1,
    Pose p2
)

Converts a pose 1 to pose 2 transform matrix.

Parameters:

  • p1 Pose to convert from
  • p2 Pose to convert to

Return: Pose 1 to pose 2 transformation matrix

function ComputeCalibrationMatrixWhileRestrictingRotationToYAxis​

static Matrix4x4 float upError ComputeCalibrationMatrixWhileRestrictingRotationToYAxis(
    Pose officialPose,
    Pose observedPose,
    bool observedPoseIsAlreadyRectified =false
)

function ExtractScaleFromMatrix​

static Vector3 ExtractScaleFromMatrix(
    Matrix4x4 matrix
)

Extracts scale in Vector3 format from a matrix.

Parameters:

  • matrix Input matrix

Return: Vector3 with scale values

function TransformParentToLocalMatrix​

static Matrix4x4 TransformParentToLocalMatrix(
    Transform t
)

Constructs a transformation matrix that converts from parent to local coordinate system.

Parameters:

  • t Local

Return:

function TransformLocalToParentMatrix​

static Matrix4x4 TransformLocalToParentMatrix(
    Transform t
)

Constructs a transformation matrix that converts from local to parent coordinate system.

Parameters:

  • t Local space transformation matrix

Return: Parent space transformation matrix

function SetTransformByMatrix​

static void SetTransformByMatrix(
    Transform transform,
    Matrix4x4 matrix,
    bool skipLocalScale =true
)

Given a matrix m sets a transform t's rotation and position and scale so that t's local coordinate transformation (from node to parent) is m.

Parameters:

  • transform Transform to multiply
  • matrix Matrix to multiply by
  • skipLocalScale A boolean to skip the computation of localScale, defaults to true

function LeftMultiplyTransform​

static void LeftMultiplyTransform(
    Transform transform,
    Matrix4x4 matrix,
    bool skipLocalScale =true
)

Multiplies input transform by a specified transformation matrix (i.e. T*M).

Parameters:

  • transform Transform to multiply
  • matrix Matrix to multiply by
  • skipLocalScale A boolean to skip the computation of localScale, defaults to true

function SnapPoseAxisTo​

static Pose float rectificationAmount SnapPoseAxisTo(
    Pose pose,
    PoseAxis axis,
    Vector3 direction
)

function SelectAxis​

static Vector3 SelectAxis(
    Pose pose,
    PoseAxis axis
)

Given a Pose and PoseAxis, returns the corresponding axis of the pose.

Parameters:

  • pose
  • axis

Return: A Vector3 that is either pose.forward, pose.right, or pose.up

function SnapPoseToNearestVertical​

static Pose float PoseAxis Vector3 verticalDirection SnapPoseToNearestVertical(
    Pose pose
)

function RestrictQuaternionToY​

static Quaternion RestrictQuaternionToY(
    Quaternion q
)

Keeps rotation only around the Y-axis.

Parameters:

  • q Rotation quaternion

Return: New rotation quaternion that has only rotation around the Y-axis

Public Attributes Documentation​

variable rectifiedRotation​

static Quaternion rectifiedRotation;

Returns a pose that has as close as possible angle to up as the 'toImitate' pose and also the absolute amount of rotation correction that was needed to achieve it.

Parameters:

  • toImitate Pose whose up axis will be used as reference
  • toRectify Pose to rectify

Return: Pose that has as close as possible angle to up as 'toImitate' and absolute amount of rotation correction

variable calibrationMatrix​

static Matrix4x4 calibrationMatrix;
  1. takes the observed pose of an object and the official pose, in some other coordinate system

Parameters:

  • officialPose
  • observedPose
  • observedPoseIsAlreadyRectified

Return: the latter matrix and the angle difference between observedPose and rectifiedObservedPose

  1. adjusts the observed pose to a new pose "rectifiedObservedPose" that only differs from the from the official pose by a rotation about the Y axis and a translation (i.e., rectifiedObservedPose has "the same angle to up" as officialPose)
  2. compute the matrix that maps rectifiedObservedPose to officialPose, zeroes out things in the matrix that should be 0 but for floating point errors if the observed pose rotational component is known to already be a rotation around the Y axis of the official pose, one can set the third optional argument to true

variable rectifiedPose​

static Pose rectifiedPose;

Returns a new pose that has a specific axis pointing in a given direction and the absolute amount of rotation correction needed to achieve this.

Parameters:

  • pose Starting pose
  • axis Axis that should be pointing in direction
  • direction Direction that the axis should point in
  • pose Pose to snap to nearest vertical

Return:

  • New pose with given axis pointing in given direction plus the absolute amount of rotation correction
  • Snapped pose, total amount of rotation that was needed for the rectification, axis which was snapped to the vertical and vertical direction to which the snapping occured (either Vector3.up or Vector3.down)

Returns a 'rectified' form of the input pose that is 'snapped' to the nearest vertical axis.

variable amountOfRectificationInDegrees​

static Pose float amountOfRectificationInDegrees;

variable axis​

static Pose float PoseAxis axis;