Auki::Ark::MathHelpers

Collection of helper functions.

Public Types

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

Public Functions

	Name
float	XY2Deg(float x, float y) Returns angle for point with coordinates X and Y in degrees.
float	NominalYRotation(Matrix4x4 m) Returns Y rotation of a specific Matrix4x4 in degrees.
void	LogMatrix(Matrix4x4 m, string label) Logs a Matrix4x4 in the Unity console.
string	PoseConstructorString(Pose p) Converts a Pose to string format.
string	MatrixConstructorString(Matrix4x4 m, string name) Converts a Matrix4x4 to string format.
float	AngleIn(Quaternion q) Gives sum of rotation around all axes of a quaternion in degrees.
float	AngleBetween(Quaternion q1, Quaternion q2) Gives angle between 2 quaternion rotations in degrees.
Quaternion float amountOfRectificationInDegrees	ClosestRotationWithSameAngleToUp(Quaternion toImitate, Quaternion toRectify)
Matrix4x4	PoseLocalToWorldMatrix(Pose pose) Constructs a local to world matrix for a pose.
Matrix4x4	PoseWorldToLocalMatrix(Pose pose) Constructs a world to local matrix for a pose.
Matrix4x4	Pose1ToPose2Matrix(Pose p1, Pose p2) Converts a pose 1 to pose 2 transform matrix.
Matrix4x4 float upError	ComputeCalibrationMatrixWhileRestrictingRotationToYAxis(Pose officialPose, Pose observedPose, bool observedPoseIsAlreadyRectified =false)
Vector3	ExtractScaleFromMatrix(Matrix4x4 matrix) Extracts scale in Vector3 format from a matrix.
Matrix4x4	TransformParentToLocalMatrix(Transform t) Constructs a transformation matrix that converts from parent to local coordinate system.
Matrix4x4	TransformLocalToParentMatrix(Transform t) Constructs a transformation matrix that converts from local to parent coordinate system.
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.
void	LeftMultiplyTransform(Transform transform, Matrix4x4 matrix, bool skipLocalScale =true) Multiplies input transform by a specified transformation matrix (i.e. T*M).
Pose float rectificationAmount	SnapPoseAxisTo(Pose pose, PoseAxis axis, Vector3 direction)
Vector3	SelectAxis(Pose pose, PoseAxis axis) Given a Pose and PoseAxis, returns the corresponding axis of the pose.
Pose float PoseAxis Vector3 verticalDirection	SnapPoseToNearestVertical(Pose pose)
Quaternion	RestrictQuaternionToY(Quaternion q) Keeps rotation only around the Y-axis.

Public Attributes

	Name
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.
Matrix4x4	calibrationMatrix 0. takes the observed pose of an object and the official pose, in some other coordinate system
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.
Pose float	amountOfRectificationInDegrees
Pose float PoseAxis	axis

Public Types Documentation

enum PoseAxis

Enumerator	Value	Description
Right	0	Right direction.
Up	1	Up direction.
Forward	2	Forward 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;

0. 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;