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# EulerAngles Values

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The EulerAngles class provides a representation for orientation in 3D space using rotation angles in degrees about each axis.

Angles can be greater than 360 and so specify multiple revolutions.

Rotations follow the right-hand-rule.

Constructors

    eulerAngles <x_degrees> <y_degrees> <z_degrees>
    <quat> as eulerAngles
    <angleAxis> as eulerAngles
    <matrix3> as eulerAngles

Extracts the rotation component as an eulerAngles.

Operators

    <eulerAngles> == <eulerAngles>
    <eulerAngles> != <eulerAngles>
    <eulerAngles> as <class>

eulerAngles can convert to Matrix3, Quat, angleAxis values

Properties

    <eulerAngles>.x: Float
    <eulerAngles>.y: Float
    <eulerAngles>.z: Float

Rotation about each primary axis in float degrees

Methods

    copy <eulerAngles>

Creates a new copy of the eulerAngles value.

The new value contains a copy of the input eulerAngles value, and is independent of the input eulerAngles value.

FOR EXAMPLE:
    newEulerAngles = copy oldEulerAngles

    random <eulerAngles> <eulerAngles>

Random rotation between the eulerAngles, but uses quat Slerp, so loses multiple revolution angles.

    quatToEuler <quat> order:<eulertype_integer>
    eulerToQuat <eulerAngle> order:<eulertype_integer>

Convert between quat and euler angle values. The optional order parameter specifies the order of application of the angles. If not specified, XYZ ordering is used. Its value can be any of the following:

    1 - XYZ
    2 - XZY
    3 - YZX
    4 - YXZ
    5 - ZXY
    6 - ZYX
    7 - XYX
    8 - YZY
    9 - ZXZ

    quatToEuler2 <quat>

Returns the same Euler value for the given Quaternion as shown in the Transform Type-In dialog.

Available in 3ds Max 2008 and higher.

Previously available in the Avguard Extensions.

    quatArrayToEulerArray <quat array>

Returns an array of smooth Euler values from the Quat array.

Available in 3ds Max 2008 and higher.

Previously available in the Avguard Extensions .

When converting a series of quat values to eulerAngles values, it is possible for sign flips to occur in the eulerAngles values. This is due to the fact that one single quat value can be expressed through many different eulerAngles values. This flip can be detected based on the eulerAngles/quat ratio. The eulerAngles/quat ratio is the relatio of the angle difference in eulerAngles space to the angle difference in quat space. If this ratio is bigger than PI the rotation between the two quat to eulerAngles conversions. This method returns the eulerAngles/quat angle ratio between the two quat to eulerAngles conversions as a float value. The actual detection of the flip is dependent on the amount of rotation in between conversions. The smaller the amount of rotation, the more accurate the detection is.

Note that the following methods were broken in versions prior to 3ds Max 2012.

    <float>GetEulerQuatAngleRatio <quat1> <quat2> <array1> <array2>

    <float>GetEulerQuatAngleRatio <quat1> <quat2> <eulerAngle1> <eulerAngle2>

    <float>GetEulerQuatAngleRatio <quat1> <quat2> &<var1> &<var2>

The function returns the eulerAngles/Quat ratio as a Float.

First two arguments are quats used as inputs. The first quat is the previous rotation, the second quat is the current rotation.

The third and fourth arguments are the previous and current converted rotation angles. They will be used as outputs.

In the first signature, the resulting Euler Angle .x, .y and .z components will be stored in the array elements 1, 2 and 3.

In the second signature, the passed arguments <eulerAngle1> and <eulerAngle2> will be modified to the converted values.

In the third signature, the EulerAngles passed as argument 3 and 4 will be written back by-reference.

    <float>GetEulerMatAngleRatio <mat1> <mat2> <array1> <array2>

    <float>GetEulerMatAngleRatio <mat1> <mat1> <eulerAngle1> <eulerAngle2>

    <float>GetEulerMatAngleRatio <mat1> <mat1> &<var1> &<var2>

This method parallels the getEulerQuatAngleRatio() method, but uses matrix3 values rather than Quat values as inputs.

The first two arguments are matrix3 inputs describing the previous and current orientations.

The third and fourth arguments are the converted previous and current Euler Angles.

In the first signature, the .x, .y and .z components will be stored in the first, second and third elements of the arrays.

In the second signature, the output Euler Angles will be stored in the passed <eulerAngle1> and <eulerAngle2> by modifying them.

In the third signature, the eulerAngles will be written back to the third and fourth by-reference arguments.

FOR EXAMPLE:
    q1 = (quat 0.412759 0.00141638 -0.113167 0.903782)
    q2 = (quat -0.150577 -0.378993 0.176638 0.895818)
    a1 = #(0,0,0)
    a2 = #(0,0,0)
    getEulerQuatAngleRatio q1 q2 a1 a2
    -->0.583444
    a1;a2
    -->#(-48.5478, 5.21315, 11.922)
    -->#(11.509, 47.0722, -17.2825)

    a1 = #()
    a2 = #()
    getEulerQuatAngleRatio q1 q2 a1 a2
    -->0.583444
    a1;a2
    -->#(-48.5478, 5.21315, 11.922)
    -->#(11.509, 47.0722, -17.2825)

    a1 = eulerAngles 0 0 0
    a2 = eulerAngles 0 0 0
    getEulerQuatAngleRatio q1 q2 a1 a2
    -->0.583444
    a1;a2
    -->(eulerAngles -48.5478 5.21315 11.922)
    -->(eulerAngles 11.509 47.0722 -17.2825)

    getEulerQuatAngleRatio q1 q2 &r1 &r2
    -->0.583444
    r1;r2
    -->(eulerAngles -48.5478 5.21315 11.922)
    -->(eulerAngles 11.509 47.0722 -17.2825)

    m1 = (quat 0.412759 0.00141638 -0.113167 0.903782) as matrix3
    m2 = (quat -0.150577 -0.378993 0.176638 0.895818) as matrix3
    a1 = #(0,0,0)
    a2 = #(0,0,0)
    GetEulerMatAngleRatio m1 m2 a1 a2
    -->0.583444
    a1;a2
    -->#(-48.5478, 5.21315, 11.922)
    -->#(11.509, 47.0722, -17.2825)

    a1 = #()
    a2 = #()
    GetEulerMatAngleRatio m1 m2 a1 a2
    -->0.583444
    a1;a2
    -->#(-48.5478, 5.21315, 11.922)
    -->#(11.509, 47.0722, -17.2825)

    a1 = eulerAngles 0 0 0
    a2 = eulerAngles 0 0 0
    GetEulerMatAngleRatio m1 m2 a1 a2
    -->0.583444
    a1;a2
    -->(eulerAngles -48.5478 5.21315 11.922)
    -->(eulerAngles 11.509 47.0722 -17.2825)

    GetEulerMatAngleRatio m1 m2 &r3 &r4
    -->0.583444
    r3;r4
    -->(eulerAngles -48.5478 5.21315 11.922)
    -->(eulerAngles 11.509 47.0722 -17.2825)

#### See Also

- AngleAxis Values

- Quat Values

- Matrix3 Values