Difference between revisions of "Quaternion Class"

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{{TDClassSummary|label=Quaternion|summary=Quaternion}}
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{{TDClassSummary|label=Quaternion|summary=Holds a Quaternion object which can be used to manipulate rotations in various ways. Quaternions can be constructed using a few different ways to describe the initial rotation:
 +
 
 +
<syntaxhighlight lang=python>
 +
# From Euler Angles
 +
q = tdu.Quaternion(tdu.Vector(30, 5, -5))
 +
# From an angle and a rotation axis
 +
q = tdu.Quaternion(30, tdu.Vector(0, 1, 0))
 +
# From two vectors, rotate from the first vector to the second vector
 +
q = tdu.Quaternion(tdu.Vector(1, 0, 0), tdu.Vector(0, 1, 0))
 +
# From a set of 4 quaternion values
 +
q = tdu.Quaternion(x, y, z, w)
 +
 
 +
</syntaxhighlight>}}
 +
See also [[Transform CHOP]] which accepts, manipulates and outputs quaternions as sets of CHOP channels.
 
<section begin=HELPBODY />
 
<section begin=HELPBODY />
 
{{ClassMemberSection|empty=
 
{{ClassMemberSection|empty=
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{{ClassMember
 
{{ClassMember
 
     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
−
     |name=w
+
     |name=x
 
     |type=float
 
     |type=float
−
     |set=0
+
     |set=1
−
     |text=Quaternion_w
+
     |text=Get or set the x component of the quaternion.
 
}}
 
}}
 
{{ClassMember
 
{{ClassMember
 
     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
−
     |name=x
+
     |name=y
 
     |type=float
 
     |type=float
−
     |set=0
+
     |set=1
−
     |text=Quaternion_x
+
     |text=Get or set the y component of the quaternion.
 
}}
 
}}
 
{{ClassMember
 
{{ClassMember
 
     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
−
     |name=y
+
     |name=z
 
     |type=float
 
     |type=float
−
     |set=0
+
     |set=1
−
     |text=Quaternion_y
+
     |text=Get or set the z component of the quaternion.
 
}}
 
}}
 
{{ClassMember
 
{{ClassMember
 
     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
−
     |name=z
+
     |name=w
 
     |type=float
 
     |type=float
−
     |set=0
+
     |set=1
−
     |text=Quaternion_z
+
     |text=Get or set the w component of the quaternion.
 
}}}}
 
}}}}
 
{{ClassMethodSection|empty=
 
{{ClassMethodSection|empty=
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     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
 
     |name=lerp
 
     |name=lerp
−
     |call=lerp(q2, lerpF)
+
     |call=lerp(q2, factor)
 
     |returns=quaternion
 
     |returns=quaternion
−
     |text=Returns a quaternion as the linear interpolation of the current quaternion (q) and another quaternion (q2) using an interpolation factor (lerpF) in the range [0,1].
+
     |text=Returns the linear interpolation of the quaternion with another quaternion and an interpolation factor.
 +
The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.
 +
The interpolation factor must be between 0 and 1.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l = q.lerp(q2, lerpF)
+
q3 = q.lerp(q2, factor)
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}
 
}}
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     |call=length()
 
     |call=length()
 
     |returns=float
 
     |returns=float
−
     |text=Returns the length of the current quaternion.
+
     |text=Returns the length of the quaternion.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
 
l = q.length()
 
l = q.length()
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     |call=cross(q2)
 
     |call=cross(q2)
 
     |returns=vector
 
     |returns=vector
−
     |text=Returns the cross product of the current quaternion and another quaternion.
+
     |text=Returns the cross product of the quaternion and argument.
 +
The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
 
l = q.cross(q2)
 
l = q.cross(q2)
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     |call=rotate(vec)
 
     |call=rotate(vec)
 
     |returns=vector
 
     |returns=vector
−
     |text=Rotates a vector using the current quaternion and returns a new vector.  
+
     |text=Rotates a vector using the current quaternion. Returns a new vector.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l= q.rotate(vec)
+
v2 = q.rotate(v1)
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}
 
}}
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     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
 
     |name=slerp
 
     |name=slerp
−
     |call=slerp(q2, slerpF)
+
     |call=slerp(q2, factor)
 
     |returns=quaternion
 
     |returns=quaternion
−
     |text=Returns a quaternion as the spherical interpolation of the current quaternion (q) and another quaternion (q2) using an interpolation factor (slerpF).
+
     |text=Returns the spherical interpolation of the quaternion with another quaternion and an interpolation factor.
 +
The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l = q.slerp(q2, slerpF)
+
q3 = q.slerp(q2, factor)
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}
 
}}
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     |call=eulerAngles(order='xyz')
 
     |call=eulerAngles(order='xyz')
 
     |returns=tuple
 
     |returns=tuple
−
     |text=Returns euler angles in degrees as a tuple (i.e. pitch as x, yaw as y, roll as z) from current quaternion. The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'.  
+
     |text=Returns euler angles in degrees as a tuple (i.e. pitch as x, yaw as y, roll as z) from current quaternion and a rotation order. The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'.  
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l = q.eulerAngles(order='xyz')
+
r = q.eulerAngles(order='xyz')
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}
 
}}
 +
{{ClassMethod
 +
    |class=tdu.Quaternion
 +
    |name=fromEuler
 +
    |call=fromEuler(order='xyz')
 +
    |returns=tuple
 +
    |text=Returns and set the current quaternion from euler angles in degrees as a 3 inputs argument (i.e. pitch as x, yaw as y, roll as z). The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'.
 +
<syntaxhighlight lang=python>r = q.fromEuler(order='xyz')</syntaxhighlight>}}
 
{{ClassMethod
 
{{ClassMethod
 
     |class=tdu.Quaternion
 
     |class=tdu.Quaternion
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     |call=axis()
 
     |call=axis()
 
     |returns=vector
 
     |returns=vector
−
     |text=Returns the rotation axis vector of the current.
+
     |text=Returns the rotation axis vector of the quaternion.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l = q.axis()
+
v = q.axis()
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}
 
}}
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     |call=dot(q2)
 
     |call=dot(q2)
 
     |returns=float
 
     |returns=float
−
     |text=Returns the dot product (float) of the current quaternion and another quaternion.
+
     |text=Returns the dot product of the quaternion and the argument.
 +
The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
 
l = q.dot(q2)
 
l = q.dot(q2)
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     |call=exp()
 
     |call=exp()
 
     |returns=quaternion
 
     |returns=quaternion
−
     |text=Returns the exponential of the current as a new quaternion.
+
     |text=Returns the exponential of the quaternion as a new quaternion.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l = q.exp()
+
q2 = q.exp()
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}
 
}}
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     |call=copy()
 
     |call=copy()
 
     |returns=quaternion
 
     |returns=quaternion
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     |text=Quaternion copy
+
     |text=Creates a copy of the quaternion with separate values.
 
}}
 
}}
 
{{ClassMethod
 
{{ClassMethod
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     |call=log()
 
     |call=log()
 
     |returns=quaternion
 
     |returns=quaternion
−
     |text=Returns the natural logarithm of the current as a new quaternion.
+
     |text=Returns the natural logarithm of the current quaternion as a new quaternion.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
 
l = q.log()
 
l = q.log()
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     |call=inverse()
 
     |call=inverse()
 
     |returns=None
 
     |returns=None
−
     |text=Invert the current quaternion.
+
     |text=Invert the quaternion in place.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
 
q.inverse()
 
q.inverse()
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     |call=angle()
 
     |call=angle()
 
     |returns=float
 
     |returns=float
−
     |text=Returns the rotation angle (in degrees) of the current.
+
     |text=Returns the rotation angle (in degrees) of the quaternion.
 
<syntaxhighlight lang=python>
 
<syntaxhighlight lang=python>
−
l = q.angle()
+
a = q.angle()
 
</syntaxhighlight>
 
</syntaxhighlight>
 
}}}}
 
}}}}
 +
{{SubSection|title=Special Functions
 +
|text=
 +
}}
 +
{{ClassMethod
 +
    |class=tdu.Quaternion
 +
    |name=*=
 +
    |call=Quaternion *= Quaternion
 +
    |returns=Quaternion
 +
    |text=Applies the rotation of one quaternion to another quaternion.
 +
<syntaxhighlight lang=python>
 +
# apply rotation of q2 to q1
 +
q1 *= q2
 +
</syntaxhighlight>
 +
}}
 
<section end=HELPBODY />
 
<section end=HELPBODY />
 
{{History}}
 
{{History}}
 
{{#invoke:Category|list|Python Reference}}
 
{{#invoke:Category|list|Python Reference}}

Latest revision as of 12:32, 20 February 2020

Holds a Quaternion object which can be used to manipulate rotations in various ways. Quaternions can be constructed using a few different ways to describe the initial rotation: 

# From Euler Angles
q = tdu.Quaternion(tdu.Vector(30, 5, -5))
# From an angle and a rotation axis
q = tdu.Quaternion(30, tdu.Vector(0, 1, 0))
# From two vectors, rotate from the first vector to the second vector
q = tdu.Quaternion(tdu.Vector(1, 0, 0), tdu.Vector(0, 1, 0))
# From a set of 4 quaternion values
q = tdu.Quaternion(x, y, z, w)


See also Transform CHOP which accepts, manipulates and outputs quaternions as sets of CHOP channels.

Members[edit]

x → float :

Get or set the x component of the quaternion.

y → float :

Get or set the y component of the quaternion.

z → float :

Get or set the z component of the quaternion.

w → float :

Get or set the w component of the quaternion.

Methods[edit]

lerp(q2, factor)→ quaternion:

Returns the linear interpolation of the quaternion with another quaternion and an interpolation factor.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc. The interpolation factor must be between 0 and 1. 

q3 = q.lerp(q2, factor)

length()→ float:

Returns the length of the quaternion. 

l = q.length()

cross(q2)→ vector:

Returns the cross product of the quaternion and argument.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc. 

l = q.cross(q2)

rotate(vec)→ vector:

Rotates a vector using the current quaternion. Returns a new vector. 

v2 = q.rotate(v1)

slerp(q2, factor)→ quaternion:

Returns the spherical interpolation of the quaternion with another quaternion and an interpolation factor.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc. 

q3 = q.slerp(q2, factor)

eulerAngles(order='xyz')→ tuple:

Returns euler angles in degrees as a tuple (i.e. pitch as x, yaw as y, roll as z) from current quaternion and a rotation order. The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'. 

r = q.eulerAngles(order='xyz')

fromEuler(order='xyz')→ tuple:

Returns and set the current quaternion from euler angles in degrees as a 3 inputs argument (i.e. pitch as x, yaw as y, roll as z). The 'order' argument can be set to any valid rotation order which by default is set to 'xyz'. 

r = q.fromEuler(order='xyz')

axis()→ vector:

Returns the rotation axis vector of the quaternion. 

v = q.axis()

dot(q2)→ float:

Returns the dot product of the quaternion and the argument.

The quaternion argument can be anything from which a quaternion can be derived ie. (x,y,z,w), Matrix, etc. 

l = q.dot(q2)

exp()→ quaternion:

Returns the exponential of the quaternion as a new quaternion. 

q2 = q.exp()

copy()→ quaternion:

Creates a copy of the quaternion with separate values.

log()→ quaternion:

Returns the natural logarithm of the current quaternion as a new quaternion. 

l = q.log()

inverse()→ None:

Invert the quaternion in place. 

q.inverse()

angle()→ float:

Returns the rotation angle (in degrees) of the quaternion. 

a = q.angle()

Special Functions[edit]

Quaternion *= Quaternion→ Quaternion:

Applies the rotation of one quaternion to another quaternion. 

# apply rotation of q2 to q1
q1 *= q2

TouchDesigner Build:

An Operator Family which operate on Channels (a series of numbers) which are used for animation, audio, mathematics, simulation, logic, UI construction, and many other applications.

Retrieved from "https://docs.derivative.ca/index.php?title=Quaternion_Class&oldid=18260"