Difference between revisions of "IC Python API:RLPy RQuaternion"

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== Detailed Description ==
 
== Detailed Description ==
  
This class represents a quaternion in mathematics.  Quaternions represetn directions as a single rotation, just as rectangular coordinates represent positions as single vector. RQuaternion also defines some constants that can be used directly:
+
This class represents a quaternion in mathematics.  Quaternions represetn directions as a single rotation, just as rectangular coordinates represent positions as single vector. [[IC_Python_API:RLPy_RQuaternion|RQuaternion]] also defines some constants that can be used directly:
  
 
{| class="wikitable"
 
{| class="wikitable"
Line 15: Line 15:
 
|-
 
|-
 
|RQuaternion.ZERO
 
|RQuaternion.ZERO
|4D x unit vector: (0, 0, 0, 0)init
+
|4D x unit vector: (0, 0, 0, 0) initialization value
 
|}
 
|}
  
 
== Constructor & Destructor ==
 
== Constructor & Destructor ==
  
=== __init__( self ) ===
+
=== __init__ ( self ) ===
  
The constructor. Initialize a new RQuaternion object without initialization.
+
The constructor. Initialize a new [[IC_Python_API:RLPy_RQuaternion|RQuaternion]] object without initialization.
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
q = RLPy.RQuaternion()
 
q = RLPy.RQuaternion()
  
Line 30: Line 30:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== __init__( self, vV ) ===
+
=== __init__ ( self, vV ) ===
  
The constructor. Initialize a new RQuaternion object from a 4D vector RVector4.
+
The constructor. Initialize a new [[IC_Python_API:RLPy_RQuaternion|RQuaternion]] object from a 4D vector.
  
 
==== Parameters ====
 
==== Parameters ====
:'''vV''' [IN]  a 4D vector - RLPy.RVector4
+
:'''vV''' [IN]  a 4D vector - [[IC_Python_API:RLPy_RVector4|RVector4]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
v = RLPy.RVector4(1, 2, 3, 4)
 
v = RLPy.RVector4(1, 2, 3, 4)
 
q = RLPy.RQuaternion(v)
 
q = RLPy.RQuaternion(v)
Line 44: Line 44:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== __init__( self, qQ ) ===
+
=== __init__ ( self, qQ ) ===
  
 
==== Parameters ====
 
==== Parameters ====
:'''qQ''' [IN]  a quaternion - RLPy.RQuaternion
+
:'''qQ''' [IN]  a quaternion - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
v = RLPy.RVector4(1, 2, 3, 4)
 
v = RLPy.RVector4(1, 2, 3, 4)
 
q = RLPy.RQuaternion(v)
 
q = RLPy.RQuaternion(v)
Line 57: Line 57:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== __init__( self, kAxis, fAngle ) ===
+
=== __init__ ( self, kAxis, fAngle ) ===
  
The constructor. Initialize a new RQuaternion object with Axis-angle. The axis is specified by a 3D vector, and the angle is specified by a float value.
+
The constructor. Initialize a new [[IC_Python_API:RLPy_RQuaternion|RQuaternion]] object with Axis-angle. The axis is specified by a 3D vector, and the angle is specified by a float value.
  
 
==== Parameters ====
 
==== Parameters ====
:'''kAxis''' [IN]  the rotation axis - RLPy.RVector3
+
:'''kAxis''' [IN]  the rotation axis - [[IC_Python_API:RLPy_RVector3|RVector3]]
 
:'''fAngle''' [IN] the rotation angle - float
 
:'''fAngle''' [IN] the rotation angle - float
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
v = RLPy.RVector3(0, 0, 1)
 
v = RLPy.RVector3(0, 0, 1)
 
q = RLPy.RQuaternion(v, math.pi/2)
 
q = RLPy.RQuaternion(v, math.pi/2)
Line 73: Line 73:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== __init__( self, kRot ) ===
+
=== __init__ ( self, kRot ) ===
  
The constructor. Initialize a new RQuaternion object with a 3x3 rotation matrix.
+
The constructor. Initialize a new [[IC_Python_API:RLPy_RQuaternion|RQuaternion]] object with a 3x3 rotation matrix.
  
 
==== Parameters ====
 
==== Parameters ====
:'''kRot''' [IN]  a 3x3 rotation matrix - RLPy.RMatrix3
+
:'''kRot''' [IN]  a 3x3 rotation matrix - [[IC_Python_API:RLPy_RMatrix3|RMatrix3]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
v = RLPy.RVector3(0, 0, 1)
 
v = RLPy.RVector3(0, 0, 1)
 
m = RLPy.RMatrix3(v, math.pi/2)
 
m = RLPy.RMatrix3(v, math.pi/2)
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</syntaxhighlight>
 
</syntaxhighlight>
  
== Operator ==
+
== Operators ==
  
 
=== = ===
 
=== = ===
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The "equal to" operator.
 
The "equal to" operator.
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
q = RLPy.RQuaternion()
 
q = RLPy.RQuaternion()
 
p = q
 
p = q
Line 106: Line 106:
 
The "not equal to" operator.
 
The "not equal to" operator.
  
<syntaxhighlight lang="Python">
+
See Also: [[#==|==]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
q = RLPy.RQuaternion(a)
 
q = RLPy.RQuaternion(a)
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The "less than" operator. Similar to string comparison: Returns '''True''' upon the first match that is less than and '''False''' if it is greater than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''False'''.
 
The "less than" operator. Similar to string comparison: Returns '''True''' upon the first match that is less than and '''False''' if it is greater than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''False'''.
  
<syntaxhighlight lang="Python">
+
See Also: [[#<=|<=]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 5, 2)
 
a = RLPy.RVector4(0, 1, 5, 2)
 
b = RLPy.RVector4(0, 1, 5, 3)
 
b = RLPy.RVector4(0, 1, 5, 3)
Line 142: Line 146:
 
The "greater than" operator. Similar to string comparison: Returns '''True''' upon the first match that is greater than and '''False''' if it is less than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''False'''.
 
The "greater than" operator. Similar to string comparison: Returns '''True''' upon the first match that is greater than and '''False''' if it is less than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''False'''.
  
<syntaxhighlight lang="Python">
+
See Also: [[#>=|>=]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 5, 2)
 
a = RLPy.RVector4(0, 1, 5, 2)
 
b = RLPy.RVector4(0, 1, 5, 3)
 
b = RLPy.RVector4(0, 1, 5, 3)
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The "less than or equal" operator. Similar to string comparison: Returns '''True''' upon the first match that is less than and '''False''' if it is greater than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''True'''.
 
The "less than or equal" operator. Similar to string comparison: Returns '''True''' upon the first match that is less than and '''False''' if it is greater than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''True'''.
  
<syntaxhighlight lang="Python">
+
See Also: [[#<|<]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 5, 2)
 
a = RLPy.RVector4(0, 1, 5, 2)
 
b = RLPy.RVector4(0, 1, 5, 3)
 
b = RLPy.RVector4(0, 1, 5, 3)
Line 188: Line 196:
 
The "greater than or equal" operator. Similar to string comparison: Returns '''True''' upon the first match that is greater than and '''False''' if it is less than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''True'''.
 
The "greater than or equal" operator. Similar to string comparison: Returns '''True''' upon the first match that is greater than and '''False''' if it is less than.  If the current comparison is equal, continue onto the next element.  If all elements are equal then return '''True'''.
  
<syntaxhighlight lang="Python">
+
See Also: [[#>|>]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 5, 2)
 
a = RLPy.RVector4(0, 1, 5, 2)
 
b = RLPy.RVector4(0, 1, 5, 3)
 
b = RLPy.RVector4(0, 1, 5, 3)
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The "addition" operator. Perform quaternion addition.
 
The "addition" operator. Perform quaternion addition.
  
<syntaxhighlight lang="Python">
+
See Also: [[#+=|+=]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 2, 3)
 
a = RLPy.RVector4(0, 1, 2, 3)
 
b = RLPy.RVector4(1, 2, 3, 4)
 
b = RLPy.RVector4(1, 2, 3, 4)
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The "subtraction" operator. Perform quaternion subtraction.
 
The "subtraction" operator. Perform quaternion subtraction.
  
<syntaxhighlight lang="Python">
+
See Also: [[#-=|-=]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 2, 3)
 
a = RLPy.RVector4(0, 1, 2, 3)
 
b = RLPy.RVector4(3, 2, 1, 0)
 
b = RLPy.RVector4(3, 2, 1, 0)
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The "multiplication" operator. Perform a scalar multiplication when the second operand is an integer or float. If the second operand is another quaternion, then the respective elements are multiplied.
 
The "multiplication" operator. Perform a scalar multiplication when the second operand is an integer or float. If the second operand is another quaternion, then the respective elements are multiplied.
  
<syntaxhighlight lang="Python">
+
See Also: [[#*=|*=]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 253: Line 269:
 
The "division" operator. Perform a scalar division with a int or float value which the second operand is limited to.
 
The "division" operator. Perform a scalar division with a int or float value which the second operand is limited to.
  
<syntaxhighlight lang="Python">
+
See Also: [[#/=|/=]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
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The "unary minus" operator. Inverse the sign of each element.
 
The "unary minus" operator. Inverse the sign of each element.
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 277: Line 295:
 
The "addition assignment" operator.
 
The "addition assignment" operator.
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 2, 3)
 
a = RLPy.RVector4(0, 1, 2, 3)
 
b = RLPy.RVector4(1, 2, 3, 4)
 
b = RLPy.RVector4(1, 2, 3, 4)
Line 291: Line 309:
 
The "subtraction assignment" operator.
 
The "subtraction assignment" operator.
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(0, 1, 4, 5)
 
a = RLPy.RVector4(0, 1, 4, 5)
 
b = RLPy.RVector4(1, 2, 3, 1)
 
b = RLPy.RVector4(1, 2, 3, 1)
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The "multiplication assignment" operator. For calculation method, refer to the '''*''' operator.
 
The "multiplication assignment" operator. For calculation method, refer to the '''*''' operator.
  
<syntaxhighlight lang="Python">
+
See Also: [[#*|*]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 317: Line 337:
 
The "division assignment" operator. For calculation method, refer to the '''/''' operator.
 
The "division assignment" operator. For calculation method, refer to the '''/''' operator.
  
<syntaxhighlight lang="Python">
+
See Also: [[#/|/]]
 +
 
 +
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
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== Member Functions ==
 
== Member Functions ==
  
=== AlmostEqual( self, qQ ) ===
+
=== AlmostEqual ( self, qQ ) ===
  
Determine the two quaternions are almost the same with tolerance: 0.00001.
+
Determine if two quaternions are almost the same within a tolerance of 0.00001.
  
 
==== Parameters ====
 
==== Parameters ====
:'''qQ''' [IN] The target quaternion to check for equivalence - RLPy.RQuaternion
+
:'''qQ''' [IN] The target quaternion to check for equivalence - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
 
==== Returns ====
 
==== Returns ====
:True if the two quaternions are almost the same - bool
+
:'''True''' if the two quaternions are almost the same, else '''False''' - bool
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
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</syntaxhighlight>
 
</syntaxhighlight>
  
=== Conjugate( self ) ===
+
=== Conjugate ( self ) ===
  
Conjugate this quaternion.
+
Get the conjugate of this quaternion. The result is a quaternion whose x, y, and z values have been negated.
  
 
==== Returns ====
 
==== Returns ====
:Returns the conjugated quaternion. The result is a quaternion whose x, y, and z values have been negated - RLPy.RQuaternion
+
:The conjugated quaternion. - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
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</syntaxhighlight>
 
</syntaxhighlight>
  
=== Dot( self, qQ ) ===
+
=== Dot ( self, qQ ) ===
  
Calculate dot product of the two quaternions.
+
Calculate the dot product of two quaternions.
  
 
==== Parameters ====
 
==== Parameters ====
:'''qQ''' [IN] The quaternion to compute dot product - RLPy.RQuaternion
+
:'''qQ''' [IN] The quaternion to compute dot product - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
 
==== Returns ====
 
==== Returns ====
:Returns the value of the dot product - float
+
:Value of the dot product - float
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
b = RLPy.RVector4(1, 2, 3, 0)
 
b = RLPy.RVector4(1, 2, 3, 0)
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</syntaxhighlight>
 
</syntaxhighlight>
  
=== FromAxisAngle( self, rkAxis, fAngle ) ===
+
=== FromAxisAngle ( self, rkAxis, fAngle ) ===
  
Quaternion from axis angle.
+
Create a quaternion from axis angle.
  
 
==== Parameters ====
 
==== Parameters ====
:'''rkAxis''' [IN] axis vector - RLPy.RVector3
+
:'''rkAxis''' [IN] axis vector - [[IC_Python_API:RLPy_RVector3|RVector3]]
 
:'''fAngle''' [IN] angle in radians - float
 
:'''fAngle''' [IN] angle in radians - float
  
 
==== Returns ====
 
==== Returns ====
:Return a new quaternion from a axis angle - RLPy.RQuaternion
+
:Return a new quaternion from a axis angle - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
p = RLPy.RQuaternion()
 
p = RLPy.RQuaternion()
 
v = RLPy.RVector3(0, 0, 1)
 
v = RLPy.RVector3(0, 0, 1)
Line 406: Line 428:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== FromRotationMatrix( self, rkRot ) ===
+
=== FromRotationMatrix ( self, rkRot ) ===
  
Quaternion from a rotation matrix.
+
Create a quaternion from a rotation matrix.
  
 
==== Parameters ====
 
==== Parameters ====
:rkRot [IN] Rotation matrix - RLPy.RMatrix3
+
:'''rkRot''' [IN] Rotation matrix - [[IC_Python_API:RLPy_RMatrix3|RMatrix3]]
  
 
==== Returns ====
 
==== Returns ====
:Return a new quaternion from a rotation matrix - RLPy.RQuaternion
+
:Return a new quaternion from a rotation matrix - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
v = RLPy.RVector3(0, 0, 1)
 
v = RLPy.RVector3(0, 0, 1)
 
m = RLPy.RMatrix3(v, math.pi/2)
 
m = RLPy.RMatrix3(v, math.pi/2)
Line 425: Line 447:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== Inverse( self, rkRot ) ===
+
=== Inverse ( self, rkRot ) ===
  
Obtain the inverse of this quaternion.
+
Get the inverse of this quaternion.
  
 
==== Returns ====
 
==== Returns ====
:The inversed quaternion - RLPy.RQuaternion
+
:The inversed quaternion - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 1, 1, 1)
 
a = RLPy.RVector4(1, 1, 1, 1)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 440: Line 462:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== Multiply( self, qQ ) ===
+
=== Multiply ( self, qQ ) ===
  
Multiply by another quaternion.
+
Multiply this quaternion by another quaternion.
  
 
==== Parameters ====
 
==== Parameters ====
:'''qQ''' [IN] The quaternion to multiply - RLPy.RQuaternion
+
:'''qQ''' [IN] The quaternion to multiply - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
 
==== Returns ====
 
==== Returns ====
:Returns the multiplied quaternion - RLPy.RQuaternion
+
:Returns the multiplied quaternion - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
b = RLPy.RVector4(1, 2, 2, 1)
 
b = RLPy.RVector4(1, 2, 2, 1)
Line 461: Line 483:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== MultiplyEqual( self, qQ ) ===
+
=== MultiplyEqual ( self, qQ ) ===
  
 
==== Parameters ====
 
==== Parameters ====
:'''qQ''' [IN] The quaternion to multiply - RLPy.RQuaternion
+
:'''qQ''' [IN] The quaternion to multiply - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
 
==== Returns ====
 
==== Returns ====
:Returns the multiplied quaternion - RLPy.RQuaternion
+
:Returns the multiplied quaternion - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
b = RLPy.RVector4(1, 2, 2, 1)
 
b = RLPy.RVector4(1, 2, 2, 1)
Line 480: Line 502:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== Normalize( self ) ===
+
=== Normalize ( self ) ===
  
Normalizes this quaternion.
+
Normalize this quaternion, e.g. with a magnitude of 2.
  
 
==== Returns ====
 
==== Returns ====
:Returns the normalized quaternion - RLPy.RQuaternion
+
:The normalized quaternion - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 1, 1, 1)
 
a = RLPy.RVector4(1, 1, 1, 1)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 496: Line 518:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== Rotate180( self ) ===
+
=== Rotate180 ( self ) ===
  
Rotate 180 degree of this quaternion.
+
Rotate this quaternion by 180 degrees.
  
 
==== Returns ====
 
==== Returns ====
:Returns the rotated quaternion - RLPy.RQuaternion
+
:The rotated quaternion - [[IC_Python_API:RLPy_RQuaternion|RQuaternion]]
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 1, 1, 1)
 
a = RLPy.RVector4(1, 1, 1, 1)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 512: Line 534:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== SetX( self, tX ) ===
+
=== SetX ( self, tX ) ===
  
 
Set the value of the x-axis.
 
Set the value of the x-axis.
Line 519: Line 541:
 
:'''tX''' [IN] the value of the x-axis - float
 
:'''tX''' [IN] the value of the x-axis - float
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 527: Line 549:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== SetY( self, tY ) ===
+
=== SetY ( self, tY ) ===
  
 
Set the value of the y-axis.
 
Set the value of the y-axis.
Line 534: Line 556:
 
:'''tY''' [IN] the value of the y-axis - float
 
:'''tY''' [IN] the value of the y-axis - float
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 542: Line 564:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== SetZ( self, tZ ) ===
+
=== SetZ ( self, tZ ) ===
  
 
Set the value of the z-axis.
 
Set the value of the z-axis.
Line 549: Line 571:
 
:'''tZ''' [IN] the value of the z-axis - float
 
:'''tZ''' [IN] the value of the z-axis - float
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)
Line 557: Line 579:
 
</syntaxhighlight>
 
</syntaxhighlight>
  
=== SetW( self, tW ) ===
+
=== SetW ( self, tW ) ===
  
 
Set the value of the w-axis.
 
Set the value of the w-axis.
Line 564: Line 586:
 
:'''tW''' [IN] the value of the w-axis - float
 
:'''tW''' [IN] the value of the w-axis - float
  
<syntaxhighlight lang="Python">
+
<syntaxhighlight lang="python" line='line'>
 
a = RLPy.RVector4(1, 2, 3, 4)
 
a = RLPy.RVector4(1, 2, 3, 4)
 
p = RLPy.RQuaternion(a)
 
p = RLPy.RQuaternion(a)

Latest revision as of 20:50, 13 April 2020

Main article: Modules. Last modified: 04/13/2020

Detailed Description

This class represents a quaternion in mathematics. Quaternions represetn directions as a single rotation, just as rectangular coordinates represent positions as single vector. RQuaternion also defines some constants that can be used directly:

Constant Description
RQuaternion.IDENTITY 4D zero vector: (0, 0, 0, 1)
RQuaternion.ZERO 4D x unit vector: (0, 0, 0, 0) initialization value

Constructor & Destructor

__init__ ( self )

The constructor. Initialize a new RQuaternion object without initialization.

1 q = RLPy.RQuaternion()
2 
3 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # random values

__init__ ( self, vV )

The constructor. Initialize a new RQuaternion object from a 4D vector.

Parameters

vV [IN] a 4D vector - RVector4
1 v = RLPy.RVector4(1, 2, 3, 4)
2 q = RLPy.RQuaternion(v)
3 
4 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # 1.0, 2.0, 3.0, 4.0

__init__ ( self, qQ )

Parameters

qQ [IN] a quaternion - RQuaternion
1 v = RLPy.RVector4(1, 2, 3, 4)
2 q = RLPy.RQuaternion(v)
3 p = RLPy.RQuaternion(q)
4 
5 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 1.0, 2.0, 3.0, 4.0

__init__ ( self, kAxis, fAngle )

The constructor. Initialize a new RQuaternion object with Axis-angle. The axis is specified by a 3D vector, and the angle is specified by a float value.

Parameters

kAxis [IN] the rotation axis - RVector3
fAngle [IN] the rotation angle - float
1 v = RLPy.RVector3(0, 0, 1)
2 q = RLPy.RQuaternion(v, math.pi/2)
3 
4 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
5     # 0.0, 0.0, 0.7071067094802856, 0.7071067690849304

__init__ ( self, kRot )

The constructor. Initialize a new RQuaternion object with a 3x3 rotation matrix.

Parameters

kRot [IN] a 3x3 rotation matrix - RMatrix3
1 v = RLPy.RVector3(0, 0, 1)
2 m = RLPy.RMatrix3(v, math.pi/2)
3 q = RLPy.RQuaternion(m)
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
6     # 0.0, 0.0, 0.7071067690849304, 0.7071067690849304

Operators

=

The "equal to" operator.

1 q = RLPy.RQuaternion()
2 p = q
3 if q == p:                         # True
4     print("equal")

!=

The "not equal to" operator.

See Also: ==

1 a = RLPy.RVector4(1, 2, 3, 4)
2 q = RLPy.RQuaternion(a)
3 b = RLPy.RVector4(2, 2, 3, 4)
4 p = RLPy.RQuaternion(b)
5 if a != b:                         #True
6     print("not equal")

<

The "less than" operator. Similar to string comparison: Returns True upon the first match that is less than and False if it is greater than. If the current comparison is equal, continue onto the next element. If all elements are equal then return False.

See Also: <=

 1 a = RLPy.RVector4(0, 1, 5, 2)
 2 b = RLPy.RVector4(0, 1, 5, 3)
 3 c = RLPy.RVector4(1, 0, 1, 0)
 4 d = RLPy.RVector4(0, 1, 5, 2)
 5 
 6 p = RLPy.RQuaternion(a)
 7 q = RLPy.RQuaternion(b)
 8 r = RLPy.RQuaternion(c)
 9 s = RLPy.RQuaternion(d)
10 
11 if p< q:                       #True
12     print('p< q')
13 if q< r:                       #True
14     print('q< r')
15 if p< s:                       #False
16     print('p< s')

>

The "greater than" operator. Similar to string comparison: Returns True upon the first match that is greater than and False if it is less than. If the current comparison is equal, continue onto the next element. If all elements are equal then return False.

See Also: >=

 1 a = RLPy.RVector4(0, 1, 5, 2)
 2 b = RLPy.RVector4(0, 1, 5, 3)
 3 c = RLPy.RVector4(1, 0, 1, 0)
 4 d = RLPy.RVector4(0, 1, 5, 2)
 5 
 6 p = RLPy.RQuaternion(a)
 7 q = RLPy.RQuaternion(b)
 8 r = RLPy.RQuaternion(c)
 9 s = RLPy.RQuaternion(d)
10 
11 if q >p:                       #True
12     print('q >p')
13 if r >q:                       #True
14     print('r >q')
15 if p >s:                       #False
16     print('p >s')

<=

The "less than or equal" operator. Similar to string comparison: Returns True upon the first match that is less than and False if it is greater than. If the current comparison is equal, continue onto the next element. If all elements are equal then return True.

See Also: <

 1 a = RLPy.RVector4(0, 1, 5, 2)
 2 b = RLPy.RVector4(0, 1, 5, 3)
 3 c = RLPy.RVector4(1, 0, 1, 0)
 4 d = RLPy.RVector4(0, 1, 5, 2)
 5 
 6 p = RLPy.RQuaternion(a)
 7 q = RLPy.RQuaternion(b)
 8 r = RLPy.RQuaternion(c)
 9 s = RLPy.RQuaternion(d)
10 
11 if p<= q:                       #True
12     print('p<= q')
13 if q<= r:                       #True
14     print('q<= r')
15 if p<= s:                       #True
16     print('p<= s')

>=

The "greater than or equal" operator. Similar to string comparison: Returns True upon the first match that is greater than and False if it is less than. If the current comparison is equal, continue onto the next element. If all elements are equal then return True.

See Also: >

 1 a = RLPy.RVector4(0, 1, 5, 2)
 2 b = RLPy.RVector4(0, 1, 5, 3)
 3 c = RLPy.RVector4(1, 0, 1, 0)
 4 d = RLPy.RVector4(0, 1, 5, 2)
 5 
 6 p = RLPy.RQuaternion(a)
 7 q = RLPy.RQuaternion(b)
 8 r = RLPy.RQuaternion(c)
 9 s = RLPy.RQuaternion(d)
10 
11 if q >= p:                       #True
12     print('q >= p')
13 if r >= q:                       #True
14     print('r >= q')
15 if p >= s:                       #True
16     print('p >= s')

+

The "addition" operator. Perform quaternion addition.

See Also: +=

1 a = RLPy.RVector4(0, 1, 2, 3)
2 b = RLPy.RVector4(1, 2, 3, 4)
3 p = RLPy.RQuaternion(a)
4 q = RLPy.RQuaternion(b)
5 r = p + q
6 
7 print(str(r.x) + ', ' + str(r.y) + ', ' + str(r.z) + ', ' + str(r.w))  # 1.0, 3.0, 5.0, 7.0

-

The "subtraction" operator. Perform quaternion subtraction.

See Also: -=

1 a = RLPy.RVector4(0, 1, 2, 3)
2 b = RLPy.RVector4(3, 2, 1, 0)
3 p = RLPy.RQuaternion(a)
4 q = RLPy.RQuaternion(b)
5 r = q - p
6 
7 print(str(r.x) + ', ' + str(r.y) + ', ' + str(r.z) + ', ' + str(r.w)) # 3.0, 1.0, -1.0, -3.0

*

The "multiplication" operator. Perform a scalar multiplication when the second operand is an integer or float. If the second operand is another quaternion, then the respective elements are multiplied.

See Also: *=

1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 q = p * 2
4 r = p * p
5 
6 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # 2.0, 4.0, 6.0, 8.0
7 print(str(r.x) + ', ' + str(r.y) + ', ' + str(r.z) + ', ' + str(r.w)) # 1.0, 4.0, 9.0, 16.0

/

The "division" operator. Perform a scalar division with a int or float value which the second operand is limited to.

See Also: /=

1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 q = p / 2
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # 0.5, 1.0, 1.5, 2.0

-

The "unary minus" operator. Inverse the sign of each element.

1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 q = -p
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # -1.0, -2.0, -3.0, -4.0

+ =

The "addition assignment" operator.

1 a = RLPy.RVector4(0, 1, 2, 3)
2 b = RLPy.RVector4(1, 2, 3, 4)
3 p = RLPy.RQuaternion(a)
4 q = RLPy.RQuaternion(b)
5 p += q
6 
7 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 1.0, 3.0, 5.0, 7.0

- =

The "subtraction assignment" operator.

1 a = RLPy.RVector4(0, 1, 4, 5)
2 b = RLPy.RVector4(1, 2, 3, 1)
3 p = RLPy.RQuaternion(a)
4 q = RLPy.RQuaternion(b)
5 p -= q
6 
7 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # -1.0, -1.0, 1.0, 4.0

*=

The "multiplication assignment" operator. For calculation method, refer to the * operator.

See Also: *

1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 p *= 2
4 
5 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 2.0, 4.0, 6.0, 8.0

/=

The "division assignment" operator. For calculation method, refer to the / operator.

See Also: /

1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 p /= 2
4 
5 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 0.5, 1.0, 1.5, 2.0

Member Functions

AlmostEqual ( self, qQ )

Determine if two quaternions are almost the same within a tolerance of 0.00001.

Parameters

qQ [IN] The target quaternion to check for equivalence - RQuaternion

Returns

True if the two quaternions are almost the same, else False - bool
 1 a = RLPy.RVector4(1, 2, 3, 4)
 2 p = RLPy.RQuaternion(a)
 3 q = RLPy.RQuaternion(a)
 4 r = RLPy.RQuaternion(a)
 5 
 6 q.w = 4.000000001
 7 r.w = 4.00001
 8 
 9 if p.AlmostEqual(q):               #True
10     print("p ≈ q")
11 if q.AlmostEqual(r):               #False
12     print("p ≈ r")

Conjugate ( self )

Get the conjugate of this quaternion. The result is a quaternion whose x, y, and z values have been negated.

Returns

The conjugated quaternion. - RQuaternion
1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 q = p.Conjugate()
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # -1.0, -2.0, -3.0, 4.0

Dot ( self, qQ )

Calculate the dot product of two quaternions.

Parameters

qQ [IN] The quaternion to compute dot product - RQuaternion

Returns

Value of the dot product - float
1 a = RLPy.RVector4(1, 2, 3, 4)
2 b = RLPy.RVector4(1, 2, 3, 0)
3 p = RLPy.RQuaternion(a)
4 q = RLPy.RQuaternion(b)
5 f = p.Dot(q)
6 
7 print(f)     # 14.0

FromAxisAngle ( self, rkAxis, fAngle )

Create a quaternion from axis angle.

Parameters

rkAxis [IN] axis vector - RVector3
fAngle [IN] angle in radians - float

Returns

Return a new quaternion from a axis angle - RQuaternion
1 p = RLPy.RQuaternion()
2 v = RLPy.RVector3(0, 0, 1)
3 p.FromAxisAngle(v, math.pi/2)
4 
5 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 0.0, 0.0, 0.7071067094802856, 0.7071067690849304

FromRotationMatrix ( self, rkRot )

Create a quaternion from a rotation matrix.

Parameters

rkRot [IN] Rotation matrix - RMatrix3

Returns

Return a new quaternion from a rotation matrix - RQuaternion
1 v = RLPy.RVector3(0, 0, 1)
2 m = RLPy.RMatrix3(v, math.pi/2)
3 p = RLPy.RQuaternion()
4 p.FromRotationMatrix(m)
5 
6 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 0.0, 0.0, 0.7071067690849304, 0.7071067690849304

Inverse ( self, rkRot )

Get the inverse of this quaternion.

Returns

The inversed quaternion - RQuaternion
1 a = RLPy.RVector4(1, 1, 1, 1)
2 p = RLPy.RQuaternion(a)
3 q = p.Inverse()
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # -0.25, -0.25, -0.25, 0.25

Multiply ( self, qQ )

Multiply this quaternion by another quaternion.

Parameters

qQ [IN] The quaternion to multiply - RQuaternion

Returns

Returns the multiplied quaternion - RQuaternion
1 a = RLPy.RVector4(1, 2, 3, 4)
2 b = RLPy.RVector4(1, 2, 2, 1)
3 
4 p = RLPy.RQuaternion(a)
5 q = RLPy.RQuaternion(b)
6 r = p.Multiply(q)
7 
8 print(str(r.x) + ', ' + str(r.y) + ', ' + str(r.z) + ', ' + str(r.w)) # 3.0, 11.0, 11.0, -7.0

MultiplyEqual ( self, qQ )

Parameters

qQ [IN] The quaternion to multiply - RQuaternion

Returns

Returns the multiplied quaternion - RQuaternion
1 a = RLPy.RVector4(1, 2, 3, 4)
2 b = RLPy.RVector4(1, 2, 2, 1)
3 
4 p = RLPy.RQuaternion(a)
5 q = RLPy.RQuaternion(b)
6 r = p.MultiplyEqual(q)
7 
8 print(str(r.x) + ', ' + str(r.y) + ', ' + str(r.z) + ', ' + str(r.w)) # 3.0, 11.0, 11.0, -7.0

Normalize ( self )

Normalize this quaternion, e.g. with a magnitude of 2.

Returns

The normalized quaternion - RQuaternion
1 a = RLPy.RVector4(1, 1, 1, 1)
2 p = RLPy.RQuaternion(a)
3 q = p.Normalize()
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
6     # 0.4999999701976776, 0.4999999701976776, 0.4999999701976776, 0.4999999701976776

Rotate180 ( self )

Rotate this quaternion by 180 degrees.

Returns

The rotated quaternion - RQuaternion
1 a = RLPy.RVector4(1, 1, 1, 1)
2 p = RLPy.RQuaternion(a)
3 q = p.Normalize()
4 
5 print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
6    #0.4999999701976776, 0.4999999701976776, 0.4999999701976776, 0.4999999701976776

SetX ( self, tX )

Set the value of the x-axis.

Parameters

tX [IN] the value of the x-axis - float
1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 p.SetX(9)
4 
5 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 9.0, 2.0, 3.0, 4.0

SetY ( self, tY )

Set the value of the y-axis.

Parameters

tY [IN] the value of the y-axis - float
1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 p.SetY(9)
4 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w))
5     #1.0, 9.0, 3.0, 4.0

SetZ ( self, tZ )

Set the value of the z-axis.

Parameters

tZ [IN] the value of the z-axis - float
1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 p.SetZ(9)
4 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w))
5     #1.0, 2.0, 9.0, 4.0

SetW ( self, tW )

Set the value of the w-axis.

Parameters

tW [IN] the value of the w-axis - float
1 a = RLPy.RVector4(1, 2, 3, 4)
2 p = RLPy.RQuaternion(a)
3 p.SetW(9)
4 print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w))
5     #1.0, 2.0, 3.0, 9.0