IC Python API:RLPy RQuaternion

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. RQuaternionalso 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)init

Constructor & Destructor

init( self )

The constructor. Initialize a new RQuaternionobject without initialization.

q = RLPy.RQuaternion()

print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # random values

init( self, vV )

The constructor. Initialize a new RQuaternionobject from a 4D vector.

Parameters

vV [IN] a 4D vector - RVector4

v = RLPy.RVector4(1, 2, 3, 4)
q = RLPy.RQuaternion(v)

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

v = RLPy.RVector4(1, 2, 3, 4)
q = RLPy.RQuaternion(v)
p = RLPy.RQuaternion(q)

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 RQuaternionobject 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

v = RLPy.RVector3(0, 0, 1)
q = RLPy.RQuaternion(v, math.pi/2)

print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
    # 0.0, 0.0, 0.7071067094802856, 0.7071067690849304

init( self, kRot )

The constructor. Initialize a new RQuaternionobject with a 3x3 rotation matrix.

Parameters

kRot [IN] a 3x3 rotation matrix - RMatrix3

v = RLPy.RVector3(0, 0, 1)
m = RLPy.RMatrix3(v, math.pi/2)
q = RLPy.RQuaternion(m)

print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
    # 0.0, 0.0, 0.7071067690849304, 0.7071067690849304

Operator

=

The "equal to" operator.

q = RLPy.RQuaternion()
p = q
if q == p:                         # True
    print("equal")

!=

The "not equal to" operator.

a = RLPy.RVector4(1, 2, 3, 4)
q = RLPy.RQuaternion(a)
b = RLPy.RVector4(2, 2, 3, 4)
p = RLPy.RQuaternion(b)
if a != b:                         #True
    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.

a = RLPy.RVector4(0, 1, 5, 2)
b = RLPy.RVector4(0, 1, 5, 3)
c = RLPy.RVector4(1, 0, 1, 0)
d = RLPy.RVector4(0, 1, 5, 2)

p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = RLPy.RQuaternion(c)
s = RLPy.RQuaternion(d)

if p< q:                       #True
    print('p< q')
if q< r:                       #True
    print('q< r')
if p< s:                       #False
    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.

a = RLPy.RVector4(0, 1, 5, 2)
b = RLPy.RVector4(0, 1, 5, 3)
c = RLPy.RVector4(1, 0, 1, 0)
d = RLPy.RVector4(0, 1, 5, 2)

p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = RLPy.RQuaternion(c)
s = RLPy.RQuaternion(d)

if q >p:                       #True
    print('q >p')
if r >q:                       #True
    print('r >q')
if p >s:                       #False
    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.

a = RLPy.RVector4(0, 1, 5, 2)
b = RLPy.RVector4(0, 1, 5, 3)
c = RLPy.RVector4(1, 0, 1, 0)
d = RLPy.RVector4(0, 1, 5, 2)

p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = RLPy.RQuaternion(c)
s = RLPy.RQuaternion(d)

if p<= q:                       #True
    print('p<= q')
if q<= r:                       #True
    print('q<= r')
if p<= s:                       #True
    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.

a = RLPy.RVector4(0, 1, 5, 2)
b = RLPy.RVector4(0, 1, 5, 3)
c = RLPy.RVector4(1, 0, 1, 0)
d = RLPy.RVector4(0, 1, 5, 2)

p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = RLPy.RQuaternion(c)
s = RLPy.RQuaternion(d)

if q >= p:                       #True
    print('q >= p')
if r >= q:                       #True
    print('r >= q')
if p >= s:                       #True
    print('p >= s')

+

The "addition" operator. Perform quaternion addition.

a = RLPy.RVector4(0, 1, 2, 3)
b = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = p + q

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.

a = RLPy.RVector4(0, 1, 2, 3)
b = RLPy.RVector4(3, 2, 1, 0)
p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = q - p

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.

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = p * 2
r = p * p

print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w)) # 2.0, 4.0, 6.0, 8.0
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.

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = p / 2

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.

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = -p

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.

a = RLPy.RVector4(0, 1, 2, 3)
b = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
p += q

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.

a = RLPy.RVector4(0, 1, 4, 5)
b = RLPy.RVector4(1, 2, 3, 1)
p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
p -= q

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.

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
p *= 2

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.

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
p /= 2

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 the 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

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(a)
r = RLPy.RQuaternion(a)

q.w = 4.000000001
r.w = 4.00001

if p.AlmostEqual(q):               #True
    print("p ≈ q")
if q.AlmostEqual(r):               #False
    print("p ≈ r")

Conjugate( self )

Conjugate this quaternion.

Returns

Returns the conjugated quaternion. The result is a quaternion whose x, y, and z values have been negated - RQuaternion

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
q = p.Conjugate()

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 dot product of the two quaternions.

Parameters

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

Returns

Returns the value of the dot product - float

a = RLPy.RVector4(1, 2, 3, 4)
b = RLPy.RVector4(1, 2, 3, 0)
p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
f = p.Dot(q)

print(f)     # 14.0

FromAxisAngle( self, rkAxis, fAngle )

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

p = RLPy.RQuaternion()
v = RLPy.RVector3(0, 0, 1)
p.FromAxisAngle(v, math.pi/2)

print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 0.0, 0.0, 0.7071067094802856, 0.7071067690849304

FromRotationMatrix( self, rkRot )

Quaternion from a rotation matrix.

Parameters

rkRot [IN] Rotation matrix - RMatrix3

Returns

Return a new quaternion from a rotation matrix - RQuaternion

v = RLPy.RVector3(0, 0, 1)
m = RLPy.RMatrix3(v, math.pi/2)
p = RLPy.RQuaternion()
p.FromRotationMatrix(m)

print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w)) # 0.0, 0.0, 0.7071067690849304, 0.7071067690849304

Inverse( self, rkRot )

Obtain the inverse of this quaternion.

Returns

The inversed quaternion - RQuaternion

a = RLPy.RVector4(1, 1, 1, 1)
p = RLPy.RQuaternion(a)
q = p.Inverse()

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 by another quaternion.

Parameters

qQ [IN] The quaternion to multiply - RQuaternion

Returns

Returns the multiplied quaternion - RQuaternion

a = RLPy.RVector4(1, 2, 3, 4)
b = RLPy.RVector4(1, 2, 2, 1)

p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = p.Multiply(q)

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

a = RLPy.RVector4(1, 2, 3, 4)
b = RLPy.RVector4(1, 2, 2, 1)

p = RLPy.RQuaternion(a)
q = RLPy.RQuaternion(b)
r = p.MultiplyEqual(q)

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

a = RLPy.RVector4(1, 1, 1, 1)
p = RLPy.RQuaternion(a)
q = p.Normalize()

print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
    # 0.4999999701976776, 0.4999999701976776, 0.4999999701976776, 0.4999999701976776

Rotate180( self )

Rotate this quaternion by 180 degrees.

Returns

The rotated quaternion - RQuaternion

a = RLPy.RVector4(1, 1, 1, 1)
p = RLPy.RQuaternion(a)
q = p.Normalize()

print(str(q.x) + ', ' + str(q.y) + ', ' + str(q.z) + ', ' + str(q.w))
   #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

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
p.SetX(9)

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

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
p.SetY(9)
print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w))
    #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

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
p.SetZ(9)
print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w))
    #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

a = RLPy.RVector4(1, 2, 3, 4)
p = RLPy.RQuaternion(a)
p.SetW(9)
print(str(p.x) + ', ' + str(p.y) + ', ' + str(p.z) + ', ' + str(p.w))
    #1.0, 2.0, 3.0, 9.0

IC Python API:RLPy RQuaternion

Contents

Detailed Description

Constructor & Destructor

__init__( self )

__init__( self, vV )

Parameters

__init__( self, qQ )

Parameters

__init__( self, kAxis, fAngle )

Parameters

__init__( self, kRot )

Parameters

Operator

=

!=

<

>

<=

>=

+

-

*

/

-

+ =

- =

*=

/=

Member Functions

AlmostEqual( self, qQ )

Parameters

Returns

Conjugate( self )

Returns

Dot( self, qQ )

Parameters

Returns

FromAxisAngle( self, rkAxis, fAngle )

Parameters

Returns

FromRotationMatrix( self, rkRot )

Parameters

Returns

Inverse( self, rkRot )

Returns

Multiply( self, qQ )

Parameters

Returns

MultiplyEqual( self, qQ )

Parameters

Returns

Normalize( self )

Returns

Rotate180( self )

Returns

SetX( self, tX )

Parameters

SetY( self, tY )

Parameters

SetZ( self, tZ )

Parameters

SetW( self, tW )

Parameters

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init( self )

init( self, vV )

init( self, qQ )

init( self, kAxis, fAngle )

init( self, kRot )