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

Main article: Modules.

## 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)init

## Constructor & Destructor

### __init__( self )

The constructor. Initialize a new RQuaternion object 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 RQuaternion object from a 4D vector RVector4.

#### Parameters

vV [IN] a 4D vector - RLPy.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 - RLPy.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 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 - RLPy.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 RQuaternion object with a 3x3 rotation matrix.

#### Parameters

kRot [IN] a 3x3 rotation matrix - RLPy.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')
```

### +

```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 with tolerance: 0.00001.

#### Parameters

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

#### Returns

True if the two quaternions are almost the same - 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 - RLPy.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 - RLPy.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 - RLPy.RVector3
fAngle [IN] angle in radians - float

#### Returns

Return a new quaternion from a axis angle - RLPy.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 - RLPy.RMatrix3

#### Returns

Return a new quaternion from a rotation matrix - RLPy.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 - RLPy.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 - RLPy.RQuaternion

#### Returns

Returns the multiplied quaternion - RLPy.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 - RLPy.RQuaternion

#### Returns

Returns the multiplied quaternion - RLPy.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 )

Normalizes this quaternion.

#### Returns

Returns the normalized quaternion - RLPy.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 180 degree of this quaternion.

#### Returns

Returns the rotated quaternion - RLPy.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
```