# IC Python API:Rotation Math

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Main article: RL Python Samples.

This article will go some recipes for common 3D rotational math. You'll find this helpful if you need to perform spacial calculations.

Converting angle radians to degrees is as simple as multiplying the radians value to RLPy.RMath.CONST_RAD_TO_DEG. However constant values in Python can not be protected. If you are frequently accessing RLPy.RMath.CONST_RAD_TO_DEG then there is a real danger that the value will be over-written by accident. This will cause all subsequent calculations dealing with this value to become increasingly unstable. You can use the following conversion methods instead:

### Pythonic Way

This is the preferred way because the math module is always available; However, you'll still have to import it.

```import math

print(math.degrees(0.5)) # 28.64788975654116
```

### Custom Function

```def radians_to_degrees(radians):

```

Converting angle degrees to radians is as simple as multiplying the degrees value to RLPy.RMath.CONST_DEG_TO_RAD. However constant values in Python can not be protected. If you are frequently accessing RLPy.RMath.CONST_DEG_TO_RAD then there is a real danger that the value will be over-written by accident. This will cause all subsequent calculations dealing with this value to become increasingly unstable. You can use the following conversion methods instead:

### Pythonic Way

This is the preferred way because the math module is always available; However, you'll still have to import it.

```import math

```

### Custom Function

```def degrees_to_radians(degrees):

return degrees * 0.017453292519943295769236907684886
```

## Delta Angle

Calculates the shortest difference between two given angles in degrees.

```def delta_angle(current, target):
num = repeat(target - current, 360)
if num > 180:
num -= 360
return num
```

### Examples

```print(delta_angle(128, 360))  # -128
print(delta_angle(5, 180))  # 175
```

## Matrix3 to Euler Angles

Converts matrix rotational data (3x3 matrix) to euler rotational data (radians).

```def matrix3_to_eulerAngle(matrix3):
x = y = z = 0
a = matrix3.ToEulerAngle(RLPy.EEulerOrder_XYZ, x, y, z)
return RLPy.RVector3(a[0], a[1], a[2])
```

## Quaternion to Matrix

Converts quaternion rotational data to matrix rotational data (3x3 matrix).

```def quaternion_to_matrix(quaterion):
matrix4 = RLPy.RMatrix4()
matrix4.MakeIdentity()
matrix3 = quaterion.ToRotationMatrix()
matrix4.SetSR(matrix3)
return matrix4
```

## From to Rotation

Creates a rotation which rotates from one direction to another direction. Usually you use this to rotate a transform so that one of its axes e.g. the y-axis follows a target direction in world-space.

```def from_to_rotation(from_vector, to_vector):
# Points the from axis towards the to vector, returns a Quaternion
result = RLPy.RQuaternion()
from_vector.Normalize()
to_vector.Normalize()
up_axis = RLPy.RVector3(RLPy.RVector3.UNIT_Z)
angle = RLPy.RMath_ACos(from_vector.Dot(to_vector))
if RLPy.RMath.AlmostZero(angle - RLPy.RMath.CONST_PI) or RLPy.RMath.AlmostZero(angle):
result.FromAxisAngle(up_axis, angle)
else:
normal = from_vector.Cross(to_vector)
normal.Normalize()
result.FromAxisAngle(normal, angle)
return result
```