Difference between revisions of "IC Python API:Rotation Math"

Latest revision as of 23:41, 9 March 2020

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.

Radians to Degrees

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):

    return radians * 57.295779513082320876798154814105

Degrees to 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

print(math.radians(90))  # 1.5707963267948966

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