# -----------------------------------------------------------------------------
# This file was autogenerated by symforce from template:
# geo_package/CLASS.py.jinja
# Do NOT modify by hand.
# -----------------------------------------------------------------------------
# ruff: noqa: PLR0915, F401, PLW0211, PLR0914
import math
import random
import typing as T
import numpy
# isort: split
from .ops import rot3 as ops
[docs]class Rot3(object):
"""
Autogenerated Python implementation of :py:class:`symforce.geo.rot3.Rot3`.
Group of three-dimensional orthogonal matrices with determinant ``+1``, representing
rotations in 3D space. Backed by a quaternion with (x, y, z, w) storage.
"""
__slots__ = ["data"]
def __repr__(self):
# type: () -> str
return "<{} {}>".format(self.__class__.__name__, self.data)
# --------------------------------------------------------------------------
# Handwritten methods included from "custom_methods/rot3.py.jinja"
# --------------------------------------------------------------------------
def __init__(self, q=None):
# type: (T.Union[T.Sequence[float], numpy.ndarray, None]) -> None
if q is None:
self.data = ops.GroupOps.identity().data # type: T.List[float]
else:
if isinstance(q, numpy.ndarray):
if q.shape in {(4, 1), (1, 4)}:
q = q.flatten()
elif q.shape != (4,):
raise IndexError(
"Expected q to be a vector of length 4; instead had shape {}".format(
q.shape
)
)
elif len(q) != 4:
raise IndexError(
"Expected q to be a sequence of length 4, was instead length {}.".format(len(q))
)
self.data = list(q)
[docs] @classmethod
def from_rotation_matrix(cls, R, epsilon=0.0):
# type: (numpy.ndarray, float) -> Rot3
"""
This implementation is based on Shepperd's method (1978)
https://arc.aiaa.org/doi/abs/10.2514/3.55767b?journalCode=jgc (this is paywalled)
See the introduction of these papers for a description of the method:
- https://digital.csic.es/bitstream/10261/179990/1/Accurate%20Computation_Sarabandi.pdf
- https://arc.aiaa.org/doi/abs/10.2514/1.31730?journalCode=jgcd
"""
assert R.shape == (3, 3)
trace = R[0, 0] + R[1, 1] + R[2, 2]
# trace is larger than any of the diagonal elements
if trace > R[0, 0] and trace > R[1, 1] and trace > R[2, 2]:
w = numpy.sqrt(1.0 + trace) / 2.0
x = (R[2, 1] - R[1, 2]) / (4.0 * w)
y = (R[0, 2] - R[2, 0]) / (4.0 * w)
z = (R[1, 0] - R[0, 1]) / (4.0 * w)
# largest diagonal element is R[0,0]
elif R[0, 0] > R[1, 1] and R[0, 0] > R[2, 2]:
x = numpy.sqrt(max(epsilon**2, 1.0 + R[0, 0] - R[1, 1] - R[2, 2])) / 2.0
y = (R[0, 1] + R[1, 0]) / (4.0 * x)
z = (R[0, 2] + R[2, 0]) / (4.0 * x)
w = (R[2, 1] - R[1, 2]) / (4.0 * x)
# largest diagonal element is R[1,1]
elif R[1, 1] > R[2, 2]:
y = numpy.sqrt(max(epsilon**2, 1.0 + R[1, 1] - R[0, 0] - R[2, 2])) / 2.0
x = (R[0, 1] + R[1, 0]) / (4.0 * y)
z = (R[1, 2] + R[2, 1]) / (4.0 * y)
w = (R[0, 2] - R[2, 0]) / (4.0 * y)
# largest diagonal element is R[2,2]
else:
z = numpy.sqrt(max(epsilon**2, 1.0 + R[2, 2] - R[0, 0] - R[1, 1])) / 2.0
x = (R[0, 2] + R[2, 0]) / (4.0 * z)
y = (R[1, 2] + R[2, 1]) / (4.0 * z)
w = (R[1, 0] - R[0, 1]) / (4.0 * z)
return Rot3.from_storage([x, y, z, w])
[docs] @classmethod
def random(cls):
# type: () -> Rot3
return Rot3.random_from_uniform_samples(
random.uniform(0, 1), random.uniform(0, 1), random.uniform(0, 1)
)
# --------------------------------------------------------------------------
# Custom generated methods
# --------------------------------------------------------------------------
[docs] def compose_with_point(self, right):
# type: (Rot3, numpy.ndarray) -> numpy.ndarray
"""
Left-multiplication. Either rotation concatenation or point transform.
"""
# Total ops: 43
# Input arrays
_self = self.data
if right.shape == (3,):
right = right.reshape((3, 1))
elif right.shape != (3, 1):
raise IndexError(
"right is expected to have shape (3, 1) or (3,); instead had shape {}".format(
right.shape
)
)
# Intermediate terms (11)
_tmp0 = 2 * _self[0]
_tmp1 = _self[1] * _tmp0
_tmp2 = 2 * _self[2]
_tmp3 = _self[3] * _tmp2
_tmp4 = 2 * _self[1] * _self[3]
_tmp5 = _self[2] * _tmp0
_tmp6 = -2 * _self[1] ** 2
_tmp7 = 1 - 2 * _self[2] ** 2
_tmp8 = _self[3] * _tmp0
_tmp9 = _self[1] * _tmp2
_tmp10 = -2 * _self[0] ** 2
# Output terms
_res = numpy.zeros(3)
_res[0] = (
right[0, 0] * (_tmp6 + _tmp7)
+ right[1, 0] * (_tmp1 - _tmp3)
+ right[2, 0] * (_tmp4 + _tmp5)
)
_res[1] = (
right[0, 0] * (_tmp1 + _tmp3)
+ right[1, 0] * (_tmp10 + _tmp7)
+ right[2, 0] * (-_tmp8 + _tmp9)
)
_res[2] = (
right[0, 0] * (-_tmp4 + _tmp5)
+ right[1, 0] * (_tmp8 + _tmp9)
+ right[2, 0] * (_tmp10 + _tmp6 + 1)
)
return _res
[docs] def to_tangent_norm(self, epsilon):
# type: (Rot3, float) -> float
"""
Returns the norm of the tangent vector corresponding to this rotation
This is equal to the angle that should be rotated through to get this Rot3, in radians.
Using this function directly is usually more efficient than computing the norm of the
tangent vector, both in symbolic and generated code; by default, symbolic APIs will not
automatically simplify to this
"""
# Total ops: 5
# Input arrays
_self = self.data
# Intermediate terms (0)
# Output terms
_res = 2 * math.acos(min(abs(_self[3]), 1 - epsilon))
return _res
[docs] def to_rotation_matrix(self):
# type: (Rot3) -> numpy.ndarray
"""
Converts to a rotation matrix
"""
# Total ops: 28
# Input arrays
_self = self.data
# Intermediate terms (11)
_tmp0 = -2 * _self[1] ** 2
_tmp1 = 1 - 2 * _self[2] ** 2
_tmp2 = 2 * _self[0]
_tmp3 = _self[1] * _tmp2
_tmp4 = 2 * _self[2]
_tmp5 = _self[3] * _tmp4
_tmp6 = 2 * _self[1] * _self[3]
_tmp7 = _self[2] * _tmp2
_tmp8 = -2 * _self[0] ** 2
_tmp9 = _self[3] * _tmp2
_tmp10 = _self[1] * _tmp4
# Output terms
_res = numpy.zeros((3, 3))
_res[0, 0] = _tmp0 + _tmp1
_res[1, 0] = _tmp3 + _tmp5
_res[2, 0] = -_tmp6 + _tmp7
_res[0, 1] = _tmp3 - _tmp5
_res[1, 1] = _tmp1 + _tmp8
_res[2, 1] = _tmp10 + _tmp9
_res[0, 2] = _tmp6 + _tmp7
_res[1, 2] = _tmp10 - _tmp9
_res[2, 2] = _tmp0 + _tmp8 + 1
return _res
[docs] def to_yaw_pitch_roll(self):
# type: (Rot3) -> numpy.ndarray
"""
Compute the yaw, pitch, and roll Euler angles in radians of this rotation
Euler angles are subject to gimbal lock: https://en.wikipedia.org/wiki/Gimbal_lock
This means that when the pitch is close to +/- pi/2, the yaw and roll angles are not
uniquely defined, so the returned values are not unique in this case.
Returns:
Scalar: Yaw angle [radians]
Scalar: Pitch angle [radians]
Scalar: Roll angle [radians]
"""
# Total ops: 27
# Input arrays
_self = self.data
# Intermediate terms (7)
_tmp0 = 2 * _self[0]
_tmp1 = 2 * _self[2]
_tmp2 = _self[2] ** 2
_tmp3 = _self[0] ** 2
_tmp4 = -(_self[1] ** 2) + _self[3] ** 2
_tmp5 = -_tmp2 + _tmp3 + _tmp4
_tmp6 = _tmp2 - _tmp3 + _tmp4
# Output terms
_res = numpy.zeros(3)
_res[0] = math.atan2(_self[1] * _tmp0 + _self[3] * _tmp1, _tmp5)
_res[1] = -math.asin(max(-1, min(1, -2 * _self[1] * _self[3] + _self[2] * _tmp0)))
_res[2] = math.atan2(_self[1] * _tmp1 + _self[3] * _tmp0, _tmp6)
return _res
[docs] @staticmethod
def from_yaw_pitch_roll(yaw, pitch, roll):
# type: (float, float, float) -> Rot3
"""
Construct from yaw, pitch, and roll Euler angles in radians
"""
# Total ops: 25
# Input arrays
# Intermediate terms (13)
_tmp0 = (1.0 / 2.0) * pitch
_tmp1 = math.sin(_tmp0)
_tmp2 = (1.0 / 2.0) * yaw
_tmp3 = math.sin(_tmp2)
_tmp4 = (1.0 / 2.0) * roll
_tmp5 = math.cos(_tmp4)
_tmp6 = _tmp3 * _tmp5
_tmp7 = math.cos(_tmp0)
_tmp8 = math.sin(_tmp4)
_tmp9 = math.cos(_tmp2)
_tmp10 = _tmp8 * _tmp9
_tmp11 = _tmp3 * _tmp8
_tmp12 = _tmp5 * _tmp9
# Output terms
_res = [0.0] * 4
_res[0] = -_tmp1 * _tmp6 + _tmp10 * _tmp7
_res[1] = _tmp1 * _tmp12 + _tmp11 * _tmp7
_res[2] = -_tmp1 * _tmp10 + _tmp6 * _tmp7
_res[3] = _tmp1 * _tmp11 + _tmp12 * _tmp7
return Rot3.from_storage(_res)
[docs] @staticmethod
def from_yaw(yaw):
# type: (float) -> Rot3
"""Construct from yaw angle in radians"""
# Total ops: 5
# Input arrays
# Intermediate terms (1)
_tmp0 = (1.0 / 2.0) * yaw
# Output terms
_res = [0.0] * 4
_res[0] = 0
_res[1] = 0
_res[2] = 1.0 * math.sin(_tmp0)
_res[3] = 1.0 * math.cos(_tmp0)
return Rot3.from_storage(_res)
[docs] @staticmethod
def from_pitch(pitch):
# type: (float) -> Rot3
"""Construct from pitch angle in radians"""
# Total ops: 5
# Input arrays
# Intermediate terms (1)
_tmp0 = (1.0 / 2.0) * pitch
# Output terms
_res = [0.0] * 4
_res[0] = 0
_res[1] = 1.0 * math.sin(_tmp0)
_res[2] = 0
_res[3] = 1.0 * math.cos(_tmp0)
return Rot3.from_storage(_res)
[docs] @staticmethod
def from_roll(roll):
# type: (float) -> Rot3
"""Construct from roll angle in radians"""
# Total ops: 5
# Input arrays
# Intermediate terms (1)
_tmp0 = (1.0 / 2.0) * roll
# Output terms
_res = [0.0] * 4
_res[0] = 1.0 * math.sin(_tmp0)
_res[1] = 0
_res[2] = 0
_res[3] = 1.0 * math.cos(_tmp0)
return Rot3.from_storage(_res)
[docs] @staticmethod
def from_angle_axis(angle, axis):
# type: (float, numpy.ndarray) -> Rot3
"""
Construct from an angle in radians and a (normalized) axis as a 3-vector.
"""
# Total ops: 6
# Input arrays
if axis.shape == (3,):
axis = axis.reshape((3, 1))
elif axis.shape != (3, 1):
raise IndexError(
"axis is expected to have shape (3, 1) or (3,); instead had shape {}".format(
axis.shape
)
)
# Intermediate terms (2)
_tmp0 = (1.0 / 2.0) * angle
_tmp1 = math.sin(_tmp0)
# Output terms
_res = [0.0] * 4
_res[0] = _tmp1 * axis[0, 0]
_res[1] = _tmp1 * axis[1, 0]
_res[2] = _tmp1 * axis[2, 0]
_res[3] = math.cos(_tmp0)
return Rot3.from_storage(_res)
[docs] @staticmethod
def from_two_unit_vectors(a, b, epsilon):
# type: (numpy.ndarray, numpy.ndarray, float) -> Rot3
"""
Return a rotation that transforms a to b. Both inputs are three-vectors that
are expected to be normalized.
Reference:
http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors
"""
# Total ops: 44
# Input arrays
if a.shape == (3,):
a = a.reshape((3, 1))
elif a.shape != (3, 1):
raise IndexError(
"a is expected to have shape (3, 1) or (3,); instead had shape {}".format(a.shape)
)
if b.shape == (3,):
b = b.reshape((3, 1))
elif b.shape != (3, 1):
raise IndexError(
"b is expected to have shape (3, 1) or (3,); instead had shape {}".format(b.shape)
)
# Intermediate terms (7)
_tmp0 = a[0, 0] * b[0, 0] + a[1, 0] * b[1, 0] + a[2, 0] * b[2, 0]
_tmp1 = math.sqrt(2 * _tmp0 + epsilon + 2)
_tmp2 = (
0.0 if -epsilon + abs(_tmp0 + 1) == 0 else math.copysign(1, -epsilon + abs(_tmp0 + 1))
) + 1
_tmp3 = (1.0 / 2.0) * _tmp2
_tmp4 = _tmp3 / _tmp1
_tmp5 = 1.0 / 2.0 - 1.0 / 2.0 * (
0.0
if a[1, 0] ** 2 + a[2, 0] ** 2 - epsilon**2 == 0
else math.copysign(1, a[1, 0] ** 2 + a[2, 0] ** 2 - epsilon**2)
)
_tmp6 = 1 - _tmp3
# Output terms
_res = [0.0] * 4
_res[0] = _tmp4 * (a[1, 0] * b[2, 0] - a[2, 0] * b[1, 0]) + _tmp6 * (1 - _tmp5)
_res[1] = _tmp4 * (-a[0, 0] * b[2, 0] + a[2, 0] * b[0, 0]) + _tmp5 * _tmp6
_res[2] = _tmp4 * (a[0, 0] * b[1, 0] - a[1, 0] * b[0, 0])
_res[3] = (1.0 / 4.0) * _tmp1 * _tmp2
return Rot3.from_storage(_res)
# --------------------------------------------------------------------------
# StorageOps concept
# --------------------------------------------------------------------------
[docs] @staticmethod
def storage_dim():
# type: () -> int
return 4
[docs] def to_storage(self):
# type: () -> T.List[float]
return list(self.data)
[docs] @classmethod
def from_storage(cls, vec):
# type: (T.Sequence[float]) -> Rot3
instance = cls.__new__(cls)
if isinstance(vec, list):
instance.data = vec
else:
instance.data = list(vec)
if len(vec) != cls.storage_dim():
raise ValueError(
"{} has storage dim {}, got {}.".format(cls.__name__, cls.storage_dim(), len(vec))
)
return instance
# --------------------------------------------------------------------------
# GroupOps concept
# --------------------------------------------------------------------------
[docs] @classmethod
def identity(cls):
# type: () -> Rot3
return ops.GroupOps.identity()
[docs] def inverse(self):
# type: () -> Rot3
return ops.GroupOps.inverse(self)
[docs] def compose(self, b):
# type: (Rot3) -> Rot3
return ops.GroupOps.compose(self, b)
[docs] def between(self, b):
# type: (Rot3) -> Rot3
return ops.GroupOps.between(self, b)
# --------------------------------------------------------------------------
# LieGroupOps concept
# --------------------------------------------------------------------------
[docs] @staticmethod
def tangent_dim():
# type: () -> int
return 3
[docs] @classmethod
def from_tangent(cls, vec, epsilon=1e-8):
# type: (numpy.ndarray, float) -> Rot3
if len(vec) != cls.tangent_dim():
raise ValueError(
"Vector dimension ({}) not equal to tangent space dimension ({}).".format(
len(vec), cls.tangent_dim()
)
)
return ops.LieGroupOps.from_tangent(vec, epsilon)
[docs] def to_tangent(self, epsilon=1e-8):
# type: (float) -> numpy.ndarray
return ops.LieGroupOps.to_tangent(self, epsilon)
[docs] def retract(self, vec, epsilon=1e-8):
# type: (numpy.ndarray, float) -> Rot3
if len(vec) != self.tangent_dim():
raise ValueError(
"Vector dimension ({}) not equal to tangent space dimension ({}).".format(
len(vec), self.tangent_dim()
)
)
return ops.LieGroupOps.retract(self, vec, epsilon)
[docs] def local_coordinates(self, b, epsilon=1e-8):
# type: (Rot3, float) -> numpy.ndarray
return ops.LieGroupOps.local_coordinates(self, b, epsilon)
[docs] def interpolate(self, b, alpha, epsilon=1e-8):
# type: (Rot3, float, float) -> Rot3
return ops.LieGroupOps.interpolate(self, b, alpha, epsilon)
# --------------------------------------------------------------------------
# General Helpers
# --------------------------------------------------------------------------
def __eq__(self, other):
# type: (T.Any) -> bool
if isinstance(other, Rot3):
return self.data == other.data
else:
return False
@T.overload
def __mul__(self, other): # pragma: no cover
# type: (Rot3) -> Rot3
pass
@T.overload
def __mul__(self, other): # pragma: no cover
# type: (numpy.ndarray) -> numpy.ndarray
pass
def __mul__(self, other):
# type: (T.Union[Rot3, numpy.ndarray]) -> T.Union[Rot3, numpy.ndarray]
if isinstance(other, Rot3):
return self.compose(other)
elif isinstance(other, numpy.ndarray) and hasattr(self, "compose_with_point"):
return self.compose_with_point(other).reshape(other.shape)
else:
raise NotImplementedError("Cannot compose {} with {}.".format(type(self), type(other)))