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#!/usr/bin/env python
#
# vector3 and rotation matrix classes
# This follows the conventions in the ArduPilot code,
# and is essentially a python version of the AP_Math library
#
# Andrew Tridgell, March 2012
#
# This library is free software; you can redistribute it and/or modify it
# under the terms of the GNU Lesser General Public License as published by the
# Free Software Foundation; either version 2.1 of the License, or (at your
# option) any later version.
#
# This library is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
# for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this library; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
'''rotation matrix class
'''
from math import sin, cos, sqrt, asin, atan2, pi, radians, acos
class Vector3:
'''a vector'''
def __init__(self, x=None, y=None, z=None):
if x != None and y != None and z != None:
self.x = float(x)
self.y = float(y)
self.z = float(z)
elif x != None and len(x) == 3:
self.x = float(x[0])
self.y = float(x[1])
self.z = float(x[2])
elif x != None:
raise ValueError('bad initialiser')
else:
self.x = float(0)
self.y = float(0)
self.z = float(0)
def __repr__(self):
return 'Vector3(%.2f, %.2f, %.2f)' % (self.x,
self.y,
self.z)
def __add__(self, v):
return Vector3(self.x + v.x,
self.y + v.y,
self.z + v.z)
__radd__ = __add__
def __sub__(self, v):
return Vector3(self.x - v.x,
self.y - v.y,
self.z - v.z)
def __neg__(self):
return Vector3(-self.x, -self.y, -self.z)
def __rsub__(self, v):
return Vector3(v.x - self.x,
v.y - self.y,
v.z - self.z)
def __mul__(self, v):
if isinstance(v, Vector3):
'''dot product'''
return self.x*v.x + self.y*v.y + self.z*v.z
return Vector3(self.x * v,
self.y * v,
self.z * v)
__rmul__ = __mul__
def __div__(self, v):
return Vector3(self.x / v,
self.y / v,
self.z / v)
def __mod__(self, v):
'''cross product'''
return Vector3(self.y*v.z - self.z*v.y,
self.z*v.x - self.x*v.z,
self.x*v.y - self.y*v.x)
def __copy__(self):
return Vector3(self.x, self.y, self.z)
copy = __copy__
def length(self):
return sqrt(self.x**2 + self.y**2 + self.z**2)
def zero(self):
self.x = self.y = self.z = 0
def angle(self, v):
'''return the angle between this vector and another vector'''
return acos(self * v) / (self.length() * v.length())
def normalized(self):
return self / self.length()
def normalize(self):
v = self.normalized()
self.x = v.x
self.y = v.y
self.z = v.z
class Matrix3:
'''a 3x3 matrix, intended as a rotation matrix'''
def __init__(self, a=None, b=None, c=None):
if a is not None and b is not None and c is not None:
self.a = a.copy()
self.b = b.copy()
self.c = c.copy()
else:
self.identity()
def __repr__(self):
return 'Matrix3((%.2f, %.2f, %.2f), (%.2f, %.2f, %.2f), (%.2f, %.2f, %.2f))' % (
self.a.x, self.a.y, self.a.z,
self.b.x, self.b.y, self.b.z,
self.c.x, self.c.y, self.c.z)
def identity(self):
self.a = Vector3(1,0,0)
self.b = Vector3(0,1,0)
self.c = Vector3(0,0,1)
def transposed(self):
return Matrix3(Vector3(self.a.x, self.b.x, self.c.x),
Vector3(self.a.y, self.b.y, self.c.y),
Vector3(self.a.z, self.b.z, self.c.z))
def from_euler(self, roll, pitch, yaw):
'''fill the matrix from Euler angles in radians'''
cp = cos(pitch)
sp = sin(pitch)
sr = sin(roll)
cr = cos(roll)
sy = sin(yaw)
cy = cos(yaw)
self.a.x = cp * cy
self.a.y = (sr * sp * cy) - (cr * sy)
self.a.z = (cr * sp * cy) + (sr * sy)
self.b.x = cp * sy
self.b.y = (sr * sp * sy) + (cr * cy)
self.b.z = (cr * sp * sy) - (sr * cy)
self.c.x = -sp
self.c.y = sr * cp
self.c.z = cr * cp
def to_euler(self):
'''find Euler angles for the matrix'''
if self.c.x >= 1.0:
pitch = pi
elif self.c.x <= -1.0:
pitch = -pi
else:
pitch = -asin(self.c.x)
roll = atan2(self.c.y, self.c.z)
yaw = atan2(self.b.x, self.a.x)
return (roll, pitch, yaw)
def __add__(self, m):
return Matrix3(self.a + m.a, self.b + m.b, self.c + m.c)
__radd__ = __add__
def __sub__(self, m):
return Matrix3(self.a - m.a, self.b - m.b, self.c - m.c)
def __rsub__(self, m):
return Matrix3(m.a - self.a, m.b - self.b, m.c - self.c)
def __mul__(self, other):
if isinstance(other, Vector3):
v = other
return Vector3(self.a.x * v.x + self.a.y * v.y + self.a.z * v.z,
self.b.x * v.x + self.b.y * v.y + self.b.z * v.z,
self.c.x * v.x + self.c.y * v.y + self.c.z * v.z)
elif isinstance(other, Matrix3):
m = other
return Matrix3(Vector3(self.a.x * m.a.x + self.a.y * m.b.x + self.a.z * m.c.x,
self.a.x * m.a.y + self.a.y * m.b.y + self.a.z * m.c.y,
self.a.x * m.a.z + self.a.y * m.b.z + self.a.z * m.c.z),
Vector3(self.b.x * m.a.x + self.b.y * m.b.x + self.b.z * m.c.x,
self.b.x * m.a.y + self.b.y * m.b.y + self.b.z * m.c.y,
self.b.x * m.a.z + self.b.y * m.b.z + self.b.z * m.c.z),
Vector3(self.c.x * m.a.x + self.c.y * m.b.x + self.c.z * m.c.x,
self.c.x * m.a.y + self.c.y * m.b.y + self.c.z * m.c.y,
self.c.x * m.a.z + self.c.y * m.b.z + self.c.z * m.c.z))
v = other
return Matrix3(self.a * v, self.b * v, self.c * v)
def __div__(self, v):
return Matrix3(self.a / v, self.b / v, self.c / v)
def __neg__(self):
return Matrix3(-self.a, -self.b, -self.c)
def __copy__(self):
return Matrix3(self.a, self.b, self.c)
copy = __copy__
def rotate(self, g):
'''rotate the matrix by a given amount on 3 axes'''
temp_matrix = Matrix3()
a = self.a
b = self.b
c = self.c
temp_matrix.a.x = a.y * g.z - a.z * g.y
temp_matrix.a.y = a.z * g.x - a.x * g.z
temp_matrix.a.z = a.x * g.y - a.y * g.x
temp_matrix.b.x = b.y * g.z - b.z * g.y
temp_matrix.b.y = b.z * g.x - b.x * g.z
temp_matrix.b.z = b.x * g.y - b.y * g.x
temp_matrix.c.x = c.y * g.z - c.z * g.y
temp_matrix.c.y = c.z * g.x - c.x * g.z
temp_matrix.c.z = c.x * g.y - c.y * g.x
self.a += temp_matrix.a
self.b += temp_matrix.b
self.c += temp_matrix.c
def normalize(self):
'''re-normalise a rotation matrix'''
error = self.a * self.b
t0 = self.a - (self.b * (0.5 * error))
t1 = self.b - (self.a * (0.5 * error))
t2 = t0 % t1
self.a = t0 * (1.0 / t0.length())
self.b = t1 * (1.0 / t1.length())
self.c = t2 * (1.0 / t2.length())
def trace(self):
'''the trace of the matrix'''
return self.a.x + self.b.y + self.c.z
def test_euler():
'''check that from_euler() and to_euler() are consistent'''
m = Matrix3()
from math import radians, degrees
for r in range(-179, 179, 3):
for p in range(-89, 89, 3):
for y in range(-179, 179, 3):
m.from_euler(radians(r), radians(p), radians(y))
(r2, p2, y2) = m.to_euler()
v1 = Vector3(r,p,y)
v2 = Vector3(degrees(r2),degrees(p2),degrees(y2))
diff = v1 - v2
if diff.length() > 1.0e-12:
print('EULER ERROR:', v1, v2, diff.length())
if __name__ == "__main__":
import doctest
doctest.testmod()
test_euler()
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