mirror of https://github.com/ArduPilot/ardupilot
347 lines
11 KiB
Python
347 lines
11 KiB
Python
#!/usr/bin/env python
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"""
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vector3 and rotation matrix classes
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This follows the conventions in the ArduPilot code,
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and is essentially a python version of the AP_Math library
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Andrew Tridgell, March 2012
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This library is free software; you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as published by the
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Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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This library is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
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for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this library; if not, write to the Free Software Foundation,
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Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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"""
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from __future__ import print_function
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from math import acos, asin, atan2, cos, pi, radians, sin, sqrt
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class Vector3:
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"""A vector."""
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def __init__(self, x=None, y=None, z=None):
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if x is not None and y is not None and z is not None:
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self.x = float(x)
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self.y = float(y)
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self.z = float(z)
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elif x is not None and len(x) == 3:
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self.x = float(x[0])
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self.y = float(x[1])
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self.z = float(x[2])
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elif x is not None:
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raise ValueError('bad initialiser')
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else:
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self.x = float(0)
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self.y = float(0)
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self.z = float(0)
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def __repr__(self):
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return 'Vector3(%.2f, %.2f, %.2f)' % (self.x,
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self.y,
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self.z)
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def __add__(self, v):
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return Vector3(self.x + v.x,
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self.y + v.y,
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self.z + v.z)
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__radd__ = __add__
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def __sub__(self, v):
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return Vector3(self.x - v.x,
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self.y - v.y,
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self.z - v.z)
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def __neg__(self):
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return Vector3(-self.x, -self.y, -self.z)
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def __rsub__(self, v):
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return Vector3(v.x - self.x,
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v.y - self.y,
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v.z - self.z)
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def __mul__(self, v):
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if isinstance(v, Vector3):
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"""dot product"""
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return self.x * v.x + self.y * v.y + self.z * v.z
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return Vector3(self.x * v,
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self.y * v,
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self.z * v)
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__rmul__ = __mul__
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def __div__(self, v):
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return Vector3(self.x / v,
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self.y / v,
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self.z / v)
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def __mod__(self, v):
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"""Cross product."""
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return Vector3(self.y * v.z - self.z * v.y,
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self.z * v.x - self.x * v.z,
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self.x * v.y - self.y * v.x)
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def __copy__(self):
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return Vector3(self.x, self.y, self.z)
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copy = __copy__
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def length(self):
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return sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
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def zero(self):
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self.x = self.y = self.z = 0
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def angle(self, v):
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"""Return the angle between this vector and another vector."""
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return acos(self * v) / (self.length() * v.length())
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def normalized(self):
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return self / self.length()
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def normalize(self):
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v = self.normalized()
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self.x = v.x
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self.y = v.y
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self.z = v.z
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class Matrix3:
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"""A 3x3 matrix, intended as a rotation matrix."""
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def __init__(self, a=None, b=None, c=None):
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if a is not None and b is not None and c is not None:
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self.a = a.copy()
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self.b = b.copy()
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self.c = c.copy()
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else:
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self.identity()
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def __repr__(self):
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return 'Matrix3((%.2f, %.2f, %.2f), (%.2f, %.2f, %.2f), (%.2f, %.2f, %.2f))' % (
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self.a.x, self.a.y, self.a.z,
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self.b.x, self.b.y, self.b.z,
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self.c.x, self.c.y, self.c.z)
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def identity(self):
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self.a = Vector3(1, 0, 0)
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self.b = Vector3(0, 1, 0)
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self.c = Vector3(0, 0, 1)
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def transposed(self):
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return Matrix3(Vector3(self.a.x, self.b.x, self.c.x),
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Vector3(self.a.y, self.b.y, self.c.y),
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Vector3(self.a.z, self.b.z, self.c.z))
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def from_euler(self, roll, pitch, yaw):
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"""Fill the matrix from Euler angles in radians."""
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cp = cos(pitch)
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sp = sin(pitch)
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sr = sin(roll)
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cr = cos(roll)
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sy = sin(yaw)
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cy = cos(yaw)
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self.a.x = cp * cy
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self.a.y = (sr * sp * cy) - (cr * sy)
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self.a.z = (cr * sp * cy) + (sr * sy)
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self.b.x = cp * sy
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self.b.y = (sr * sp * sy) + (cr * cy)
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self.b.z = (cr * sp * sy) - (sr * cy)
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self.c.x = -sp
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self.c.y = sr * cp
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self.c.z = cr * cp
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def to_euler(self):
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"""Find Euler angles (321 convention) for the matrix."""
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if self.c.x >= 1.0:
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pitch = pi
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elif self.c.x <= -1.0:
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pitch = -pi
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else:
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pitch = -asin(self.c.x)
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roll = atan2(self.c.y, self.c.z)
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yaw = atan2(self.b.x, self.a.x)
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return (roll, pitch, yaw)
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def to_euler312(self):
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"""Find Euler angles (312 convention) for the matrix.
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See http://www.atacolorado.com/eulersequences.doc
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"""
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T21 = self.a.y
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T22 = self.b.y
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T23 = self.c.y
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T13 = self.c.x
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T33 = self.c.z
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yaw = atan2(-T21, T22)
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roll = asin(T23)
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pitch = atan2(-T13, T33)
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return (roll, pitch, yaw)
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def from_euler312(self, roll, pitch, yaw):
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"""Fill the matrix from Euler angles in radians in 312 convention."""
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c3 = cos(pitch)
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s3 = sin(pitch)
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s2 = sin(roll)
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c2 = cos(roll)
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s1 = sin(yaw)
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c1 = cos(yaw)
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self.a.x = c1 * c3 - s1 * s2 * s3
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self.b.y = c1 * c2
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self.c.z = c3 * c2
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self.a.y = -c2 * s1
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self.a.z = s3 * c1 + c3 * s2 * s1
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self.b.x = c3 * s1 + s3 * s2 * c1
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self.b.z = s1 * s3 - s2 * c1 * c3
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self.c.x = -s3 * c2
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self.c.y = s2
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def __add__(self, m):
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return Matrix3(self.a + m.a, self.b + m.b, self.c + m.c)
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__radd__ = __add__
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def __sub__(self, m):
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return Matrix3(self.a - m.a, self.b - m.b, self.c - m.c)
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def __rsub__(self, m):
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return Matrix3(m.a - self.a, m.b - self.b, m.c - self.c)
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def __mul__(self, other):
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if isinstance(other, Vector3):
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v = other
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return Vector3(self.a.x * v.x + self.a.y * v.y + self.a.z * v.z,
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self.b.x * v.x + self.b.y * v.y + self.b.z * v.z,
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self.c.x * v.x + self.c.y * v.y + self.c.z * v.z)
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elif isinstance(other, Matrix3):
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m = other
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return Matrix3(Vector3(self.a.x * m.a.x + self.a.y * m.b.x + self.a.z * m.c.x,
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self.a.x * m.a.y + self.a.y * m.b.y + self.a.z * m.c.y,
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self.a.x * m.a.z + self.a.y * m.b.z + self.a.z * m.c.z),
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Vector3(self.b.x * m.a.x + self.b.y * m.b.x + self.b.z * m.c.x,
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self.b.x * m.a.y + self.b.y * m.b.y + self.b.z * m.c.y,
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self.b.x * m.a.z + self.b.y * m.b.z + self.b.z * m.c.z),
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Vector3(self.c.x * m.a.x + self.c.y * m.b.x + self.c.z * m.c.x,
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self.c.x * m.a.y + self.c.y * m.b.y + self.c.z * m.c.y,
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self.c.x * m.a.z + self.c.y * m.b.z + self.c.z * m.c.z))
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v = other
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return Matrix3(self.a * v, self.b * v, self.c * v)
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def __div__(self, v):
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return Matrix3(self.a / v, self.b / v, self.c / v)
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def __neg__(self):
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return Matrix3(-self.a, -self.b, -self.c)
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def __copy__(self):
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return Matrix3(self.a, self.b, self.c)
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copy = __copy__
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def rotate(self, g):
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"""Rotate the matrix by a given amount on 3 axes."""
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temp_matrix = Matrix3()
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a = self.a
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b = self.b
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c = self.c
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temp_matrix.a.x = a.y * g.z - a.z * g.y
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temp_matrix.a.y = a.z * g.x - a.x * g.z
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temp_matrix.a.z = a.x * g.y - a.y * g.x
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temp_matrix.b.x = b.y * g.z - b.z * g.y
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temp_matrix.b.y = b.z * g.x - b.x * g.z
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temp_matrix.b.z = b.x * g.y - b.y * g.x
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temp_matrix.c.x = c.y * g.z - c.z * g.y
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temp_matrix.c.y = c.z * g.x - c.x * g.z
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temp_matrix.c.z = c.x * g.y - c.y * g.x
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self.a += temp_matrix.a
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self.b += temp_matrix.b
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self.c += temp_matrix.c
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def normalize(self):
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"""Re-normalise a rotation matrix."""
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error = self.a * self.b
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t0 = self.a - (self.b * (0.5 * error))
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t1 = self.b - (self.a * (0.5 * error))
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t2 = t0 % t1
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self.a = t0 * (1.0 / t0.length())
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self.b = t1 * (1.0 / t1.length())
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self.c = t2 * (1.0 / t2.length())
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def trace(self):
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"""The trace of the matrix."""
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return self.a.x + self.b.y + self.c.z
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def test_euler():
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"""Check that from_euler() and to_euler() are consistent."""
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m = Matrix3()
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from math import radians, degrees
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for r in range(-179, 179, 3):
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for p in range(-89, 89, 3):
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for y in range(-179, 179, 3):
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m.from_euler(radians(r), radians(p), radians(y))
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(r2, p2, y2) = m.to_euler()
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v1 = Vector3(r, p, y)
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v2 = Vector3(degrees(r2), degrees(p2), degrees(y2))
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diff = v1 - v2
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if diff.length() > 1.0e-12:
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print('EULER ERROR:', v1, v2, diff.length())
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def test_euler312_single(r, p, y):
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"""Check that from_euler312() and to_euler312() are consistent for one set of values."""
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from math import degrees, radians
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m = Matrix3()
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m.from_euler312(radians(r), radians(p), radians(y))
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(r2, p2, y2) = m.to_euler312()
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v1 = Vector3(r, p, y)
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v2 = Vector3(degrees(r2), degrees(p2), degrees(y2))
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diff = v1 - v2
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if diff.length() > 1.0e-12:
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print('EULER ERROR:', v1, v2, diff.length())
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def test_one_axis(r, p, y):
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"""Check that from_euler312() and from_euler() are consistent for one set of values on one axis."""
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from math import degrees, radians
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m = Matrix3()
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m.from_euler312(radians(r), radians(p), radians(y))
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(r2, p2, y2) = m.to_euler()
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v1 = Vector3(r, p, y)
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v2 = Vector3(degrees(r2), degrees(p2), degrees(y2))
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diff = v1 - v2
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if diff.length() > 1.0e-12:
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print('EULER ERROR:', v1, v2, diff.length())
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def test_euler312():
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"""Check that from_euler312() and to_euler312() are consistent."""
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m = Matrix3()
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for x in range(-89, 89, 3):
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test_one_axis(x, 0, 0)
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test_one_axis(0, x, 0)
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test_one_axis(0, 0, x)
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for r in range(-89, 89, 3):
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for p in range(-179, 179, 3):
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for y in range(-179, 179, 3):
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test_euler312_single(r, p, y)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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test_euler()
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test_euler312()
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