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<!DOCTYPE html>
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<title>spatialmath.pose3d — Spatial Maths package 0.7.0
documentation</title>
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<h1>Source code for spatialmath.pose3d</h1><div class="highlight"><pre>
<span></span><span class="ch">#!/usr/bin/env python3</span>
<span class="c1"># -*- coding: utf-8 -*-</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">UserList</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">from</span> <span class="nn">spatialmath.base</span> <span class="kn">import</span> <span class="n">argcheck</span>
<span class="kn">import</span> <span class="nn">spatialmath.base</span> <span class="k">as</span> <span class="nn">tr</span>
<span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">super_pose</span> <span class="k">as</span> <span class="n">sp</span>
<span class="c1"># ============================== SO3 =====================================#</span>
<div class="viewcode-block" id="SO3"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3">[docs]</a><span class="k">class</span> <span class="nc">SO3</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">SMPose</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> SO(3) subclass</span>
<span class="sd"> This subclass represents rotations in 3D space. Internally it is a 3x3 orthogonal matrix belonging</span>
<span class="sd"> to the group SO(3).</span>
<span class="sd"> .. inheritance-diagram::</span>
<span class="sd"> """</span>
<div class="viewcode-block" id="SO3.__init__"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.__init__">[docs]</a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct new SO(3) object</span>
<span class="sd"> - ``SO3()`` is an SO3 instance representing null rotation -- the identity matrix</span>
<span class="sd"> - ``SO3(R)`` is an SO3 instance with rotation matrix R which is a 3x3 numpy array representing an valid rotation matrix. If ``check``</span>
<span class="sd"> is ``True`` check the matrix value.</span>
<span class="sd"> - ``SO3([R1, R2, ... RN])`` where each Ri is a 3x3 numpy array of rotation matrices, is</span>
<span class="sd"> an SO3 instance containing N rotations. If ``check`` is ``True``</span>
<span class="sd"> then each matrix is checked for validity.</span>
<span class="sd"> - ``SO3([X1, X2, ... XN])`` where each Xi is an SO3 instance, is an SO3 instance containing N rotations.</span>
<span class="sd"> :seealso: `SMPose.pose_arghandler`</span>
<span class="sd"> """</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span> <span class="c1"># activate the UserList semantics</span>
<span class="k">if</span> <span class="n">arg</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># empty constructor</span>
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="ow">is</span> <span class="n">SO3</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">3</span><span class="p">)]</span> <span class="c1"># identity rotation</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">_arghandler</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="n">check</span><span class="p">)</span></div>
<span class="c1"># ------------------------------------------------------------------------ #</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">R</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> SO(3) or SE(3) as rotation matrix</span>
<span class="sd"> :return: rotational component</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(3,3)</span>
<span class="sd"> ``x.R`` returns the rotation matrix, when `x` is `SO3` or `SE3`. If `len(x)` is:</span>
<span class="sd"> </span>
<span class="sd"> - 1, return an ndarray with shape=(3,3)</span>
<span class="sd"> - N>1, return ndarray with shape=(N,3,3)</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">x</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">]</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">])</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">n</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Normal vector of SO(3) or SE(3)</span>
<span class="sd"> :return: normal vector</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(3,)</span>
<span class="sd"> Is the first column of the rotation submatrix, sometimes called the normal</span>
<span class="sd"> vector. Parallel to the x-axis of the frame defined by this pose.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">o</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Orientation vector of SO(3) or SE(3)</span>
<span class="sd"> :return: orientation vector</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(3,)</span>
<span class="sd"> Is the second column of the rotation submatrix, sometimes called the orientation</span>
<span class="sd"> vector. Parallel to the y-axis of the frame defined by this pose.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">a</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Approach vector of SO(3) or SE(3)</span>
<span class="sd"> :return: approach vector</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(3,)</span>
<span class="sd"> Is the third column of the rotation submatrix, sometimes called the approach</span>
<span class="sd"> vector. Parallel to the z-axis of the frame defined by this pose.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
<span class="c1"># ------------------------------------------------------------------------ #</span>
<div class="viewcode-block" id="SO3.inv"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.inv">[docs]</a> <span class="k">def</span> <span class="nf">inv</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Inverse of SO(3)</span>
<span class="sd"> :param self: pose</span>
<span class="sd"> :type self: SE3 instance</span>
<span class="sd"> :return: inverse</span>
<span class="sd"> :rtype: SO2</span>
<span class="sd"> Returns the inverse, which for elements of SO(3) is the transpose.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">SO3</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">SO3</span><span class="p">([</span><span class="n">x</span><span class="o">.</span><span class="n">T</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">])</span></div>
<div class="viewcode-block" id="SO3.eul"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.eul">[docs]</a> <span class="k">def</span> <span class="nf">eul</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'deg'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> SO(3) or SE(3) as Euler angles</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 3-vector of Euler angles</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(3,)</span>
<span class="sd"> ``x.eul`` is the Euler angle representation of the rotation. Euler angles are</span>
<span class="sd"> a 3-vector :math:`(\phi, \theta, \psi)` which correspond to consecutive</span>
<span class="sd"> rotations about the Z, Y, Z axes respectively.</span>
<span class="sd"> If `len(x)` is:</span>
<span class="sd"> </span>
<span class="sd"> - 1, return an ndarray with shape=(3,)</span>
<span class="sd"> - N>1, return ndarray with shape=(N,3)</span>
<span class="sd"> - ndarray with shape=(3,), if len(R) == 1</span>
<span class="sd"> - ndarray with shape=(N,3), if len(R) = N > 1</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.Eul`, ::func:`spatialmath.base.transforms3d.tr2eul`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">tr</span><span class="o">.</span><span class="n">tr2eul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">tr2eul</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">])</span><span class="o">.</span><span class="n">T</span></div>
<div class="viewcode-block" id="SO3.rpy"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.rpy">[docs]</a> <span class="k">def</span> <span class="nf">rpy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'deg'</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s1">'zyx'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> SO(3) or SE(3) as roll-pitch-yaw angles</span>
<span class="sd"> :param order: angle sequence order, default to 'zyx'</span>
<span class="sd"> :type order: str</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 3-vector of roll-pitch-yaw angles</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(3,)</span>
<span class="sd"> ``x.rpy`` is the roll-pitch-yaw angle representation of the rotation. The angles are</span>
<span class="sd"> a 3-vector :math:`(r, p, y)` which correspond to successive rotations about the axes</span>
<span class="sd"> specified by ``order``:</span>
<span class="sd"> - 'zyx' [default], rotate by yaw about the z-axis, then by pitch about the new y-axis,</span>
<span class="sd"> then by roll about the new x-axis. Convention for a mobile robot with x-axis forward</span>
<span class="sd"> and y-axis sideways.</span>
<span class="sd"> - 'xyz', rotate by yaw about the x-axis, then by pitch about the new y-axis,</span>
<span class="sd"> then by roll about the new z-axis. Covention for a robot gripper with z-axis forward</span>
<span class="sd"> and y-axis between the gripper fingers.</span>
<span class="sd"> - 'yxz', rotate by yaw about the y-axis, then by pitch about the new x-axis,</span>
<span class="sd"> then by roll about the new z-axis. Convention for a camera with z-axis parallel</span>
<span class="sd"> to the optic axis and x-axis parallel to the pixel rows.</span>
<span class="sd"> If `len(x)` is:</span>
<span class="sd"> </span>
<span class="sd"> - 1, return an ndarray with shape=(3,)</span>
<span class="sd"> - N>1, return ndarray with shape=(N,3)</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.RPY`, ::func:`spatialmath.base.transforms3d.tr2rpy`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">tr</span><span class="o">.</span><span class="n">tr2rpy</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">tr2rpy</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">])</span><span class="o">.</span><span class="n">T</span></div>
<div class="viewcode-block" id="SO3.Ad"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Ad">[docs]</a> <span class="k">def</span> <span class="nf">Ad</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Adjoint of SO(3)</span>
<span class="sd"> </span>
<span class="sd"> :return: adjoint matrix</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(6,6)</span>
<span class="sd"> </span>
<span class="sd"> - ``SE3.Ad`` is the 6x6 adjoint matrix</span>
<span class="sd"> </span>
<span class="sd"> :seealso: Twist.ad.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">R</span><span class="p">,</span> <span class="n">tr</span><span class="o">.</span><span class="n">skew</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">t</span><span class="p">)</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">R</span><span class="p">],</span>
<span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">)),</span> <span class="bp">self</span><span class="o">.</span><span class="n">R</span><span class="p">]</span>
<span class="p">]</span></div>
<span class="c1"># ------------------------------------------------------------------------ #</span>
<div class="viewcode-block" id="SO3.isvalid"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.isvalid">[docs]</a> <span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">isvalid</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Test if matrix is valid SO(3)</span>
<span class="sd"> :param x: matrix to test</span>
<span class="sd"> :type x: numpy.ndarray</span>
<span class="sd"> :return: true if the matrix is a valid element of SO(3), ie. it is a 3x3</span>
<span class="sd"> orthonormal matrix with determinant of +1.</span>
<span class="sd"> :rtype: bool</span>
<span class="sd"> :seealso: :func:`~spatialmath.base.transform3d.isrot`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">tr</span><span class="o">.</span><span class="n">isrot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
<span class="c1"># ---------------- variant constructors ---------------------------------- #</span>
<div class="viewcode-block" id="SO3.Rx"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Rx">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Rx</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from X-axis rotation</span>
<span class="sd"> :param theta: rotation angle about the X-axis</span>
<span class="sd"> :type theta: float or array_like</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> - ``SE3.Rx(theta)`` is an SO(3) rotation of ``theta`` radians about the x-axis</span>
<span class="sd"> - ``SE3.Rx(theta, "deg")`` as above but ``theta`` is in degrees</span>
<span class="sd"> </span>
<span class="sd"> If ``theta`` is an array then the result is a sequence of rotations defined by consecutive</span>
<span class="sd"> elements.</span>
<span class="sd"> </span>
<span class="sd"> Example::</span>
<span class="sd"> </span>
<span class="sd"> >>> x = SO3.Rx(np.linspace(0, math.pi, 20))</span>
<span class="sd"> >>> len(x)</span>
<span class="sd"> 20</span>
<span class="sd"> >>> x[7]</span>
<span class="sd"> SO3(array([[ 1. , 0. , 0. ],</span>
<span class="sd"> [ 0. , 0.40169542, -0.91577333],</span>
<span class="sd"> [ 0. , 0.91577333, 0.40169542]]))</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">rotx</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">getvector</span><span class="p">(</span><span class="n">theta</span><span class="p">)],</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SO3.Ry"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Ry">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Ry</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from Y-axis rotation</span>
<span class="sd"> :param theta: rotation angle about Y-axis</span>
<span class="sd"> :type theta: float or array_like</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> - ``SO3.Ry(theta)`` is an SO(3) rotation of ``theta`` radians about the y-axis</span>
<span class="sd"> - ``SO3.Ry(theta, "deg")`` as above but ``theta`` is in degrees</span>
<span class="sd"> </span>
<span class="sd"> If ``theta`` is an array then the result is a sequence of rotations defined by consecutive</span>
<span class="sd"> elements.</span>
<span class="sd"> Example::</span>
<span class="sd"> </span>
<span class="sd"> >>> x = SO3.Ry(np.linspace(0, math.pi, 20))</span>
<span class="sd"> >>> len(x)</span>
<span class="sd"> 20</span>
<span class="sd"> >>> x[7]</span>
<span class="sd"> >>> x[7]</span>
<span class="sd"> SO3(array([[ 0.40169542, 0. , 0.91577333],</span>
<span class="sd"> [ 0. , 1. , 0. ],</span>
<span class="sd"> [-0.91577333, 0. , 0.40169542]]))</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">roty</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">getvector</span><span class="p">(</span><span class="n">theta</span><span class="p">)],</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SO3.Rz"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Rz">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Rz</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from Z-axis rotation</span>
<span class="sd"> :param theta: rotation angle about Z-axis</span>
<span class="sd"> :type theta: float or array_like</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> </span>
<span class="sd"> - ``SO3.Rz(theta)`` is an SO(3) rotation of ``theta`` radians about the z-axis</span>
<span class="sd"> - ``SO3.Rz(theta, "deg")`` as above but ``theta`` is in degrees</span>
<span class="sd"> </span>
<span class="sd"> If ``theta`` is an array then the result is a sequence of rotations defined by consecutive</span>
<span class="sd"> elements.</span>
<span class="sd"> Example::</span>
<span class="sd"> </span>
<span class="sd"> >>> x = SE3.Rz(np.linspace(0, math.pi, 20))</span>
<span class="sd"> >>> len(x)</span>
<span class="sd"> 20</span>
<span class="sd"> SO3(array([[ 0.40169542, -0.91577333, 0. ],</span>
<span class="sd"> [ 0.91577333, 0.40169542, 0. ],</span>
<span class="sd"> [ 0. , 0. , 1. ]]))</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">rotz</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">getvector</span><span class="p">(</span><span class="n">theta</span><span class="p">)],</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SO3.Rand"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Rand">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Rand</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">N</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from random rotation</span>
<span class="sd"> :param N: number of random rotations</span>
<span class="sd"> :type N: int</span>
<span class="sd"> :return: SO(3) rotation matrix</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> - ``SO3.Rand()`` is a random SO(3) rotation.</span>
<span class="sd"> - ``SO3.Rand(N)`` is a sequence of N random rotations.</span>
<span class="sd"> </span>
<span class="sd"> Example::</span>
<span class="sd"> </span>
<span class="sd"> >>> x = SO3.Rand()</span>
<span class="sd"> >>> x</span>
<span class="sd"> SO3(array([[ 0.1805082 , -0.97959019, 0.08842995],</span>
<span class="sd"> [-0.98357187, -0.17961408, 0.01803234],</span>
<span class="sd"> [-0.00178104, -0.0902322 , -0.99591916]]))</span>
<span class="sd"> :seealso: :func:`spatialmath.quaternion.UnitQuaternion.Rand`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">q2r</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">rand</span><span class="p">())</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)],</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SO3.Eul"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Eul">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Eul</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">angles</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from Euler angles</span>
<span class="sd"> :param angles: Euler angles</span>
<span class="sd"> :type angles: array_like or numpy.ndarray with shape=(N,3)</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> ``SO3.Eul(angles)`` is an SO(3) rotation defined by a 3-vector of Euler angles :math:`(\phi, \theta, \psi)` which</span>
<span class="sd"> correspond to consecutive rotations about the Z, Y, Z axes respectively.</span>
<span class="sd"> </span>
<span class="sd"> If ``angles`` is an Nx3 matrix then the result is a sequence of rotations each defined by Euler angles</span>
<span class="sd"> correponding to the rows of ``angles``.</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.eul`, :func:`~spatialmath.pose3d.SE3.Eul`, :func:`spatialmath.base.transforms3d.eul2r`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">isvector</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="mi">3</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">eul2r</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">eul2r</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">angles</span><span class="p">])</span></div>
<div class="viewcode-block" id="SO3.RPY"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.RPY">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">RPY</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">angles</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s1">'zyx'</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from roll-pitch-yaw angles</span>
<span class="sd"> :param angles: roll-pitch-yaw angles</span>
<span class="sd"> :type angles: array_like or numpy.ndarray with shape=(N,3)</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :param unit: rotation order: 'zyx' [default], 'xyz', or 'yxz'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> ``SO3.RPY(angles)`` is an SO(3) rotation defined by a 3-vector of roll, pitch, yaw angles :math:`(r, p, y)`</span>
<span class="sd"> which correspond to successive rotations about the axes specified by ``order``:</span>
<span class="sd"> - 'zyx' [default], rotate by yaw about the z-axis, then by pitch about the new y-axis,</span>
<span class="sd"> then by roll about the new x-axis. Convention for a mobile robot with x-axis forward</span>
<span class="sd"> and y-axis sideways.</span>
<span class="sd"> - 'xyz', rotate by yaw about the x-axis, then by pitch about the new y-axis,</span>
<span class="sd"> then by roll about the new z-axis. Covention for a robot gripper with z-axis forward</span>
<span class="sd"> and y-axis between the gripper fingers.</span>
<span class="sd"> - 'yxz', rotate by yaw about the y-axis, then by pitch about the new x-axis,</span>
<span class="sd"> then by roll about the new z-axis. Convention for a camera with z-axis parallel</span>
<span class="sd"> to the optic axis and x-axis parallel to the pixel rows.</span>
<span class="sd"> If ``angles`` is an Nx3 matrix then the result is a sequence of rotations each defined by RPY angles</span>
<span class="sd"> correponding to the rows of angles.</span>
<span class="sd"> </span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.rpy`, :func:`~spatialmath.pose3d.SE3.RPY`, :func:`spatialmath.base.transforms3d.rpy2r`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">isvector</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="mi">3</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">rpy2r</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="n">order</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">rpy2r</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="n">order</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">angles</span><span class="p">])</span></div>
<div class="viewcode-block" id="SO3.OA"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.OA">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">OA</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">o</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) from two vectors</span>
<span class="sd"> :param o: 3-vector parallel to Y- axis</span>
<span class="sd"> :type o: array_like</span>
<span class="sd"> :param a: 3-vector parallel to the Z-axis</span>
<span class="sd"> :type o: array_like</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> ``SO3.OA(O, A)`` is an SO(3) rotation defined in terms of</span>
<span class="sd"> vectors parallel to the Y- and Z-axes of its reference frame. In robotics these axes are</span>
<span class="sd"> respectively called the *orientation* and *approach* vectors defined such that</span>
<span class="sd"> R = [N, O, A] and N = O x A.</span>
<span class="sd"> Notes:</span>
<span class="sd"> - Only the ``A`` vector is guaranteed to have the same direction in the resulting</span>
<span class="sd"> rotation matrix</span>
<span class="sd"> - ``O`` and ``A`` do not have to be unit-length, they are normalized</span>
<span class="sd"> - ``O`` and ``A` do not have to be orthogonal, so long as they are not parallel</span>
<span class="sd"> :seealso: :func:`spatialmath.base.transforms3d.oa2r`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">oa2r</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SO3.AngVec"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.AngVec">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">AngVec</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Construct a new SO(3) rotation matrix from rotation angle and axis</span>
<span class="sd"> :param theta: rotation</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :param v: rotation axis, 3-vector</span>
<span class="sd"> :type v: array_like</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> ``SO3.AngVec(theta, V)`` is an SO(3) rotation defined by</span>
<span class="sd"> a rotation of ``THETA`` about the vector ``V``.</span>
<span class="sd"> If :math:`\theta \eq 0` the result in an identity matrix, otherwise</span>
<span class="sd"> ``V`` must have a finite length, ie. :math:`|V| > 0`.</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.angvec`, :func:`spatialmath.base.transforms3d.angvec2r`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">angvec2r</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">),</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SO3.Exp"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SO3.Exp">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Exp</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">so3</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create an SO(3) rotation matrix from so(3)</span>
<span class="sd"> :param S: Lie algebra so(3)</span>
<span class="sd"> :type S: numpy ndarray</span>
<span class="sd"> :param check: check that passed matrix is valid so(3), default True</span>
<span class="sd"> :type check: bool</span>
<span class="sd"> :param so3: input is an so(3) matrix (default True)</span>
<span class="sd"> :type so3: bool</span>
<span class="sd"> :return: SO(3) rotation</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> - ``SO3.Exp(S)`` is an SO(3) rotation defined by its Lie algebra</span>
<span class="sd"> which is a 3x3 so(3) matrix (skew symmetric)</span>
<span class="sd"> - ``SO3.Exp(t)`` is an SO(3) rotation defined by a 3-element twist</span>
<span class="sd"> vector (the unique elements of the so(3) skew-symmetric matrix)</span>
<span class="sd"> - ``SO3.Exp(T)`` is a sequence of SO(3) rotations defined by an Nx3 matrix</span>
<span class="sd"> of twist vectors, one per row.</span>
<span class="sd"> </span>
<span class="sd"> Note:</span>
<span class="sd"> - if :math:`\theta \eq 0` the result in an identity matrix</span>
<span class="sd"> - an input 3x3 matrix is ambiguous, it could be the first or third case above. In this</span>
<span class="sd"> case the parameter `so3` is the decider.</span>
<span class="sd"> :seealso: :func:`spatialmath.base.transforms3d.trexp`, :func:`spatialmath.base.transformsNd.skew`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">ismatrix</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">so3</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">trexp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="n">check</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">S</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">trexp</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="n">check</span><span class="p">),</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div></div>
<span class="c1"># ============================== SE3 =====================================#</span>
<div class="viewcode-block" id="SE3"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3">[docs]</a><span class="k">class</span> <span class="nc">SE3</span><span class="p">(</span><span class="n">SO3</span><span class="p">):</span>
<div class="viewcode-block" id="SE3.__init__"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.__init__">[docs]</a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct new SE(3) object</span>
<span class="sd"> :param x: translation distance along the X-axis</span>
<span class="sd"> :type x: float</span>
<span class="sd"> :param y: translation distance along the Y-axis</span>
<span class="sd"> :type y: float</span>
<span class="sd"> :param z: translation distance along the Z-axis</span>
<span class="sd"> :type z: float</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> </span>
<span class="sd"> - ``SE3()`` is a null motion -- the identity matrix</span>
<span class="sd"> - ``SE3(x, y, z)`` is a pure translation of (x,y,z)</span>
<span class="sd"> - ``SE3(T)`` where T is a 4x4 numpy array representing an SE(3) matrix. If ``check``</span>
<span class="sd"> is ``True`` check the matrix belongs to SE(3).</span>
<span class="sd"> - ``SE3([T1, T2, ... TN])`` where each Ti is a 4x4 numpy array representing an SE(3) matrix, is</span>
<span class="sd"> an SE3 instance containing N rotations. If ``check`` is ``True``</span>
<span class="sd"> check the matrix belongs to SE(3).</span>
<span class="sd"> - ``SE3([X1, X2, ... XN])`` where each Xi is an SE3 instance, is an SE3 instance containing N rotations.</span>
<span class="sd"> """</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span> <span class="c1"># activate the UserList semantics</span>
<span class="k">if</span> <span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># SE3()</span>
<span class="c1"># empty constructor</span>
<span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">4</span><span class="p">)]</span>
<span class="k">elif</span> <span class="n">y</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">z</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># SE3(x, y, z)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)]</span>
<span class="k">elif</span> <span class="n">y</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">z</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">if</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">isvector</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">3</span><span class="p">):</span>
<span class="c1"># SE3( [x, y, z] )</span>
<span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="n">x</span><span class="p">)]</span>
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="ow">and</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
<span class="c1"># SE3( Nx3 )</span>
<span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="n">T</span><span class="p">)</span> <span class="k">for</span> <span class="n">T</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">_arghandler</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="n">check</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'bad argument to constructor'</span><span class="p">)</span></div>
<span class="c1"># ------------------------------------------------------------------------ #</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">t</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Translational component of SE(3)</span>
<span class="sd"> :param self: SE(3)</span>
<span class="sd"> :type self: SE3 instance</span>
<span class="sd"> :return: translational component</span>
<span class="sd"> :rtype: numpy.ndarray</span>
<span class="sd"> ``T.t`` returns an:</span>
<span class="sd"> - ndarray with shape=(3,), if len(T) == 1</span>
<span class="sd"> - ndarray with shape=(N,3), if len(T) = N > 1</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">x</span><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">])</span>
<span class="c1"># ------------------------------------------------------------------------ #</span>
<div class="viewcode-block" id="SE3.inv"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.inv">[docs]</a> <span class="k">def</span> <span class="nf">inv</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Inverse of SE(3)</span>
<span class="sd"> :return: inverse</span>
<span class="sd"> :rtype: SE3</span>
<span class="sd"> Returns the inverse taking into account its structure</span>
<span class="sd"> :math:`T = \left[ \begin{array}{cc} R & t \\ 0 & 1 \end{array} \right], T^{-1} = \left[ \begin{array}{cc} R^T & -R^T t \\ 0 & 1 \end{array} \right]`</span>
<span class="sd"> </span>
<span class="sd"> :seealso: :func:`~spatialmath.base.transform3d.trinv`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">SE3</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">trinv</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">SE3</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">trinv</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">])</span></div>
<div class="viewcode-block" id="SE3.delta"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.delta">[docs]</a> <span class="k">def</span> <span class="nf">delta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X2</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Difference of SE(3)</span>
<span class="sd"> :param X1: </span>
<span class="sd"> :type X1: SE3</span>
<span class="sd"> :return: differential motion vector</span>
<span class="sd"> :rtype: numpy.ndarray, shape=(6,)</span>
<span class="sd"> </span>
<span class="sd"> - ``X1.delta(T2)`` is the differential motion (6x1) corresponding to </span>
<span class="sd"> infinitessimal motion (in the X1 frame) from pose X1 to X2.</span>
<span class="sd"> </span>
<span class="sd"> The vector :math:`d = [\delta_x, \delta_y, \delta_z, \theta_x, \theta_y, \theta_z`</span>
<span class="sd"> represents infinitessimal translation and rotation.</span>
<span class="sd"> </span>
<span class="sd"> Notes:</span>
<span class="sd"> </span>
<span class="sd"> - the displacement is only an approximation to the motion T, and assumes</span>
<span class="sd"> that X1 ~ X2.</span>
<span class="sd"> - Can be considered as an approximation to the effect of spatial velocity over a</span>
<span class="sd"> a time interval, average spatial velocity multiplied by time.</span>
<span class="sd"> </span>
<span class="sd"> Reference: Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p67.</span>
<span class="sd"> </span>
<span class="sd"> :seealso: :func:`~spatialmath.base.transform3d.tr2delta`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">tr</span><span class="o">.</span><span class="n">tr2delta</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">X1</span><span class="o">.</span><span class="n">A</span><span class="p">)</span></div>
<span class="c1"># ------------------------------------------------------------------------ #</span>
<div class="viewcode-block" id="SE3.isvalid"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.isvalid">[docs]</a> <span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">isvalid</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Test if matrix is valid SE(3)</span>
<span class="sd"> :param x: matrix to test</span>
<span class="sd"> :type x: numpy.ndarray</span>
<span class="sd"> :return: true of the matrix is 4x4 and a valid element of SE(3), ie. it is an</span>
<span class="sd"> homogeneous transformation matrix.</span>
<span class="sd"> :rtype: bool</span>
<span class="sd"> :seealso: :func:`~spatialmath.base.transform3d.ishom`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">tr</span><span class="o">.</span><span class="n">ishom</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">check</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
<span class="c1"># ---------------- variant constructors ---------------------------------- #</span>
<div class="viewcode-block" id="SE3.Rx"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Rx">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Rx</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) pure rotation about the X-axis</span>
<span class="sd"> :param theta: rotation angle about X-axis</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> - ``SE3.Rx(THETA)`` is an SO(3) rotation of THETA radians about the x-axis</span>
<span class="sd"> - ``SE3.Rx(THETA, "deg")`` as above but THETA is in degrees</span>
<span class="sd"> </span>
<span class="sd"> If ``theta`` is an array then the result is a sequence of rotations defined by consecutive</span>
<span class="sd"> elements.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">trotx</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">getvector</span><span class="p">(</span><span class="n">theta</span><span class="p">)])</span></div>
<div class="viewcode-block" id="SE3.Ry"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Ry">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Ry</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) pure rotation about the Y-axis</span>
<span class="sd"> :param theta: rotation angle about X-axis</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> - ``SE3.Ry(THETA)`` is an SO(3) rotation of THETA radians about the y-axis</span>
<span class="sd"> - ``SE3.Ry(THETA, "deg")`` as above but THETA is in degrees</span>
<span class="sd"> If ``theta`` is an array then the result is a sequence of rotations defined by consecutive</span>
<span class="sd"> elements.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">troty</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">getvector</span><span class="p">(</span><span class="n">theta</span><span class="p">)])</span></div>
<div class="viewcode-block" id="SE3.Rz"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Rz">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Rz</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) pure rotation about the Z-axis</span>
<span class="sd"> :param theta: rotation angle about Z-axis</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> - ``SE3.Rz(THETA)`` is an SO(3) rotation of THETA radians about the z-axis</span>
<span class="sd"> - ``SE3.Rz(THETA, "deg")`` as above but THETA is in degrees</span>
<span class="sd"> </span>
<span class="sd"> If ``theta`` is an array then the result is a sequence of rotations defined by consecutive</span>
<span class="sd"> elements.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">trotz</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">getvector</span><span class="p">(</span><span class="n">theta</span><span class="p">)])</span></div>
<div class="viewcode-block" id="SE3.Rand"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Rand">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Rand</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">xrange</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">yrange</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">zrange</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">N</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create a random SE(3)</span>
<span class="sd"> :param xrange: x-axis range [min,max], defaults to [-1, 1]</span>
<span class="sd"> :type xrange: 2-element sequence, optional</span>
<span class="sd"> :param yrange: y-axis range [min,max], defaults to [-1, 1]</span>
<span class="sd"> :type yrange: 2-element sequence, optional</span>
<span class="sd"> :param zrange: z-axis range [min,max], defaults to [-1, 1]</span>
<span class="sd"> :type zrange: 2-element sequence, optional</span>
<span class="sd"> :param N: number of random transforms</span>
<span class="sd"> :type N: int</span>
<span class="sd"> :return: homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> </span>
<span class="sd"> Return an SE3 instance with random rotation and translation.</span>
<span class="sd"> - ``SE3.Rand()`` is a random SE(3) translation.</span>
<span class="sd"> - ``SE3.Rand(N)`` is an SE3 object containing a sequence of N random</span>
<span class="sd"> poses.</span>
<span class="sd"> :seealso: `~spatialmath.quaternion.UnitQuaternion.Rand`</span>
<span class="sd"> """</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="n">xrange</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">high</span><span class="o">=</span><span class="n">xrange</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">)</span> <span class="c1"># random values in the range</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="n">yrange</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">high</span><span class="o">=</span><span class="n">yrange</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">)</span> <span class="c1"># random values in the range</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="n">yrange</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">high</span><span class="o">=</span><span class="n">zrange</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">)</span> <span class="c1"># random values in the range</span>
<span class="n">R</span> <span class="o">=</span> <span class="n">SO3</span><span class="o">.</span><span class="n">Rand</span><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="n">N</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span> <span class="o">@</span> <span class="n">tr</span><span class="o">.</span><span class="n">r2t</span><span class="p">(</span><span class="n">r</span><span class="o">.</span><span class="n">A</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">R</span><span class="p">)])</span></div>
<div class="viewcode-block" id="SE3.Eul"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Eul">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Eul</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">angles</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create an SE(3) pure rotation from Euler angles</span>
<span class="sd"> :param angles: 3-vector of Euler angles</span>
<span class="sd"> :type angles: array_like or numpy.ndarray with shape=(N,3)</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> ``SE3.Eul(ANGLES)`` is an SO(3) rotation defined by a 3-vector of Euler angles :math:`(\phi, \theta, \psi)` which</span>
<span class="sd"> correspond to consecutive rotations about the Z, Y, Z axes respectively.</span>
<span class="sd"> </span>
<span class="sd"> If ``angles`` is an Nx3 matrix then the result is a sequence of rotations each defined by Euler angles</span>
<span class="sd"> correponding to the rows of angles.</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.eul`, :func:`~spatialmath.pose3d.SE3.Eul`, :func:`spatialmath.base.transforms3d.eul2r`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">isvector</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="mi">3</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">eul2tr</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">eul2tr</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">angles</span><span class="p">])</span></div>
<div class="viewcode-block" id="SE3.RPY"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.RPY">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">RPY</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">angles</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s1">'zyx'</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create an SO(3) pure rotation from roll-pitch-yaw angles</span>
<span class="sd"> :param angles: 3-vector of roll-pitch-yaw angles</span>
<span class="sd"> :type angles: array_like or numpy.ndarray with shape=(N,3)</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :param unit: rotation order: 'zyx' [default], 'xyz', or 'yxz'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> ``SE3.RPY(ANGLES)`` is an SE(3) rotation defined by a 3-vector of roll, pitch, yaw angles :math:`(r, p, y)`</span>
<span class="sd"> which correspond to successive rotations about the axes specified by ``order``:</span>
<span class="sd"> - 'zyx' [default], rotate by yaw about the z-axis, then by pitch about the new y-axis,</span>
<span class="sd"> then by roll about the new x-axis. Convention for a mobile robot with x-axis forward</span>
<span class="sd"> and y-axis sideways.</span>
<span class="sd"> - 'xyz', rotate by yaw about the x-axis, then by pitch about the new y-axis,</span>
<span class="sd"> then by roll about the new z-axis. Covention for a robot gripper with z-axis forward</span>
<span class="sd"> and y-axis between the gripper fingers.</span>
<span class="sd"> - 'yxz', rotate by yaw about the y-axis, then by pitch about the new x-axis,</span>
<span class="sd"> then by roll about the new z-axis. Convention for a camera with z-axis parallel</span>
<span class="sd"> to the optic axis and x-axis parallel to the pixel rows.</span>
<span class="sd"> </span>
<span class="sd"> If ``angles`` is an Nx3 matrix then the result is a sequence of rotations each defined by RPY angles</span>
<span class="sd"> correponding to the rows of angles.</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.rpy`, :func:`~spatialmath.pose3d.SE3.RPY`, :func:`spatialmath.base.transforms3d.rpy2r`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">argcheck</span><span class="o">.</span><span class="n">isvector</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="mi">3</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">rpy2tr</span><span class="p">(</span><span class="n">angles</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="n">order</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">rpy2tr</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="n">order</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">angles</span><span class="p">])</span></div>
<div class="viewcode-block" id="SE3.OA"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.OA">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">OA</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">o</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) pure rotation from two vectors</span>
<span class="sd"> :param o: 3-vector parallel to Y- axis</span>
<span class="sd"> :type o: array_like</span>
<span class="sd"> :param a: 3-vector parallel to the Z-axis</span>
<span class="sd"> :type o: array_like</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> ``SE3.OA(O, A)`` is an SE(3) rotation defined in terms of</span>
<span class="sd"> vectors parallel to the Y- and Z-axes of its reference frame. In robotics these axes are</span>
<span class="sd"> respectively called the orientation and approach vectors defined such that</span>
<span class="sd"> R = [N O A] and N = O x A.</span>
<span class="sd"> Notes:</span>
<span class="sd"> - The A vector is the only guaranteed to have the same direction in the resulting</span>
<span class="sd"> rotation matrix</span>
<span class="sd"> - O and A do not have to be unit-length, they are normalized</span>
<span class="sd"> - O and A do not have to be orthogonal, so long as they are not parallel</span>
<span class="sd"> - The vectors O and A are parallel to the Y- and Z-axes of the equivalent coordinate frame.</span>
<span class="sd"> :seealso: :func:`spatialmath.base.transforms3d.oa2r`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">oa2tr</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">a</span><span class="p">))</span></div>
<div class="viewcode-block" id="SE3.AngVec"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.AngVec">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">AngVec</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'rad'</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create an SE(3) pure rotation matrix from rotation angle and axis</span>
<span class="sd"> :param theta: rotation</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :param unit: angular units: 'rad' [default], or 'deg'</span>
<span class="sd"> :type unit: str</span>
<span class="sd"> :param v: rotation axis, 3-vector</span>
<span class="sd"> :type v: array_like</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> ``SE3.AngVec(THETA, V)`` is an SE(3) rotation defined by</span>
<span class="sd"> a rotation of ``THETA`` about the vector ``V``.</span>
<span class="sd"> Notes:</span>
<span class="sd"> - If ``THETA == 0`` then return identity matrix.</span>
<span class="sd"> - If ``THETA ~= 0`` then ``V`` must have a finite length.</span>
<span class="sd"> :seealso: :func:`~spatialmath.pose3d.SE3.angvec`, :func:`spatialmath.base.transforms3d.angvec2r`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">angvec2tr</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="n">unit</span><span class="p">))</span></div>
<div class="viewcode-block" id="SE3.Exp"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Exp">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Exp</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">S</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create an SE(3) rotation matrix from se(3)</span>
<span class="sd"> :param S: Lie algebra se(3)</span>
<span class="sd"> :type S: numpy ndarray</span>
<span class="sd"> :return: 3x3 rotation matrix</span>
<span class="sd"> :rtype: SO3 instance</span>
<span class="sd"> - ``SE3.Exp(S)`` is an SE(3) rotation defined by its Lie algebra</span>
<span class="sd"> which is a 3x3 se(3) matrix (skew symmetric)</span>
<span class="sd"> - ``SE3.Exp(t)`` is an SE(3) rotation defined by a 6-element twist</span>
<span class="sd"> vector (the unique elements of the se(3) skew-symmetric matrix)</span>
<span class="sd"> :seealso: :func:`spatialmath.base.transforms3d.trexp`, :func:`spatialmath.base.transformsNd.skew`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">S</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)</span> <span class="ow">and</span> <span class="n">S</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mi">6</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">([</span><span class="n">tr</span><span class="o">.</span><span class="n">trexp</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">S</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">trexp</span><span class="p">(</span><span class="n">S</span><span class="p">),</span> <span class="n">check</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></div>
<div class="viewcode-block" id="SE3.Tx"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Tx">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Tx</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) translation along the X-axis</span>
<span class="sd"> :param theta: translation distance along the X-axis</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> `SE3.Tz(D)`` is an SE(3) translation of D along the x-axis</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
<div class="viewcode-block" id="SE3.Ty"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Ty">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Ty</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) translation along the Y-axis</span>
<span class="sd"> :param theta: translation distance along the Y-axis</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> `SE3.Tz(D)`` is an SE(3) translation of D along the y-axis</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
<div class="viewcode-block" id="SE3.Tz"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Tz">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Tz</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Create SE(3) translation along the Z-axis</span>
<span class="sd"> :param theta: translation distance along the Z-axis</span>
<span class="sd"> :type theta: float</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> `SE3.Tz(D)`` is an SE(3) translation of D along the z-axis</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="bp">cls</span><span class="p">(</span><span class="n">tr</span><span class="o">.</span><span class="n">transl</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="p">))</span></div>
<div class="viewcode-block" id="SE3.Delta"><a class="viewcode-back" href="../../spatialmath.html#spatialmath.pose3d.SE3.Delta">[docs]</a> <span class="nd">@classmethod</span>
<span class="k">def</span> <span class="nf">Delta</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Create SE(3) from diffential motion</span>
<span class="sd"> :param d: differential motion</span>
<span class="sd"> :type d: 6-element array_like</span>
<span class="sd"> :return: 4x4 homogeneous transformation matrix</span>
<span class="sd"> :rtype: SE3 instance</span>
<span class="sd"> </span>
<span class="sd"> - ``T = delta2tr(d)`` is an SE(3) representing differential </span>
<span class="sd"> motion :math:`d = [\delta_x, \delta_y, \delta_z, \theta_x, \theta_y, \theta_z`.</span>
<span class="sd"> </span>
<span class="sd"> Reference: Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p67.</span>
<span class="sd"> </span>
<span class="sd"> :seealso: :func:`~delta`, :func:`~spatialmath.base.transform3d.delta2tr`</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">tr</span><span class="o">.</span><span class="n">tr2delta</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">X1</span><span class="o">.</span><span class="n">A</span><span class="p">)</span></div></div>
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span> <span class="c1"># pragma: no cover</span>
<span class="kn">import</span> <span class="nn">pathlib</span>
<span class="kn">import</span> <span class="nn">os.path</span>
<span class="n">exec</span><span class="p">(</span><span class="nb">open</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">pathlib</span><span class="o">.</span><span class="n">Path</span><span class="p">(</span><span class="vm">__file__</span><span class="p">)</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">absolute</span><span class="p">(),</span> <span class="s2">"test_pose3d.py"</span><span class="p">))</span><span class="o">.</span><span class="n">read</span><span class="p">())</span>
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<p class="blurb">Spatial maths and geometry for Python</p>
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