Development branch, release 3.14.2

README.md

@@ -1,6 +1,5 @@
 <img src="https://raw.githubusercontent.com/dfki-ric/pytransform3d/main/doc/source/_static/logo.png" />
 
-[![CircleCI](https://dl.circleci.com/status-badge/img/gh/dfki-ric/pytransform3d/tree/main.svg?style=svg)](https://dl.circleci.com/status-badge/redirect/gh/dfki-ric/pytransform3d/tree/main)
 [![codecov](https://codecov.io/gh/dfki-ric/pytransform3d/branch/main/graph/badge.svg?token=jB10RM3Ujj)](https://codecov.io/gh/dfki-ric/pytransform3d)
 [![Paper DOI](http://joss.theoj.org/papers/10.21105/joss.01159/status.svg)](https://doi.org/10.21105/joss.01159)
 [![Release DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.2553450.svg)](https://doi.org/10.5281/zenodo.2553450)

doc/source/_static/custom.css

@@ -0,0 +1,12 @@
+:root {
+  --pst-sidebar-width: 100px;
+  --pst-secondary-sidebar-width: 100px;
+}
+
+.bd-main .bd-content .bd-article-container {
+  max-width: 100%; /* Allows content to expand if sidebars are smaller */
+}
+
+.bd-page-width {
+  max-width: 100%; /* Ensures the overall page uses more width */
+}

doc/source/_static/overview.tex

@@ -0,0 +1,165 @@
+\documentclass{article}
+\usepackage{amssymb,amsmath}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+
+% converted to png via
+% pdflatex overview.tex
+% pdftoppm -png overview.pdf > overview.png
+
+\usepackage{tikz}
+\usetikzlibrary{arrows, arrows.meta, positioning}
+
+\begin{document}
+\begin{preview}
+\newcommand{\matx}{10.1}
+\newcommand{\maty}{14.2}
+
+\begin{tikzpicture}
+\node[draw,shape=rectangle,rounded corners,fill=cyan!10] (legendconversionrot) at (7.5,18.7) {\large\texttt{pytransform3d.rotations}};
+
+\node[draw,shape=rectangle,rounded corners,fill=blue!10] (legendconversiontr) at (21.5,18.7) {\large\texttt{pytransform3d.transformations}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=blue!15] (tmat) at (17,15) {\begin{minipage}{4cm}\textbf{transformation matrix}\\[0.3em]
+$\boldsymbol{T} \in SE(3)$\\[0.3em]
+\texttt{transform}\\[0.3em]
+shape (4, 4)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=blue!15] (dquat) at (21.5,15) {\begin{minipage}{4cm}\textbf{(unit) dual quaternion}\\[0.3em]
+$\boldsymbol{\sigma}$\\[0.3em]
+\texttt{dual\_quaternion}\\[0.3em]
+shape (8,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=blue!15] (pq) at (26.5,15) {\begin{minipage}{5cm}\textbf{position and unit quaternion}\\[0.3em]
+$(\boldsymbol{p}, \boldsymbol{q}) \in \mathbb{R}^3 \times S^3$\\[0.3em]
+\texttt{pq}\\[0.3em]
+shape (7,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=blue!15] (logtr) at (17,11) {\begin{minipage}{4.9cm}\textbf{logarithm of transformation}\\[0.3em]
+$\left[\mathcal{S}\right]\theta \in se(3)$\\[0.3em]
+\texttt{transform\_log}\\[0.3em]
+shape (4, 4)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (screwmat) at (22.5,11) {\begin{minipage}{3.8cm}\textbf{screw matrix}\\[0.3em]
+$\left[\mathcal{S}\right] \in se(3)$\\[0.3em]
+\texttt{screw\_matrix}\\[0.3em]
+shape (4, 4)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=blue!15] (expcoord) at (17,7) {\begin{minipage}{7.5cm}\textbf{exponential coordinates of transformation}\\[0.3em]
+$\mathcal{S}\theta \in \mathbb{R}^6$\\[0.3em]
+\texttt{exponential\_coordinates}\\[0.3em]
+shape (6,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (spvel) at (24,7) {\begin{minipage}{4cm}\textbf{twist / spatial velocity}\\[0.3em]
+$\mathcal{S}\dot{\theta} \in \mathbb{R}^6$\\[0.3em]
+shape (6,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (spacc) at (29,7) {\begin{minipage}{3.5cm}\textbf{spatial acceleration}\\[0.3em]
+$\mathcal{S}\ddot{\theta} \in \mathbb{R}^6$\\[0.3em]
+shape (6,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (scrax) at (17,2) {\begin{minipage}{2.2cm}\textbf{screw axis}\\[0.3em]
+$\mathcal{S} \in \mathbb{R}^6$\\[0.3em]
+\texttt{screw\_axis}\\[0.3em]
+shape (6,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (screw) at (22,2) {\begin{minipage}{5.2cm}\textbf{screw parameters}\\[0.3em]
+$(\boldsymbol{q}, \hat{\boldsymbol{s}}, h) \in \mathbb{R}^3 \times S^2 \times \mathbb{R}$\\[0.3em]
+\texttt{screw\_parameters}\\[0.3em]
+tuple[shape (3,), shape (3,), float]
+\end{minipage}};
+
+\draw[<->] (tmat) -- (logtr) node[midway,left] {exp./log. map};
+\draw[->] (expcoord) -- (logtr) node[midway,left] {$\left[\cdot\right]$};
+\draw[->] (expcoord) -- (spvel) node[midway,above] {$\frac{\partial \mathcal{S}\theta}{\partial t}$};
+\draw[->] (spvel) -- (spacc) node[midway,above] {$\frac{\partial \mathcal{S}\dot{\theta}}{\partial t}$};
+\draw[->] (scrax) -- (expcoord) node[midway,left] {$\theta$};
+\draw[->] (screwmat) -- (logtr) node[midway,above] {$\theta$};
+\draw[<->] (screw) -- (scrax) node[midway,above] {};
+
+\draw [thick,rounded corners,fill=cyan!15] (\matx-0.2,\maty-0.5) rectangle (\matx+3.1,\maty+2.2);
+\node[anchor=west] (rotmatname) at (\matx,\maty+1.8) {\textbf{rotation matrix}};
+\node[anchor=west] (rotmatsymbol) at (\matx,\maty+1.2) {$\boldsymbol{R}$};
+\node[anchor=west] (rotmatset) at (\matx+0.4,\maty+1.178) {$\in SO(3)$};
+\node[anchor=west] (rotmatpname) at (\matx,\maty+0.6) {\texttt{matrix}};
+\node[anchor=west] (rotmatarray) at (\matx,\maty) {shape (3, 3)};
+
+\node (legendname) at (\matx-2,\maty+3) {representation};
+\draw[red] (rotmatname) edge (legendname);
+\node (legendsymbol) at (\matx-3,\maty+1.9) {mathematical symbol};
+\draw[red] (rotmatsymbol) edge (legendsymbol);
+\node (legendset) at (\matx+4,\maty+1.2) {set};
+\draw[red] (rotmatset) edge (legendset);
+\node (legendpname) at (\matx-3.3,\maty+0.7) {\begin{minipage}{3.1cm}\centering name in pytransform3d\end{minipage}};
+\draw[red] (rotmatpname) edge (legendpname);
+\node (legendarray) at (\matx-2,\maty-0.5) {NumPy array};
+\draw[red] (rotmatarray) edge (legendarray);
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=cyan!15] (quat) at (1.8,15) {\begin{minipage}{6cm}\textbf{(unit) quaternion / versor / rotor}\\[0.3em]
+$\boldsymbol{q} \in S^3$\\[0.3em]
+\texttt{quaternion}\\[0.3em]
+shape (4,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=cyan!15] (logrot) at (11.2,11) {\begin{minipage}{3.8cm}\textbf{logarithm of rotation}\\[0.3em]
+$\left[\boldsymbol{\omega}\right] \in so(3)$\\[0.3em]
+\texttt{rot\_log}\\[0.3em]
+shape (3, 3)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=cyan!15] (rotvec) at (11.2,7) {\begin{minipage}{3.3cm}\textbf{rotation vector}\\[0.3em]
+$\boldsymbol{\omega} = \hat{\boldsymbol{\omega}}\theta \in \mathbb{R}^3$\\[0.3em]
+\texttt{compact\_axis\_angle}\\[0.3em]
+shape (3,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (angvel) at (6.9,7) {\begin{minipage}{2.8cm}\textbf{angular velocity}\\[0.3em]
+$\dot{\boldsymbol{\omega}} = \hat{\boldsymbol{\omega}}\dot{\theta} \in \mathbb{R}^3$\\[0.3em]
+shape (3,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (angacc) at (2.5,7) {\begin{minipage}{3.6cm}\textbf{angular acceleration}\\[0.3em]
+$\hat{\boldsymbol{\omega}}\ddot{\theta} \in \mathbb{R}^3$\\[0.3em]
+shape (3,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=cyan!15] (axan) at (11.2,3.7) {\begin{minipage}{2.4cm}\textbf{axis-angle}\\[0.3em]
+$(\hat{\boldsymbol{\omega}}, \theta) \in S^2 \times \mathbb{R}$\\[0.3em]
+\texttt{axis\_angle}\\[0.3em]
+shape (4,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners] (rotax) at (11.2,1.5) {\begin{minipage}{3.8cm}\textbf{rotation axis}\\[0.3em]
+$\hat{\boldsymbol{\omega}} \in S^2$
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=cyan!15] (euler) at (3,1) {\begin{minipage}{7.5cm}\textbf{proper Euler / Cardan / Tait-Bryan angles}\\[0.3em]
+$(\alpha, \beta, \gamma) \in \mathbb{R}^3$\\[0.3em]
+\texttt{euler}\\[0.3em]
+shape (3,)
+\end{minipage}};
+
+\node[draw,shape=rectangle,thick,rounded corners,fill=cyan!15] (mrp) at (6,3.7) {\begin{minipage}{5.6cm}\textbf{modified Rodrigues parameters}\\[0.3em]
+$\boldsymbol{\psi} = \hat{\boldsymbol{\omega}} \tan{\frac{\theta}{4}} \in \mathbb{R}^3$\\[0.3em]
+\texttt{mrp}\\[0.3em]
+shape (3,)
+\end{minipage}};
+
+\draw[<->] (rotmatarray) -- (logrot) node[midway,left] {exp./log. map};
+\draw[->] (rotvec) -- (logrot) node[midway,left] {cross product matrix};
+\draw[->] (rotvec) -- (angvel) node[midway,above] {$\frac{\partial \boldsymbol{\omega}}{\partial t}$};
+\draw[->] (angvel) -- (angacc) node[midway,above] {$\frac{\partial \dot{\boldsymbol{\omega}}}{\partial t}$};
+\draw[->] (axan) -- (rotvec) node[midway,left] {product};
+\draw[->] (rotax) -- (axan) node[midway,left] {$\theta$};
+\end{tikzpicture}
+\end{preview}
+\end{document}

doc/source/conf.py

@@ -68,6 +68,7 @@
     "api": [],
 }
 html_static_path = ['_static']
+html_css_files = ['custom.css']
 html_last_updated_fmt = '%b %d, %Y'
 html_use_smartypants = True
 html_show_sourcelink = False

doc/source/user_guide/introduction.rst

@@ -104,53 +104,14 @@ representations.
 We can use many different representations of rotation and / or translation.
 Here is an overview of the representations that are available in pytransform3d.
 All representations are stored in NumPy arrays, of which the corresponding
-shape is shown in this table. You will find more details on these
+shape is shown in this figure. You will find more details on these
 representations on the following pages.
 
-+----------------------------------------+---------------------+------------------+---------------+
-|                                        |                     | Rigid Transformation - SE(3)     |
-+                                        |                     +------------------+---------------+
-| Representation and Mathematical Symbol | NumPy Array Shape   | Rotation - SO(3) | Translation   |
-+========================================+=====================+==================+===============+
-| Rotation matrix                        | (3, 3)              | X                |               |
-| :math:`\pmb{R}`                        |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Axis-angle                             | (4,)                | X                |               |
-| :math:`(\hat{\pmb{\omega}}, \theta)`   |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Rotation vector                        | (3,)                | X                |               |
-| :math:`\pmb{\omega}`                   |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Logarithm of rotation                  | (3, 3)              | X                |               |
-| :math:`\left[\pmb{\omega}\right]`      |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Quaternion                             | (4,)                | X                |               |
-| :math:`\pmb{q}`                        |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Rotor                                  | (4,)                | X                |               |
-| :math:`R`                              |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Euler angles                           | (3,)                | X                |               |
-| :math:`(\alpha, \beta, \gamma)`        |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Modified Rodrigues parameters          | (3,)                | X                |               |
-| :math:`\pmb{\psi}`                     |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Transformation matrix                  | (4, 4)              | X                | X             |
-| :math:`\pmb{T}`                        |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Exponential coordinates                | (6,)                | X                | X             |
-| :math:`\mathcal{S}\theta`              |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Logarithm of transformation            | (4, 4)              | X                | X             |
-| :math:`\left[\mathcal{S}\right]\theta` |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Position and quaternion                | (7,)                | X                | X             |
-| :math:`(\pmb{p}, \pmb{q})`             |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
-| Dual quaternion                        | (8,)                | X                | X             |
-| :math:`\boldsymbol{\sigma}`            |                     |                  |               |
-+----------------------------------------+---------------------+------------------+---------------+
+
+.. figure:: ../_static/overview.png
+   :alt: Overview of representations for rotations and transformations in 3D.
+   :align: center
+   :width: 100%
 
 ----------
 References

pytransform3d/__init__.py

@@ -1,3 +1,3 @@
 """3D transformations for Python."""
 
-__version__ = "3.14.1"
+__version__ = "3.14.2"

pytransform3d/transform_manager/_transform_graph_base.py

@@ -1,6 +1,7 @@
 """Common base class of transformation graphs."""
 
 import abc
+import copy
 
 import numpy as np
 import scipy.sparse as sp
@@ -319,27 +320,22 @@ def connected_components(self):
     def check_consistency(self):
         """Check consistency of the known transformations.
 
-        The complexity of this is between :math:`O(n^2)` and :math:`O(n^3)`,
-        where :math:`n` is the number of nodes. In graphs where each pair of
-        nodes is directly connected the complexity is :math:`O(n^2)`. In graphs
-        that are actually paths, the complexity is :math:`O(n^3)`.
+        The computational cost of this operation is very high.
 
         Returns
         -------
         consistent : bool
-            Is the graph consistent, i.e. is A2B always the same as the inverse
-            of B2A?
+            Is the graph consistent, i.e., if there are two ways of computing
+            A2B, do they give almost identical results?
         """
-        consistent = True
-        for node1 in self.nodes:
-            for node2 in self.nodes:
-                try:
-                    node1_to_node2 = self.get_transform(node1, node2)
-                    node2_to_node1 = self.get_transform(node2, node1)
-                    node1_to_node2_inv = invert_transform(node2_to_node1)
-                    consistent = consistent and np.allclose(
-                        node1_to_node2, node1_to_node2_inv
-                    )
-                except KeyError:
-                    pass  # Frames are not connected
-        return consistent
+        for (from_frame, to_frame), A2B in self.transforms.items():
+            clone = copy.deepcopy(self)
+            clone.remove_transform(from_frame, to_frame)
+            try:
+                A2B_from_path = clone.get_transform(from_frame, to_frame)
+                if not np.allclose(A2B, A2B_from_path):
+                    return False
+            except KeyError:
+                # A2B cannot be computed in any other way
+                continue
+        return True