Spatial Math for Python

https://spatialmath-python.rai-inst.com/
Admin
Python package providing classes and functions to represent, manipulate, and convert between spatial...
Tokens:267,928
Snippets:3,139
Trust Score:9.3
Update:4 months ago
Show doc for...
Tokens:
Raw
### Animate2 Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/animate.html

Example of setting up and running an animation using Animate2.

```python
anim = animate.Animate(dims=[0,2]) # set up the 3D axes
anim.trplot(T, frame='A', color='green')  # draw the frame
anim.run(loop=True)  # animate it
```

--------------------------------

### SO3.EulerVec Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/pose3d.html

Example usage of SO3.EulerVec.

```python
>>> from spatialmath import SO3
>>> SO3.EulerVec([0.5,0,0])
```

--------------------------------

### Animate Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/animate.html

Example of how to use the Animate class to set up and run an animation.

```python
anim = animate.Animate(dims=[0,2]) # set up the 3D axes
anim.trplot(T, frame='A', color='green')  # draw the frame
anim.run(repeat=True)  # animate it
```

--------------------------------

### so(3) examples

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transforms3d.html

Examples of using trexp for so(3) matrices and vectors.

```python
from spatialmath.base import trexp, skew
trexp(skew([1, 2, 3]))
trexp(skew([1, 0, 0]), 2)  # revolute unit twist
trexp([1, 2, 3])
trexp([1, 0, 0], 2)  # revolute unit twist
```

--------------------------------

### Polygon2 Bounding Box Example

Source: https://spatialmath-python.rai-inst.com/classes-2d.html

Example of getting the bounding box of a Polygon2 object.

```Python
>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.bbox()
array([1., 2., 3., 4.])
```

--------------------------------

### Creating MATLAB-like Environment

Source: https://spatialmath-python.rai-inst.com/intro.html

Example of importing all functions and classes to create a MATLAB-like environment in Python.

```python
>>> from spatialmath  import *
>>> from spatialmath.base  import *
>>> R = rotx(0.3)
>>> R2 = rpy2r(0.1, 0.2, 0.3)
>>> T = SE3(1, 2, 3)
```

--------------------------------

### bresenham example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/numeric.html

Example of using the bresenham function to get points along a line.

```pycon
>>> from spatialmath.base import bresenham
>>> bresenham((2, 4), (10, 10))
```

--------------------------------

### Creating a MATLAB-like environment in Python

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Shows how to import all functions and classes from spatialmath and spatialmath.base to create a familiar environment with classic functions and classes like SE3.

```python
>>> from spatialmath  import *
>>> from spatialmath.base  import *
```

```python
R = rotx(0.3)
R2 = rpy2r(0.1, 0.2, 0.3)

T = SE3(1, 2, 3)
```

--------------------------------

### SO3 constructor examples

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/pose3d.html

Demonstrates various ways to initialize an SO3 object.

```python
from spatialmath import SO3

x = SO3()
x = SO3(R=np.eye(3))
x = SO3([R1, R2, R3])
x = SO3([X1, X2, X3])
```

--------------------------------

### gauss2d example

Source: https://spatialmath-python.rai-inst.com/func_numeric.html

Example of the gauss2d function for a 2D Gaussian, including meshgrid and covariance matrix setup.

```python
from spatialmath.base import gauss2d
a = np.linspace(-5, 5, 100)
X, Y = np.meshgrid(a, a)
P = np.diag([1, 2])**2;
g = gauss2d(X, Y, [0, 0], P)
```

--------------------------------

### Symbolic Rotation Example

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Demonstrates how to create a symbolic rotation matrix using SymPy.

```python
from spatialmath import *
import spatialmath.base.symbolic as sym
theta = sym.symbol('theta')
SE3.Rx(theta)
```

--------------------------------

### DualQuaternion Vector Representation

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/DualQuaternion.html

Example of getting the vector representation of a DualQuaternion.

```python
>>> from spatialmath import DualQuaternion, Quaternion
>>> d = DualQuaternion(Quaternion([1,2,3,4]), Quaternion([5,6,7,8]))
>>> d.vec
```

--------------------------------

### DualQuaternion Matrix Representation

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/DualQuaternion.html

Example of getting the matrix representation of a DualQuaternion and its application.

```python
>>> from spatialmath import DualQuaternion, Quaternion
>>> d = DualQuaternion(Quaternion([1,2,3,4]), Quaternion([5,6,7,8]))
>>> d.matrix()
>>> d.matrix() @ d.vec
>>> d * d
```

--------------------------------

### Rotation matrix examples

Source: https://spatialmath-python.rai-inst.com/intro.html

Demonstrates the creation of rotation matrices using rotx and roty, and matrix multiplication using the @ operator.

```python
1>>> from spatialmath.base import *
2>>> rotx(0.3)
3array([[ 1.    ,  0.    ,  0.    ],
4       [ 0.    ,  0.9553, -0.2955],
5       [ 0.    ,  0.2955,  0.9553]])
6>>> rotx(30, unit='deg')
7array([[ 1.   ,  0.   ,  0.   ],
8       [ 0.   ,  0.866, -0.5  ],
9       [ 0.   ,  0.5  ,  0.866]])
10>>> R = rotx(0.3) @ roty(0.2)
11>>> R
12array([[ 0.9801,  0.    ,  0.1987],
13       [ 0.0587,  0.9553, -0.2896],
14       [-0.1898,  0.2955,  0.9363]])
```

--------------------------------

### Creating an SE3 class instance

Source: https://spatialmath-python.rai-inst.com/intro.html

Example of creating an SE3 class instance for a rotation around the x-axis.

```python
>>> from spatialmath import *
>>> T = SE3.Rx(30, 'deg')
>>> type(T)
<class 'spatialmath.pose3d.SE3'>
>>> print(T)
   1         0         0         0         
   0         0.866    -0.5       0         
   0         0.5       0.866     0         
   0         0         0         1         


```

--------------------------------

### Bounding box of polygon

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/geom2d.html

Example of how to get the bounding box of a polygon.

```pycon
>>> from spatialmath import Polygon2
>>> p = Polygon2([(1, 2), (3, 2), (2, 4)])
>>> p.bbox()
```

--------------------------------

### SO3.R property example

Source: https://spatialmath-python.rai-inst.com/3d_orient_SO3.html

Shows how to get the rotation matrix component of an SO3 object.

```python
>>> from spatialmath import SO3
>>> x = SO3.Rx(0.3)
>>> x.R
array([[ 1.    ,  0.    ,  0.    ],
       [ 0.    ,  0.9553, -0.2955],
       [ 0.    ,  0.2955,  0.9553]])

```

--------------------------------

### Symbolic operations example

Source: https://spatialmath-python.rai-inst.com/intro.html

Demonstrates the use of SymPy for symbolic operations with SE3 objects.

```python
>>> from spatialmath import *
>>> import spatialmath.base.symbolic as sym
>>> theta = sym.symbol('theta')
>>> SE3.Rx(theta)
SE3(array([[1, 0, 0, 0],
           [0, cos(theta), -sin(theta), 0],
           [0, sin(theta), cos(theta), 0],
           [0, 0, 0, 1]], dtype=object))
```

--------------------------------

### Example of prod() method

Source: https://spatialmath-python.rai-inst.com/2d_pose_SE2.html

Demonstrates calculating the product of elements in a pose instance.

```python
>>> from spatialmath import SE3
>>> x = SE3.Rx([0, 0.1, 0.2, 0.3])
>>> x.prod()
SE3(array([[ 1.    ,  0.    ,  0.    ,  0.    ],
           [ 0.    ,  0.8253, -0.5646,  0.    ],
           [ 0.    ,  0.5646,  0.8253,  0.    ],
           [ 0.    ,  0.    ,  0.    ,  1.    ]]))
```

--------------------------------

### Pitch of a 3D twist

Source: https://spatialmath-python.rai-inst.com/3d_pose_twist.html

Example demonstrating how to get the pitch of a 3D twist.

```python
>>> from spatialmath import SE3, Twist3
>>> T = SE3(1, 2, 3) * SE3.Rx(0.3)
>>> S = Twist3(T)
>>> S.pitch
0.3
```

--------------------------------

### N property example

Source: https://spatialmath-python.rai-inst.com/2d_pose_twist.html

Shows how to get the dimension of the object's group using the N property.

```python
>>> from spatialmath import Twist2
>>> x = Twist2()
>>> x.N
2
```

--------------------------------

### Controlling colorization

Source: https://spatialmath-python.rai-inst.com/intro.html

Illustrates how to control foreground and background colors for pose matrix elements.

```python
>>> SE3._rotcolor = 'green'   # rotation part in green

```

```python
>>> SE3._color = False

```

--------------------------------

### List capability example

Source: https://spatialmath-python.rai-inst.com/intro.html

Demonstrates the list-like behavior of SO3 objects, including length, indexing, slicing, and iteration.

```python
>>> from spatialmath import *
>>> import numpy as np
>>> R = SO3.Rx(0.3)
>>> len(R)
1
>>> R = SO3.Rx(np.arange(0, 2*np.pi, 0.2))
>>> len(R)
32
>>> R[0]
SO3(array([[1., 0., 0.],
           [0., 1., 0.],
           [0., 0., 1.]]))
>>> R[-1]
SO3(array([[ 1.    ,  0.    ,  0.    ],
           [ 0.    ,  0.9965,  0.0831],
           [ 0.    , -0.0831,  0.9965]]))
>>> R[2:4]
SO3([
array([[ 1.    ,  0.    ,  0.    ],
       [ 0.    ,  0.9211, -0.3894],
       [ 0.    ,  0.3894,  0.9211]]),
array([[ 1.    ,  0.    ,  0.    ],
       [ 0.    ,  0.8253, -0.5646],
       [ 0.    ,  0.5646,  0.8253]]) ])
```

--------------------------------

### Displaying values

Source: https://spatialmath-python.rai-inst.com/intro.html

Demonstrates the use of `__repr__`, `str()`, and `printline()` methods for displaying class instances.

```python
>>> from spatialmath import *
>>> X = SE3.Rand()
>>> _ = X.printline()
t = -0.0759, 0.901, 0.623; rpy/zyx = 38.8°, -25.6°, -147°

```

--------------------------------

### unittwist2_norm example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/vectors.html

Example usage of unittwist2_norm function.

```python
from spatialmath.base import *
unittwist2([2, 4, 2)
unittwist2([2, 0, 0])
```

--------------------------------

### Plot Cuboid Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/graphics.html

Example usage of the plot_cuboid function.

```python
from spatialmath.base import plot_cuboid, plotvol3

plotvol3(5)
plot_cuboid(sides=(3,2,1), centre=(0,1,2))
```

--------------------------------

### Plotting a Pose

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Example of plotting a pose using the plot() method.

```python
>>> X = SE3.Rand()
>>> X.plot()
```

--------------------------------

### Plot Cone Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/graphics.html

Example usage of the plot_cone function.

```python
from spatialmath.base import plot_cone, plotvol3

plotvol3(5)
plot_cone(radius=1, height=2)
```

--------------------------------

### Vector Transformation with SO3, SE3, and UnitQuaternion

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Examples of transforming a vector using SO3, SE3, and UnitQuaternion objects.

```pycon
>>> from spatialmath import *
>>> v = [1, 2, 3]
>>> SO3.Rx(0.3) * v
>>> SE3.Rx(0.3) * v
>>> UnitQuaternion.Rx(0.3) * v
```

--------------------------------

### iseye Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transformsNd.html

Examples of testing if a matrix is an identity matrix.

```Python
from spatialmath.base import *
import numpy as np
iseye(np.array([[1,0], [0,1]]))
iseye(np.array([[1,2], [0,1]]))
```

--------------------------------

### Symbolic Rotation Matrix

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Shows how to create a symbolic rotation matrix using symbolic variables.

```pycon
>>> from spatialmath.base import *
>>> import spatialmath.base.symbolic as sym
>>> theta = sym.symbol('theta')
>>> print(rotx(theta))
```

--------------------------------

### isskew Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transformsNd.html

Examples of testing if a matrix belongs to so(n).

```Python
from spatialmath.base import *
import numpy as np
isskew(np.zeros((3,3)))
isskew(np.array([[0, -2], [2, 0]]))
isskew(np.eye(3))
```

--------------------------------

### isR Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transformsNd.html

Examples of testing if a matrix belongs to SO(n).

```Python
from spatialmath.base import *
isR(np.eye(3))
isR(rot2(0.5))
isR(np.zeros((3,3)))
```

--------------------------------

### SO2 Initialization Examples

Source: https://spatialmath-python.rai-inst.com/2d_orient_SO2.html

Demonstrates various ways to initialize an SO2 instance, including null rotation, rotation by angle, and from an SO(2) matrix.

```python
SO2()
SO2(np.pi/2)
SO2(np.pi/2, unit='deg')
SO2(R)
SO2([R1, R2])
SO2([X1, X2])
```

--------------------------------

### mpq_point example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/numeric.html

Examples of calculating polygon moments.

```pycon
>>> from spatialmath.base import mpq_point
>>> import numpy as np
>>> p = np.array([[1, 3, 2], [2, 2, 4]])
>>> mpq_point(p, 0, 0)  # area
>>> mpq_point(p, 3, 0)
```

--------------------------------

### Example Usage

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/pose2d.html

Demonstrates how to import and use the SE2 class from the spatialmath.pose2d module.

```python
from spatialmath.pose2d import *
import spatialmath as sm

T = SE2(1, 2, 0.3)
T = sm.SE2.Rx(1, 2, 0.3)
```

--------------------------------

### Closest point between lines (example)

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/geom3d.html

Example usage of the closest_to_line method.

```python
>>> from spatialmath import Line3
>>> line1 = Line3.Join([1, 1, 0], [1, 1, 1])
>>> line2 = Line3.Join([0, 0, 0], [2, 3, 5])
>>> line1.closest_to_line(line2)
```

--------------------------------

### Displaying Values with printline()

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Example of using the printline() method for tabular listing.

```pycon
>>> from spatialmath import *
>>> X = SE3.Rand()
>>> _ = X.printline()
```

--------------------------------

### trplot2 examples

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transforms2d.html

Examples of using the trplot2 function with various options.

```python
trplot2(T, frame='A')
trplot2(T, frame='A', color='green')
trplot2(T1, 'labels', 'AB')
```

```python
import matplotlib.pyplot as plt
from spatialmath.base import trplot2, transl2, trot2
import math
fig, ax = plt.subplots(3,3, figsize=(10,10))
text_opts = dict(bbox=dict(boxstyle="round",
    fc="w",
    alpha=0.9),
    zorder=20,
    family='monospace',
    fontsize=8,
    verticalalignment='top')
T = transl2(2, 1)@trot2(math.pi/3)
trplot2(T, ax=ax[0][0], dims=[0,4,0,4])
ax[0][0].text(0.2, 3.8, "trplot2(T)", **text_opts)
trplot2(T, ax=ax[0][1], dims=[0,4,0,4], originsize=0)
ax[0][1].text(0.2, 3.8, "trplot2(T, originsize=0)", **text_opts)
trplot2(T, ax=ax[0][2], dims=[0,4,0,4], arrow=False)
ax[0][2].text(0.2, 3.8, "trplot2(T, arrow=False)", **text_opts)
trplot2(T, ax=ax[1][0], dims=[0,4,0,4], axislabel=False)
ax[1][0].text(0.2, 3.8, "trplot2(T, axislabel=False)", **text_opts)
trplot2(T, ax=ax[1][1], dims=[0,4,0,4], width=3)
ax[1][1].text(0.2, 3.8, "trplot2(T, width=3)", **text_opts)
trplot2(T, ax=ax[1][2], dims=[0,4,0,4], frame='B')
ax[1][2].text(0.2, 3.8, "trplot2(T, frame='B')", **text_opts)
trplot2(T, ax=ax[2][0], dims=[0,4,0,4], color='r', textcolor='k')
ax[2][0].text(0.2, 3.8, "trplot2(T, color='r',textcolor='k')", **text_opts)
trplot2(T, ax=ax[2][1], dims=[0,4,0,4], labels=("u", "v"))
ax[2][1].text(0.2, 3.8, "trplot2(T, labels=('u', 'v'))", **text_opts)
trplot2(T, ax=ax[2][2], dims=[0,4,0,4], rviz=True)
ax[2][2].text(0.2, 3.8, "trplot2(T, rviz=True)", **text_opts)
```

--------------------------------

### DualQuaternion Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/DualQuaternion.html

Demonstrates the creation and basic usage of DualQuaternion.

```python
from spatialmath import DualQuaternion, SE3
T = SE3.Rand()
print(T)
d = UnitDualQuaternion(T)
print(d)
print(d.T)
```

--------------------------------

### plot_polygon example

Source: https://spatialmath-python.rai-inst.com/func_2d_graphics.html

Example demonstrating the basic usage of the plot_polygon function.

```python
from spatialmath.base import plotvol2, plot_polygon
plotvol2(5)
```

--------------------------------

### Example Usage

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/pose3d.html

This snippet shows how to execute tests for the pose3d module.

```python
#         raise ValueError('expecting SO3 or rotation matrix')
#     if t is None:
#         return cls(base.r2t(R))
#     else:
#         return cls(base.rt2tr(R, t))


if __name__ == "__main__":  # pragma: no cover
    import pathlib

    exec(
        open(
            pathlib.Path(__file__).parent.parent.absolute() / "tests" / "test_pose3d.py"
        ).read()
    )  # pylint: disable=exec-used
```

--------------------------------

### Identity element constructor

Source: https://spatialmath-python.rai-inst.com/intro.html

Examples of creating identity elements for UnitQuaternion and SE3 classes.

```python
>>> from spatialmath import *
>>> UnitQuaternion()
UnitQuaternion(array([1., 0., 0., 0.]))
>>> SE3()
SE3(array([[1., 0., 0., 0.],
           [0., 1., 0., 0.],
           [0., 0., 1., 0.],
           [0., 0., 0., 1.]]))

```

--------------------------------

### plot_circle example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/graphics.html

Examples of plotting circles with different styles and positions.

```python
from spatialmath.base import plotvol2, plot_circle
plotvol2(5)
plot_circle(1, (0,0), 'r')  # red circle
plot_circle(2, (1, 2), 'b--')  # blue dashed circle
plot_circle(0.5, (3,4), filled=True, facecolor='y')  # yellow filled circle
```

--------------------------------

### SE3.Rx Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/pose3d.html

Demonstrates creating an SE(3) pure rotation about the X-axis with different inputs.

```pycon
>>> from spatialmath import SE3
>>> SE3.Rx(0.3)
>>> SE3.Rx([0.3, 0.4])
```

--------------------------------

### plot_polygon example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/graphics.html

Example of plotting a polygon with a specified face color.

```python
from spatialmath.base import plotvol2, plot_polygon
plotvol2(5)
vertices = np.array([[-1, 2, -1], [1, 0, -1]])
plot_polygon(vertices, filled=True, facecolor='g')  # green filled triangle
```

--------------------------------

### List Capability: Length and Indexing

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Demonstrating list capabilities like length and indexing for SO3 objects.

```python
>>> from spatialmath import *
>>> import numpy as np
>>> R = SO3.Rx(0.3)
>>> len(R)
>>> R = SO3.Rx(np.arange(0, 2*np.pi, 0.2))
>>> len(R)
>>> R[0]
>>> R[-1]
>>> R[2:4]
```

--------------------------------

### isskewa Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transformsNd.html

Examples of testing if a matrix belongs to se(n).

```Python
from spatialmath.base import *
import numpy as np
isskewa(np.zeros((3,3)))
isskewa(np.array([[0, -2], [2, 0]])) # this matrix is skew but not skewa
isskewa(np.array([[0, -2, 5], [2, 0, 6], [0, 0, 0]]))
```

--------------------------------

### Ab2M Example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/transformsNd.html

Example of packing a matrix and vector into a transformation matrix.

```Python
from spatialmath.base import *
A = np.c_[[1, 2], [3, 4]].T
b = [5, 6]
Ab2M(A, b)
```

--------------------------------

### Ellipse Initialization Example

Source: https://spatialmath-python.rai-inst.com/classes-2d.html

Demonstrates different ways to initialize an Ellipse instance.

```python
>>> from spatialmath import Ellipse
>>> import numpy as np
>>> Ellipse(radii=(1,2), theta=0)
Ellipse(radii=[1. 2.], centre=(0, 0), theta=0.0)
>>> Ellipse(E=np.array([[1, 1], [1, 2]]))
Ellipse(radii=[1.618 0.618], centre=(0, 0), theta=1.0172219678978514)
```

--------------------------------

### Interpolation Example

Source: https://spatialmath-python.rai-inst.com/3d_orient_SO3.html

Example of interpolating between two SE3 poses.

```python
>>> x = SE3(-1, -2, 0) * SE3.Rx(-0.3)
>>> y = SE3(1, 2, 0) * SE3.Rx(0.3)
>>> x.interp(y, 0)    # this is x
SE3(array([[ 1.    ,  0.    ,  0.    , -1.    ],
           [ 0.    ,  0.9553,  0.2955, -2.    ],
           [ 0.    , -0.2955,  0.9553,  0.    ],
           [ 0.    ,  0.    ,  0.    ,  1.    ]]))
>>> x.interp(y, 1)    # this is y
SE3(array([[ 1.    ,  0.    ,  0.    ,  1.    ],
           [ 0.    ,  0.9553, -0.2955,  2.    ],
```

--------------------------------

### Quaternion constructor examples

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/quaternion.html

Demonstrates various ways to construct a Quaternion object.

```Python
>>> from spatialmath import Quaternion
>>> Quaternion()
>>> Quaternion(1, [2,3,4])
>>> Quaternion([1,2,3,4])
>>> q=Quaternion([np.r_[1,2,3,4], np.r_[5,6,7,8]])
>>> len(q)
>>> print(q)
```

--------------------------------

### Example Usage

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/animate.html

Example of using tranimate2 to create an HTML animation.

```python
import spatialmath.base as smb

T = smb.rot2(2)
s = smb.tranimate2(T, movie=True)
with open("zz.html", "w") as f:
    print(f"<html>{s}</html>", file=f)
```

--------------------------------

### Alloc method example

Source: https://spatialmath-python.rai-inst.com/6d_acceleration.html

Example demonstrating the usage of the Alloc class method to construct an instance with a specified number of default values.

```python
>>> x = X.Alloc(10)
>>> len(x)
10
```

--------------------------------

### Basic Rotation and Matrix Multiplication

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Demonstrates importing base functions, creating rotations, and performing matrix multiplication using the '@' operator.

```pycon
>>> from spatialmath.base import *
>>> rotx(0.3)
>>> rotx(30, unit='deg')
>>> R = rotx(0.3) @ roty(0.2)
>>> R
```

--------------------------------

### Unit twist example

Source: https://spatialmath-python.rai-inst.com/3d_pose_twist.html

Example for a unit twist.

```python
NameError: name 'S' is not defined
```

--------------------------------

### gauss1d example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/numeric.html

Example of generating a 1D Gaussian function.

```python
g = gauss1d(5, 2, np.linspace(0, 10, 100))
```

--------------------------------

### Translational transformation in 2D

Source: https://spatialmath-python.rai-inst.com/intro.html

Shows how to create a 2D translational transformation matrix using transl2.

```python
>>> from spatialmath.base import *
>>> transl2(1, 2)
array([[1., 0., 1.],
       [0., 1., 2.],
       [0., 0., 1.]])
```

--------------------------------

### List Superpowers with SE3 Objects

Source: https://spatialmath-python.rai-inst.com/_sources/intro.rst.txt

Demonstrates how SE3 objects can hold a sequence of values and be treated like Python lists.

```pycon
>>> from spatialmath import *
>>> X = SE3.Rx([0, 0.2, 0.4, 0.6])
>>> len(X)
>>> print(X[1])
```

--------------------------------

### str2array example

Source: https://spatialmath-python.rai-inst.com/_modules/spatialmath/base/numeric.html

Examples of converting strings to NumPy arrays.

```pycon
>>> from spatialmath.base import str2array
>>> str2array("5")
>>> str2array("[1 2 3]")
>>> str2array("[1 2; 3 4]")
>>> str2array(" [  1  , 2 ; 3 4  ] ")
>>> str2array("[1; 2; 3]")
```
Tokens:
Raw