```python
from sympy import init_printing; init_printing();
from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = "all"
```


```python
from sympy import symbols, cos, sin, Array
from silkpy.symbolic.geometry_map import GeometryMap
from silkpy.symbolic.curve.curve import ParametricCurve

a, b = symbols("a, b", positive=True); t = symbols("t", real=True)
line_on_cylind = ParametricCurve(t, [a*cos(t), a*sin(t), b*t])
```


```python
line_on_cylind.T_N_B
line_on_cylind.jacobian
```

    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The to_png function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)
    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The to_rgba function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)
    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The to_mask function was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)
    /home/wenyin/pyvenv/vsym/lib/python3.8/site-packages/IPython/lib/latextools.py:126: MatplotlibDeprecationWarning: 
    The MathtextBackendBitmap class was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use mathtext.math_to_image instead.
      mt.to_png(f, s, fontsize=12, dpi=dpi, color=color)





$\displaystyle \left( \left[\begin{matrix}- \frac{a \sin{\left(t \right)}}{\sqrt{a^{2} + b^{2}}} & \frac{a \cos{\left(t \right)}}{\sqrt{a^{2} + b^{2}}} & \frac{b}{\sqrt{a^{2} + b^{2}}}\end{matrix}\right], \  \left[\begin{matrix}- \cos{\left(t \right)} & - \sin{\left(t \right)} & 0\end{matrix}\right], \  \left[\begin{matrix}\frac{b \sin{\left(t \right)}}{\sqrt{a^{2} + b^{2}}} & - \frac{b \cos{\left(t \right)}}{\sqrt{a^{2} + b^{2}}} & \frac{a}{\sqrt{a^{2} + b^{2}}}\end{matrix}\right]\right)$






$\displaystyle \left[\left[\begin{matrix}- a \sin{\left(t \right)} & a \cos{\left(t \right)} & b\end{matrix}\right]\right]$




```python
from silkpy.symbolic.curve.transform import curve_normalize
line_on_cylind_normalized = curve_normalize(line_on_cylind)
```


```python
line_on_cylind_normalized.T_N_B
```




$\displaystyle \left( \left[\begin{matrix}- \frac{a \sin{\left(\frac{s}{\sqrt{a^{2} + b^{2}}} \right)}}{\sqrt{a^{2} + b^{2}}} & \frac{a \cos{\left(\frac{s}{\sqrt{a^{2} + b^{2}}} \right)}}{\sqrt{a^{2} + b^{2}}} & \frac{b}{\sqrt{a^{2} + b^{2}}}\end{matrix}\right], \  \left[\begin{matrix}- \cos{\left(\frac{s}{\sqrt{a^{2} + b^{2}}} \right)} & - \sin{\left(\frac{s}{\sqrt{a^{2} + b^{2}}} \right)} & 0\end{matrix}\right], \  \left[\begin{matrix}\frac{b \sin{\left(\frac{s}{\sqrt{a^{2} + b^{2}}} \right)}}{\sqrt{a^{2} + b^{2}}} & - \frac{b \cos{\left(\frac{s}{\sqrt{a^{2} + b^{2}}} \right)}}{\sqrt{a^{2} + b^{2}}} & \frac{a}{\sqrt{a^{2} + b^{2}}}\end{matrix}\right]\right)$




```python

```


```python

```

ebdecacdf2f7fa2b1c205623059c807eb662a581
ipynb
Jupyter Notebook
nb/construct_curve.ipynb
WenyinWei/silkpy
2e3773e15fbebc4914f5627d8361a24d35fb5935
MIT
2021-05-13T09:23:03.000Z
2021-05-13T09:23:03.000Z
nb/construct_curve.ipynb
WenyinWei/silkpy
2e3773e15fbebc4914f5627d8361a24d35fb5935
MIT
nb/construct_curve.ipynb
WenyinWei/silkpy
2e3773e15fbebc4914f5627d8361a24d35fb5935
MIT
2021-05-27T14:13:24.000Z
2021-05-27T14:13:24.000Z
Qwen/Qwen-72B
1. YES
2. YES