.. _tdnote2022rattrapage2rst:

===================================
1A - Enoncé 3 mars 2022- rattrapage
===================================


.. only:: html

    **Links:** :download:`notebook <td_note_2022_rattrapage2.ipynb>`, :downloadlink:`html <td_note_2022_rattrapage22html.html>`, :download:`python <td_note_2022_rattrapage2.py>`, :downloadlink:`slides <td_note_2022_rattrapage2.slides.html>`, :githublink:`GitHub|_doc/notebooks/exams/td_note_2022_rattrapage2.ipynb|*`


Correction de l’examen du 3 mars 2022. L’objectif est de construire un
arbre de façon algorithmique.

.. code:: ipython3

    from jyquickhelper import add_notebook_menu
    add_notebook_menu()






.. contents::
    :local:





Dessin d’une liste de segments
------------------------------

.. code:: ipython3

    import matplotlib.pyplot as plt
    
    
    def draw(segments, L=1):
        fig, ax = plt.subplots(1, 1, figsize=(4, 4))
        maxxy = 0
        for seg in segments:
            ax.plot([seg['x1'], seg['x2']], [seg['y1'], seg['y2']], 'b-', lw=seg['E'] * 10000)
        ax.set_xlim([0, 2 * L])
        ax.set_ylim([-L, L])
        return ax
    
    draw([{'x1': 0, 'y1': 0, 'x2': 1.0, 'y2': 0.0, 'E': 0.001, 'angle': 0}]);



.. image:: td_note_2022_rattrapage2_3_0.png


Distance d’un segment
---------------------

.. code:: ipython3

    def distance(seg):
        x1, x2, y1, y2 = seg['x1'], seg['x2'], seg['y1'], seg['y2']
        return ((x2 - x1) ** 2 + (y2 - y1) ** 2) ** 0.5
    
    distance({'x1': 0, 'y1': 0, 'x2': 1.0, 'y2': 0.0, 'E': 0.001, 'angle': 0})




.. parsed-literal::
    1.0



Calcul du segment suivant
-------------------------

.. code:: ipython3

    from math import cos, sin, pi
    
    
    def segment(x=0, y=0, angle=0, L=1, E=0.001):
        x2 = x + cos(angle) * L
        y2 = y + sin(angle) * L
        return dict(x1=x, y1=y, x2=x2, y2=y2, E=E, angle=angle)
    
    segment()




.. parsed-literal::
    {'x1': 0, 'y1': 0, 'x2': 1.0, 'y2': 0.0, 'E': 0.001, 'angle': 0}



Calcul des trois segments suivants
----------------------------------

.. code:: ipython3

    def tree3(seg, angle=pi/3, re=0.33, rl=0.66):
        x, y = seg['x2'], seg['y2']
        e = seg['E'] * re
        le = distance(seg) * rl
        a = seg['angle']
        segments = [
            segment(x, y, angle=a-angle, L=le, E=e),
            segment(x, y, angle=a, L=le, E=e),
            segment(x, y, angle=a+angle, L=le, E=e),
        ]
        return segments
    
    premier = segment()
    segs = [premier] + tree3(premier, 1)
    draw(segs);



.. image:: td_note_2022_rattrapage2_9_0.png


Construction de tous les niveaux de l’arbre
-------------------------------------------

.. code:: ipython3

    def tree_recursive(level, seg, angle=pi/6, re=0.6, rl=0.95):
        all_segs = [seg]
        iter_segs = [seg]
        for i in range(level):
            new_segs = []
            for seg in iter_segs:
                new_segs.extend(tree3(seg, angle=angle, re=re, rl=rl))
            all_segs.extend(new_segs)
            iter_segs = new_segs
        return all_segs
    
    premier = segment()
    segs = tree_recursive(3, premier)
    draw(segs, L=3);



.. image:: td_note_2022_rattrapage2_11_0.png


Construction de trois segments aléatoires
-----------------------------------------

.. code:: ipython3

    import random
    
    def tree3_alea(seg, angle=pi/3, re=0.33, rl=0.66, rnd=0.1):
        re_rnd = re * (1 + random.random() * rnd)
        rl_rnd = rl * (1 + random.random() * rnd)
        
        x, y = seg['x2'], seg['y2']
        e = seg['E'] * re_rnd
        le = distance(seg) * rl_rnd
    
        a = seg['angle']
        a1 = a - (1 + random.random() * rnd) * angle
        a2 = a + random.random() * rnd * angle
        a3 = a + (1 + random.random() * rnd) * angle
        
        segments = [
            segment(x, y, angle=a1, L=le, E=e),
            segment(x, y, angle=a2, L=le, E=e),
            segment(x, y, angle=a3, L=le, E=e),
        ]
        return segments
    
    premier = segment()
    segs = [premier] + tree3_alea(premier, 1)
    draw(segs);



.. image:: td_note_2022_rattrapage2_13_0.png


Construction d’un arbre aléatoire
---------------------------------

L’idée est d’ajouter 40% d’aléatoire sur trois paramètres : la réduction
des longueurs, la réduction des épaisseurs, les angles des trois
segments suivants.

.. code:: ipython3

    def tree_recursive_alea(level, seg, angle=pi/6, re=0.6, rl=0.95, rnd=0.4):
        all_segs = [seg]
        iter_segs = [seg]
        for i in range(level):
            new_segs = []
            for seg in iter_segs:
                new_segs.extend(tree3_alea(seg, angle=angle, re=re, rl=rl, rnd=rnd))
            all_segs.extend(new_segs)
            iter_segs = new_segs
        return all_segs
    
    premier = segment()
    segs = tree_recursive_alea(3, premier)
    draw(segs, L=3.5);



.. image:: td_note_2022_rattrapage2_15_0.png


.. code:: ipython3

    premier = segment()
    segs = tree_recursive_alea(4, premier)
    draw(segs, L=5);



.. image:: td_note_2022_rattrapage2_16_0.png