#!/usr/bin/env python
# coding: utf-8

# # Geometrie

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# ## Konvexe Hülle
# 
# SciPy's [spatial Modul](http://docs.scipy.org/doc/scipy-dev/reference/spatial.html)
# beinhaltet zum Beispiel eine Methode um die [konvexe Hülle](http://docs.scipy.org/doc/scipy-dev/reference/generated/scipy.spatial.ConvexHull.html) von Punkten finden zu können.
# Es ist ein front-end für [QHull](http://www.qhull.org/).

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import numpy as np
from scipy.spatial import ConvexHull

pts = np.random.normal(size=(100,2))
chull = ConvexHull(pts)
chull.vertices


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get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
for simplex in chull.simplices:
    plt.plot(pts[simplex, 0], pts[simplex, 1], "g-", lw=2, zorder=1)
plt.scatter(pts[:,0], pts[:,1], zorder=2)


# ## Sympy Geometry Module

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import sympy as sy
from sympy.geometry import Point, Segment, Circle, Line, Triangle


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x = Point(0, 0)
y = Point(1, 1)
z = Point(2, 2)
zp = Point(1, 0) 


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Point.is_collinear(x, y, z)


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Point.is_collinear(x, y, zp)


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seg1 = Segment(x, z)
seg2 = Segment(y, zp)


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seg1.intersection(seg2)


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seg1.midpoint


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c = Circle(x, 5)
l = Line(Point(5, -5), Point(5, 5)) 


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c.is_tangent(l)


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l2 = Line(Point(2, -4), Point(3, -2))
c.intersection(l2)


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