geometry > 中心からの線と交わるstar shape(星形)のedgeとその交点を探す > find_rayCrossing_starShapedEged_180417 v0.4 > sympy intersection使用

```txt:動作環境
GeForce GTX 1070 (8GB)
ASRock Z170M Pro4S [Intel Z170chipset]
Ubuntu 16.04.4 LTS desktop amd64
TensorFlow v1.7.0
cuDNN v5.1 for Linux
CUDA v8.0
Python 3.5.2
IPython 6.0.0 -- An enhanced Interactive Python.
gcc (Ubuntu 5.4.0-6ubuntu1~16.04.4) 5.4.0 20160609
GNU bash, version 4.3.48(1)-release (x86_64-pc-linux-gnu)
scipy v0.19.1
geopandas v0.3.0
MATLAB R2017b (Home Edition)
ADDA v.1.3b6
gnustep-gui-runtime v0.24.0-3.1
PyMieScatt v1.7.0
```


前回: [geometry > 中心からの線と交わるstar shape(星形)のedgeを探す > geometry_lineintersect_180415 v0.3 | find_rayCrossing_starShapedEged_180417 v0.3](https://qiita.com/7of9/items/f14f0e8e30fc7f2e42ba)

### 処理概要

- 星形の中心からrayを飛ばす
- rayが交差する星形の辺を見つける
- rayとの交点を見つける

### sympy intersection

rayと星形の辺の交点はsympy intersectionを使う。

- [sympyで線分と線分の交点](https://qiita.com/mrrclb48z/items/c30155fb2ade53ebf2e7) by @mrrclb48zさん

情報感謝です。

### code v0.4

```py:find_rayCrossing_starShapedEged_180417.ipynb
%matplotlib inline

import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
from pylab import rcParams
from itertools import combinations
import geometry_starShaped_180428 as GSS
#import geometry_lineintersect_180415 as GLI

'''
v0.4 Apr. 29, 2018
  - find crossing point instead of crossing edge
     + remove: import [geometry_lineintersect_180415]
     + import sympy
v0.3 Apr. 28, 2018
  - import geometry_starShaped_180428 (v0.3)
v0.2 Apr. 28, 2018
  - exclude vertices pairs not included in the output from [geometry_starShaped_180428]
  - import geometry_starShaped_180428 (v0.2)
  - remove: import geometry_starShaped_180415
v0.1 Apr. 17, 2018
  - check the crossing
      + import [geometry_lineintersect_180415]
  - define the ray from the center
    + draw the ray
    + add [xs_ray], [ys_ray]
    + add [theta_deg]
  - add idxs_seq[], combs[]
  - import [combinations]
  - branched from [geometry_starShaped_180414.ipynb]
'''

rcParams['figure.figsize'] = 14, 7
rcParams['figure.dpi'] = 110

# 1. obtain star shaped points
RAD_INNER = 5
RAD_OUTER = 10
xs_str, ys_str, edgeidx = GSS.get_starShaped(RAD_INNER, RAD_OUTER)

# 2. obtain combinations of points
idxs_seq = range(len(xs_str))  # sequential indices to obtain combinations
combs = []  # combinations to obtain all the edges
for acomb in combinations(idxs_seq, 2):
    combs += [acomb]
print(combs)

# 3. define the ray from the center
theta_deg = 0.0  # [deg] 0 for rightward direction, 90 for downward direction
radius = RAD_OUTER * 1.1  # 1.1 to cross the outmost edge
xs_ray, ys_ray = [0.0], [0.0]  # center
xs_ray += [radius * np.cos(np.deg2rad(theta_deg))]  # outmost
ys_ray += [radius * np.sin(np.deg2rad(theta_deg))]  # outmost
print(xs_ray, ys_ray)

fig = plt.figure()

ax1 = fig.add_subplot(1, 2, 1)
ax1.scatter(xs_str, ys_str)
ax1.set_xlabel('x')
ax1.set_ylabel('y')
ax1.plot(xs_ray, ys_ray)
ax1.grid(True)

# 4. find crossing edges
pa1 = sp.Point(xs_ray[0], ys_ray[0])
pa2 = sp.Point(xs_ray[1], ys_ray[1])
sga = sp.Segment(pa1, pa2)
for aidx in combs:
    if list(aidx) not in edgeidx:
        continue
    b1 = np.array([xs_str[aidx[0]], ys_str[aidx[0]]])
    b2 = np.array([xs_str[aidx[1]], ys_str[aidx[1]]])
    pb1 = sp.Point(xs_str[aidx[0]], ys_str[aidx[0]])
    pb2 = sp.Point(xs_str[aidx[1]], ys_str[aidx[1]])
    sgb = sp.Segment(pb2, pb1)
    crp = sp.intersection(sga, sgb)
    if crp:
        xs_draw = [b1[0], b2[0]]
        ys_draw = [b1[1], b2[1]]
        ax1.plot(xs_draw, ys_draw)
        xs_draw = [xs_ray[0], crp[0][0]]
        ys_draw = [ys_ray[0], crp[0][1]]
        ax1.plot(xs_draw, ys_draw)


fig.tight_layout()

```

![qiita.png](https://qiita-image-store.s3.amazonaws.com/0/32870/c6295dec-8bff-e940-cb9a-de584a834648.png)