geometry > star shape(星形)の内部をdipoleでfillする > findDipolesInisideStarShape_180429 v0.1 > sympy使用 > 3分かかる (MESH_RESOL=20)

```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star shape(星形)のedgeの交点を見つけて、線分を引く (平面角すべての範囲で行う) > find_rayCrossing_starShapedEged_180417 v0.5](https://qiita.com/7of9/items/3b2405641e71d7f4aa76)

Gaussian random sphereの形状情報をもとにADDAで光散乱数値シミュレーションを行うには、dipoleでfillした形状に変換する必要がある。

星形をもとに方法を検討してきた。

### 処理方法

下記としてみた。

- 格子状のdipoleを用意する
- 中心からdipoleの線分を検討する。
- 線分が形状の線分と交差しているか
    - 交差あり: 外側
    - 交差なし: 内側

 内側のdipoleだけを残すことで、形状をdipoleでfillした状態になる。

### code v0.1

```py:findDipolesInisideStarShape_180429.ipynb
%matplotlib inline

import numpy as np
import sympy as sp
import sys
import matplotlib.pyplot as plt
from pylab import rcParams
from itertools import combinations
import geometry_starShaped_180428 as GSS
import datetime as dt

'''
v0.1 Apr. 29, 2018
  - use algorithm to check inside/outside the given shape
      + segment (from center to dipole and segment of the shape
      + crossing segments indicates dipole is located outside the shape
=== branched from [find_rayCrossing_starShapedEged_180417.ipynb] ===
v0.5 Apr. 29, 2018
  - loop through [theta_deg]
  - add get_linesegment()
  - add calc_raylinegeometry()
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


def calc_raylinegeometry(theta_deg):
    # define the ray from the center
    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
    return xs_ray, ys_ray


def get_linesegment(xs, ys, idx0, idx1):
    pa1 = sp.Point(xs[idx0], ys[idx0])
    pa2 = sp.Point(xs[idx1], ys[idx1])
    return sp.Segment(pa1, pa2)

MESH_RESOL = 20
inx = np.linspace(-11, 11, MESH_RESOL, endpoint=True)
iny = np.linspace(-11, 11, MESH_RESOL, endpoint=True)
mx, my = np.meshgrid(inx, iny)

# 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)


fig = plt.figure()

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

print(dt.datetime.now())

for idx in range(len(mx)):
    print(idx, end='.')
    for idy in range(len(my)):
        # segment from center to dipole
        pa1 = sp.Point(0.0, 0.0)
        pa2 = sp.Point(mx[idx][idy], my[idx][idy])
        sga = sp.Segment(pa1, pa2)
        # edge of the shape
        isinside = True
        for aidx in combs:
            if not isinside:
                continue
            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]]])
            sgb = get_linesegment(xs_str, ys_str, aidx[0], aidx[1])
            its = sp.intersection(sga, sgb)
            if its:  # outside
                isinside = False
                continue
        if isinside:
            ax1.scatter(mx[idx][idy], my[idx][idy])
   

print(dt.datetime.now())

fig.tight_layout()

```

![qiita.png](https://qiita-image-store.s3.amazonaws.com/0/32870/50ed458c-8b0d-cff6-f460-b884e208554f.png)

処理に3分かかる。

3次元にした場合、膨大な待ち時間になる。