'''
MIT License

Copyright (c) 2022 sup39[サポミク]

Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:

The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
'''

import numpy as np
array = np.array
import matplotlib.pyplot as plt
from matplotlib.path import Path
from matplotlib import patches
normalize = lambda x: x/np.linalg.norm(x)

# 多角形
class Polygon():
  def __init__(self, verts):
    '''
    * self.verts:
      頂点の配列
      Array of vertices
    '''
    self.verts = np.array(verts)
  def clipLine(self, p, n, c):
    '''
    半平面 (x-p)・n >= c との共通部分を取る
    Take intersection with half plane (x-p)・n >= c
    * p:
      直線上の一点
      Any point on the line
    * n:
      直線の法線ベクトル
      Normal vector of the line
    * c:
      定数
      Constant
    '''
    p, n, c = map(array, (p, n, c))
    r = np.dot(self.verts-p, n)-c
    verts = []
    for i in range(len(r)):
      v0, r0 = self.verts[i-1], r[i-1]
      v1, r1 = self.verts[i], r[i]
      if r1 >= 0:
        if r0 < 0: # (- +)
          verts.append((r1*v0-r0*v1)/(-r0+r1))
        verts.append(v1)
      elif r0 >= 0: # (+ -)
        verts.append((-r1*v0+r0*v1)/(r0-r1))
    self.verts = np.array(verts) if len(verts) else self.verts[:0]
  @property # getter
  def path(self):
    if self.verts.shape[0] == 0: return None
    verts = self.verts
    assert verts.shape[-1] == 2, 'verts should be 2D'
    return Path([*verts, (0, 0)], [
      Path.MOVETO,
      *(Path.LINETO for _ in range(1, verts.shape[0])),
      Path.CLOSEPOLY,
    ])
  def plot(self, margin=0.05, facecolor='#2ee5b8', lw=1):
    '''
    この多角形を描画し、figとaxを返す
    Plot this polygon and return ``fig'' and ``ax''
    * margin:
      Set margin of the plot
    * facecolor:
      面の色
      Face color
    * lw:
      線の太さ
      Line width
    '''
    fig, ax = plt.subplots()
    if self.verts.shape[0] == 0: return ax
    # path
    path = self.path
    patch = patches.PathPatch(path, facecolor=facecolor, lw=lw)
    ax.add_patch(patch)
    verts = self.verts
    xMax, yMax = verts.max(axis=0)
    xMin, yMin = verts.min(axis=0)
    xMg, yMg = verts.ptp(axis=0)*margin
    ax.set_xlim(xMin-xMg, xMax+xMg)
    ax.set_ylim(yMin-yMg, yMax+yMg)
    return fig, ax
  def __repr__(self):
    return 'Polygon with %d vertices:\n%s'%(
      len(self.verts),
      array(self.verts, 'f'),
    )

# 多面体
class Polyhedron:
  def __init__(self, verts, edges):
    '''
    * self.verts:
      頂点の配列
      Array of vertices
    * self.edges:
      辺(2頂点の番号)の配列
      Array of edges (indices of 2 vertices)
    '''
    self.verts = np.array(verts)
    self.edges = edges
  def clipPlane(self, p, n, c=0):
    '''
    半空間 (x-p)・n >= c との共通部分を取る
    Take intersection with half space (x-p)・n >= c
    * p:
      平面上の一点
      Any point on the plane
    * n:
      直線の法線ベクトル
      Normal vector of the plane
    * c:
      定数
      Constant
    '''
    p, n, c = map(array, (p, n, c))
    r = np.dot(self.verts-p, n)-c
    rb = [s>=0 for s in r]
    # map vertex indices old to new
    io2n = {
      iO: iN
      for iN, iO in enumerate(iO for iO, sb in enumerate(rb) if sb)
    }
    # handle old vert
    verts = [v for v, sb in zip(self.verts, rb) if sb]
    edges = []
    for i0, i1 in self.edges:
      if rb[i0] and rb[i1]:
        # remain
        edges.append((io2n[i0], io2n[i1]))
      elif rb[i0] or rb[i1]:
        # new vert
        v0, r0 = self.verts[i0], abs(r[i0])
        v1, r1 = self.verts[i1], abs(r[i1])
        vN = (r1*v0+r0*v1)/(r0+r1)
        edges.append((io2n[i0 if rb[i0] else i1], len(verts)))
        verts.append(vN)
      # else drop edge
    # add new face
    nOld = len(io2n)
    vNews = verts[nOld:]
    if len(vNews):
      assert len(vNews) >= 3
      p0, p1 = vNews[:2]
      # choose p1-p0 as e1
      e1 = normalize(p1-p0)
      # choose e2 that ⊥ n, e1
      e2 = normalize(np.cross(n, e1))
      # set (p0+p1)/2 as new origin, and use {e1, e2} as new basis
      cNews = np.dot(vNews-(p0+p1)/2, array([e1, e2]).transpose())
      # indices of new verts CCW
      jNews = nOld+np.arctan2(cNews[:,0], cNews[:,1]).argsort()
      # add to edge
      for i in range(len(vNews)):
        edges.append((jNews[i-1], jNews[i]))
    # final
    self.verts = array(verts)
    self.edges = edges
  def slicePlane(self, p, n):
    '''
    平面 (x-p)･n=0 との共通部分(多角形)の頂点を返す
    Return vertices of intersection(polygon) with plane (x-p)･n=0
    * p:
      平面上の一点
      Any point on the plane
    * n:
      平面の法線ベクトル
      Normal vector of the plane
    '''
    p, n = map(array, (p, n))
    r = np.dot(self.verts-p, n)
    vNews = []
    # handle old verts
    for i0, i1 in self.edges:
      # two vertices on other side of the plane
      if np.sign(r[i0]) != np.sign(r[i1]):
        v0, r0 = self.verts[i0], abs(r[i0])
        v1, r1 = self.verts[i1], abs(r[i1])
        vN = (r1*v0+r0*v1)/(r0+r1)
        vNews.append(vN)
    # new verts
    if len(vNews):
      assert len(vNews) >= 2
      p0, p1 = vNews[:2]
      e1 = normalize(p1-p0)
      e2 = normalize(np.cross(n, e1))
      cNews = np.dot(vNews-(p0+p1)/2, array([e1, e2]).transpose())
      jNews = np.arctan2(cNews[:,0], cNews[:,1]).argsort()
      return array([vNews[j] for j in jNews])
    else:
      return self.verts[:0]
  def __repr__(self):
    return 'Polyhedron with %d vertices and %d edges:\n%s'%(
      len(self.verts), len(self.edges),
      array([self.verts[[i0, i1]] for i0, i1 in self.edges], 'f')
    )