#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
MIT License

Copyright (c) 2022 Jongrae.K

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
import matplotlib.pyplot as plt

# number of samples
num_sample = 500

# map size
map_width = 10
map_height = 5

# x,y coordinates of start and destination of the path to be calculated
xy_start = np.array([0,0])
xy_dest = np.array([9,4])

# spread num_sample random points over the map area
xy_points = np.random.rand(num_sample,2)
xy_points[::,0] = xy_points[::,0]*map_width
xy_points[::,1] = xy_points[::,1]*map_height

# stacking them all together with start and destination
xy_points = np.vstack((xy_start,xy_dest,xy_points))
start_node = 0
end_node = 1

# circular obstacle at [3,3], radius 1.5 & define the boundary
obs_xy = [3,3]
obs_rad = 1.5
th = np.arange(0,2*np.pi+0.01,0.01)
x_obs_0 = obs_rad*np.cos(th)+obs_xy[0]
y_obs_0 = obs_rad*np.sin(th)+obs_xy[1]
xy_obs_0 = np.vstack((x_obs_0,y_obs_0)).T

# non-convex obstacle boundary
x_obs_1 = np.array([6,8,8,5,5,7,7,6,6])
y_obs_1 = np.array([1,1,4,4,3,3,2,2,1])
xy_obs_1 = np.vstack((x_obs_1,y_obs_1)).T

# define obstacle using Path in matplotlib.path
from matplotlib.path import Path
Obs_0 = Path(xy_obs_0)
Obs_1 = Path(xy_obs_1)

# found points are not inside the circular obstacle
mask_0 = ~Obs_0.contains_points(xy_points)
xy_points = xy_points[mask_0,::]

mask_1 = ~Obs_1.contains_points(xy_points)
xy_points = xy_points[mask_1,::]

# construct graph using delaunay
from scipy.spatial import Delaunay
tri = Delaunay(xy_points)

# found triangle definition index
temp_idx=tri.simplices[::,0]
temp_jdx=tri.simplices[::,1]
temp_kdx=tri.simplices[::,2]

# remove longer paths, which are likely passing through the obstacle
dist_ij = np.sqrt(np.sum((xy_points[temp_idx,::]-xy_points[temp_jdx,::])**2,1))
dist_jk = np.sqrt(np.sum((xy_points[temp_jdx,::]-xy_points[temp_kdx,::])**2,1))
dist_ki = np.sqrt(np.sum((xy_points[temp_kdx,::]-xy_points[temp_idx,::])**2,1))
dd_all = np.hstack((dist_ij,dist_jk,dist_ki))
cut_dist = np.mean(dd_all)+1*np.std(dd_all)

# distance thereshold for removing longer paths
cut_mask_ij = dist_ij<cut_dist
cut_mask_jk = dist_jk<cut_dist
cut_mask_ki = dist_ki<cut_dist
temp_xy_ij = np.vstack((temp_idx[cut_mask_ij],temp_jdx[cut_mask_ij]))
temp_xy_jk = np.vstack((temp_jdx[cut_mask_jk],temp_kdx[cut_mask_jk]))
temp_xy_ki = np.vstack((temp_kdx[cut_mask_ki],temp_idx[cut_mask_ki]))

# corresponding distance to the paths
dist_ij = dist_ij[cut_mask_ij]
dist_jk = dist_jk[cut_mask_jk]
dist_ki = dist_ki[cut_mask_ki]

# change format into row, column and the distance
xy_index = np.hstack((temp_xy_ij,temp_xy_jk,temp_xy_ki)).T
row_org = xy_index[::,0]
col_org = xy_index[::,1]
row = np.hstack((row_org,col_org))
col = np.hstack((col_org,row_org))
dist = np.hstack((dist_ij,dist_jk,dist_ki))
dist = np.hstack((dist,dist))
num_node = xy_points.shape[0]

# construct the distance matrix
from scipy.sparse import csr_matrix
dist_sparse = csr_matrix((dist,(row,col)), shape=(num_node,num_node))

# calculate the shortest path
from scipy.sparse.csgraph import dijkstra
dist, pred = dijkstra(dist_sparse, indices = start_node, return_predecessors=True)
print(f'distance from node #{start_node:0d} to node #{end_node:0d}: {dist[end_node]:4.2f}')

# obtain the shortest path
path = []
i=end_node
if np.isinf(dist[end_node]):
    print('the path does not exist!')
else:
    while i!=start_node:
        path.append(i)
        i = pred[i]
    path.append(start_node)
    print('path=',path[::-1])

opt_path = np.asarray(path[::-1])

# plot all paths, obstacles
plt.figure(1)
#plt.triplot(xy_points[:,0], xy_points[:,1], tri.simplices)
plt.plot(x_obs_0,y_obs_0,'r',linewidth=4)
plt.plot(x_obs_1,y_obs_1,'r',linewidth=4)
plt.plot(xy_start[0],xy_start[1],'x')
plt.plot(xy_dest[0],xy_dest[1],'o')
plt.text(0,0.2,'Initial Location')
plt.text(7.5,4.2,'Destination')
plt.axis([-0.2,10,-0.2,5])
#plt.savefig('../book_v0_3/figures/python_nonconvex_obstacle_path_planning.pdf',dpi=250)

# plot the optimal path
for idx in range(0,opt_path.size-1,1):
    p_idx = opt_path[idx]
    q_idx = opt_path[idx+1]
    op_xx = [xy_points[p_idx,0], xy_points[q_idx,0]]
    op_yy = [xy_points[p_idx,1], xy_points[q_idx,1]]
    plt.plot(op_xx,op_yy,'g-.',linewidth=2)
    
#------------------------------------------------------------------------------
# resampling
#------------------------------------------------------------------------------
xy_opt_points = xy_points[opt_path,:]
dxy_opt_dist = np.sqrt(np.sum((xy_opt_points[0:-1]-xy_opt_points[1::])**2,1))
N_new_samp = 1000

xy_samp = np.empty((0,2))

for crd, dst in zip(xy_opt_points,dxy_opt_dist):
    xy_samp = np.append(xy_samp,crd + np.random.randn(N_new_samp,2)*dst,axis=0)

# found points are not inside the circular obstacle
mask_0 = ~Obs_0.contains_points(xy_samp)
xy_samp = xy_samp[mask_0,::]

mask_1 = ~Obs_1.contains_points(xy_samp)
xy_samp = xy_samp[mask_1,::]

# add start and destination node at 0 and 1st row
xy_samp = np.vstack((xy_start,xy_dest,xy_samp))

# construct graph
tri_updated = Delaunay(xy_samp)

# found triangle definition index
temp_idx=tri_updated.simplices[::,0]
temp_jdx=tri_updated.simplices[::,1]
temp_kdx=tri_updated.simplices[::,2]

# calculate the distance
dist_ij = np.sqrt(np.sum((xy_samp[temp_idx,::]-xy_samp[temp_jdx,::])**2,1))
dist_jk = np.sqrt(np.sum((xy_samp[temp_jdx,::]-xy_samp[temp_kdx,::])**2,1))
dist_ki = np.sqrt(np.sum((xy_samp[temp_kdx,::]-xy_samp[temp_idx,::])**2,1))
cut_dist = 0.1*np.sqrt(np.max(np.sum((xy_points[opt_path[0:-1],:]-xy_points[opt_path[1::],:])**2,axis=1)))

# distance thereshold for removing longer paths
cut_mask_ij = dist_ij<cut_dist
cut_mask_jk = dist_jk<cut_dist
cut_mask_ki = dist_ki<cut_dist
temp_xy_ij = np.vstack((temp_idx[cut_mask_ij],temp_jdx[cut_mask_ij]))
temp_xy_jk = np.vstack((temp_jdx[cut_mask_jk],temp_kdx[cut_mask_jk]))
temp_xy_ki = np.vstack((temp_kdx[cut_mask_ki],temp_idx[cut_mask_ki]))

# corresponding distance to the paths
dist_ij = dist_ij[cut_mask_ij]
dist_jk = dist_jk[cut_mask_jk]
dist_ki = dist_ki[cut_mask_ki]

# change format into row, column and the distance
xy_index = np.hstack((temp_xy_ij,temp_xy_jk,temp_xy_ki)).T
row_org = xy_index[::,0]
col_org = xy_index[::,1]
row = np.hstack((row_org,col_org))
col = np.hstack((col_org,row_org))
dist = np.hstack((dist_ij,dist_jk,dist_ki))
dist = np.hstack((dist,dist))
num_node = xy_samp.shape[0]

dist_sparse = csr_matrix((dist,(row,col)), shape=(num_node,num_node))
dist, pred = dijkstra(dist_sparse, indices = start_node, return_predecessors=True)

# obtain the shortest path
path = []
i=end_node
if np.isinf(dist[end_node]):
    print('the path does not exist!')
else:
    while i!=start_node:
        path.append(i)
        i = pred[i]
    path.append(start_node)
    print('path=',path[::-1])

opt_path_updated = np.asarray(path[::-1])

# plot all paths, obstacles
plt.figure(2)
plt.triplot(xy_samp[:,0], xy_samp[:,1], tri_updated.simplices)
plt.plot(x_obs_0,y_obs_0,'r',linewidth=4)
plt.plot(x_obs_1,y_obs_1,'r',linewidth=4)
plt.plot(xy_start[0],xy_start[1],'x')
plt.plot(xy_dest[0],xy_dest[1],'o')
plt.text(0,0.2,'Initial Location')
plt.text(7.5,4.2,'Destination')
plt.axis([-0.2,10,-0.2,5])

# plot the updated optimal path
plt.figure(1)
for idx in range(0,opt_path_updated.size-1,1):
    p_idx = opt_path_updated[idx]
    q_idx = opt_path_updated[idx+1]
    op_xx = [xy_samp[p_idx,0], xy_samp[q_idx,0]]
    op_yy = [xy_samp[p_idx,1], xy_samp[q_idx,1]]
    plt.plot(op_xx,op_yy,'m',linewidth=4)
    
plt.figure(2)
for idx in range(0,opt_path_updated.size-1,1):
    p_idx = opt_path_updated[idx]
    q_idx = opt_path_updated[idx+1]
    op_xx = [xy_samp[p_idx,0], xy_samp[q_idx,0]]
    op_yy = [xy_samp[p_idx,1], xy_samp[q_idx,1]]
    plt.plot(op_xx,op_yy,'m',linewidth=4)