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Code Editor : polysimplify.py

# coding=utf-8
# https://github.com/Permafacture/Py-Visvalingam-Whyatt
"""
Visvalingam-Whyatt method of poly-line vertex reduction

Visvalingam, M and Whyatt J D (1993)
"Line Generalisation by Repeated Elimination of Points", Cartographic J., 30 (1), 46 - 51

Described here:
http://web.archive.org/web/20100428020453/http://www2.dcs.hull.ac.uk/CISRG/publications/DPs/DP10/DP10.html

=========================================

The MIT License (MIT)

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.

================================
"""
from __future__ import absolute_import

from builtins import range
from typing import Iterable, List

import numpy as np

def triangle_area(p1, p2, p3):
    """
    calculates the area of a triangle given its vertices
    """
    return abs(p1[0]*(p2[1]-p3[1])+p2[0]*(p3[1]-p1[1])+p3[0]*(p1[1]-p2[1]))/2.

def triangle_areas_from_array(arr):
    """
    take an (N,2) array of points and return an (N,1)
    array of the areas of those triangles, where the first
    and last areas are np.inf

see triangle_area for algorithm
    """

result = np.empty((len(arr),), arr.dtype)
    result[0] = np.inf
    result[-1] = np.inf

p1 = arr[:-2]
    p2 = arr[1:-1]
    p3 = arr[2:]

# an accumulators to avoid unnecessary intermediate arrays
    accr = result[1:-1]  # Accumulate directly into result
    acc1 = np.empty_like(accr)

np.subtract(p2[:, 1], p3[:, 1], out=accr)
    np.multiply(p1[:, 0], accr,    out=accr)
    np.subtract(p3[:, 1], p1[:, 1], out=acc1)
    np.multiply(p2[:, 0], acc1,    out=acc1)
    np.add(acc1, accr,            out=accr)
    np.subtract(p1[:, 1], p2[:, 1], out=acc1)
    np.multiply(p3[:, 0], acc1,    out=acc1)
    np.add(acc1, accr,            out=accr)
    np.abs(accr, out=accr)
    accr /= 2.
    # Notice: accr was writing into result, so the answer is in there
    return result

# the final value in thresholds is np.inf, which will never be
# the min value.  So, I am safe in "deleting" an index by
# just shifting the array over on top of it

def remove(s, i):
    """
    Quick trick to remove an item from a numpy array without
    creating a new object.  Rather than the array shape changing,
    the final value just gets repeated to fill the space.

~3.5x faster than numpy.delete
    """
    s[i:-1] = s[i+1:]

class VWSimplifier(object):

def __init__(self, pts: Iterable[List[float]]) -> None:
        """
        Initialize with points. takes some time to build
        the thresholds but then all threshold filtering later 
        is ultra fast
        """
        self.pts = np.array(pts, dtype=np.float32)
        self.thresholds = self.build_thresholds()
        self.ordered_thresholds = sorted(self.thresholds, reverse=True)

def build_thresholds(self):
        """
        compute the area value of each vertex, which one would
        use to mask an array of points for any threshold value.

returns a numpy.array (length of pts)  of the areas.
        """
        pts = self.pts
        nmax = len(pts)
        real_areas = triangle_areas_from_array(pts)
        real_indices = list(range(nmax))

# destructable copies
        # ARG! areas=real_areas[:] doesn't make a copy!
        areas = np.copy(real_areas)
        i = real_indices[:]

# pick first point and set up for loop
        min_vert = np.argmin(areas)
        this_area = areas[min_vert]
        #  areas and i are modified for each point finished
        remove(areas, min_vert)   # faster
        # areas = np.delete(areas, min_vert) # slower
        # noinspection PyTypeChecker
        i.pop(min_vert)

# cntr = 3
        while this_area < np.inf:
            # min_vert was removed from areas and i.  Now,
            # adjust the adjacent areas and remove the new
            # min_vert.

# Now that min_vert was filtered out, min_vert points
            # to the point after the deleted point.

skip = False  # modified area may be the next minvert

try:
                right_area = triangle_area(pts[i[min_vert-1]],
                                           pts[i[min_vert]], pts[i[min_vert+1]])
            except IndexError:
                # trying to update area of endpoint. Don't do it
                pass
            else:
                right_idx = i[min_vert]
                if right_area <= this_area:
                    # even if the point now has a smaller area,
                    # it ultimately is not more significant than
                    # the last point, which needs to be removed
                    # first to justify removing this point.
                    # Though this point is the next most significant
                    right_area = this_area

# min_vert refers to the point to the right of
                    # the previous min_vert, so we can leave it
                    # unchanged if it is still the min_vert
                    skip = min_vert

# update both collections of areas
                real_areas[right_idx] = right_area
                areas[min_vert] = right_area

if min_vert > 1:
                # cant try/except because 0-1=-1 is a valid index
                left_area = triangle_area(pts[i[min_vert-2]],
                                          pts[i[min_vert-1]], pts[i[min_vert]])
                if left_area <= this_area:
                    # same justification as above
                    left_area = this_area
                    skip = min_vert-1
                real_areas[i[min_vert-1]] = left_area
                areas[min_vert-1] = left_area

# only np.argmin if we have too.
            min_vert = skip or np.argmin(areas)
            i.pop(min_vert)
            this_area = areas[min_vert]
            # areas = np.delete(areas,min_vert) #slower
            remove(areas, min_vert)  # f aster
        return real_areas

def from_threshold(self, threshold) -> List[List[float]]:
        return (self.pts[self.thresholds >= threshold]).tolist()

def from_number(self, n) -> List[List[float]]:
        thresholds = self.ordered_thresholds
        try:
            threshold = thresholds[int(n)]
        except IndexError:
            result = self.pts
        else:
            result = self.pts[self.thresholds > threshold]
        return result.tolist()

def from_ratio(self, r) -> List[List[float]]:
        if r <= 0 or r > 1:
            raise ValueError("Ratio must be 0<r<=1")
        else:
            return self.from_number(r*len(self.thresholds))

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Code Editor : polysimplify.py