Find the plane passing through the most of a set of 3D points

plane_and_points.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Dec 13 11:35:48 2022

@author: s.k.

LICENSE:

MIT License
Copyright (c) 2022-now() s.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
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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
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

Except as contained in this notice, the name of the copyright holders shall
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"""

import numpy as np
from shapely import wkt
from shapely.geometry import Polygon, MultiLineString

def find_plane2(points):
    #Find the coefficients (a,b,c,d) satisfying the plane equation:
    # ax + by + cz + d = 0 given a 3x3 array of row-wise points.
    
    # I need to to that otherwise the feeded numpy array get modified!!!:
    pts = points.copy() 
    p0 = points[2,:].copy()
    center = np.average(pts, axis=0, keepdims=True)
    pts -= center # reduce large coordinates
    u, v = pts[1:,:] - pts[0,:]
    n = np.cross(u, v)
    n_unit = n / np.linalg.norm(n)
    d = -1 * (p0 @ n_unit)

    return (np.append(n_unit, d), center)
    
def closest_distance_to_plane2(points,plane):
    if len(points.shape) == 1:
        points = points.reshape(1,len(points)) # reshape 1dim vectors to 2D

    nbpts, lp = points.shape
    # here we can work with homogeneous coordinates
    points = np.append(points, np.ones(nbpts).reshape(nbpts,1), axis=1)
    dists = points @ plane

    return dists

def project_points_on_plane2(points, plane, pt_on_plane):
    new_points = None
    if len(points.shape) == 1:
        points = points.reshape(1,len(points)) # reshape 1dim vectors to 2D

    nbpts, lp = points.shape
    n = plane[:-1]
    new_points = points - ((points - pt_on_plane) @ n) * n

    return new_points

def get_distances_to_planes2(points):
    lp = np.size(points,0)
    shift = 2
    p = np.append(points, points[:shift,:], axis=0)
    planes = []
    dists = np.zeros((lp, lp), dtype=np.double)
    for i in range(lp): # loop over planes
        include_idx = np.arange(i,i+3)
        mask = np.zeros(lp+shift, dtype=bool)
        mask[include_idx] = True
        plane, pt_on_plane = find_plane2(p[mask,:])
        planes.append(plane)
        mask2 = mask.copy()
        if i > 1:
            mask2[:shift] = mask2[-shift:]

        mask2 = mask2[:-shift]
        for j, pt in enumerate(p[:-shift]): # loop over remaning points
            if ~mask2[j]:
                dist = closest_distance_to_plane2(pt, plane)
                dists[i,j] = dist
    
    return dists
 
def clean_plane2(wkt_geom):
    k = 1
    dists = np.array([1])
    P = wkt.loads(wkt_geom)
    p = np.array(P.geoms[0].coords)
    if P.is_closed or (p[0] == p[-1]).all():
        # remove last point as it's a duplicate of the first
        p = p[:-1]

    lp = np.size(p,0)
    dists = get_distances_to_planes2(p)
    max_dists = np.max(np.abs(dists))
    print(f"max_dists init: {max_dists}")
    while max_dists != 0 and k <= 20:
        print(f"Iter {k}...")
        idx_max_sum = np.argwhere(dists == np.amax(dists))
        planes_max, pts_max = set(idx_max_sum[:,0]), set(idx_max_sum[:,1])
        # pick only the first plane for the moment:
        plane_idx = list(planes_max)[0]
        include_idx = np.arange(plane_idx, plane_idx+3)
        include_idx = include_idx%lp
        mask = np.zeros(lp, dtype=bool)
        mask[include_idx] = True
        plane, pt_on_plane = find_plane2(p[mask,:]) # TODO: verify for singularities...
        for pt_max in pts_max:
            p[pt_max] = project_points_on_plane2(p[pt_max], plane, pt_on_plane)
        
        dists = get_distances_to_planes2(p)
        max_dists = np.max(np.abs(dists))
        print(f"max_dists: {max_dists}")
        k += 1 if max_dists != 0 else 21

    new_geom = Polygon(p)

    return new_geom.wkt


wkt_geom1 = '''MULTILINESTRING Z ((
    2481328.563000001 1108008.2252000012 58.66020000015851,
    2481328.563000001 1108008.2252000012 62.312500000349246,
    2481331.731899999 1108001.7289999984 62.312500000349246,
    2481331.731899999 1108001.7289999984 20.79300000029616,
    2481328.083999999 1108009.2069999985 20.79300000029616,
    2481328.083999999 1108009.2069999985 58.66020000015851,
    2481328.563000001 1108008.2252000012 58.66020000015851
))'''
    
wkt_geom2 = '''MULTILINESTRING Z ((
    481328.563000001 108008.2252000012 58.66020000015851,
    481328.563000001 108008.2252000012 62.312500000349246,
    481331.731899999 108001.7289999984 62.312500000349246,
    481331.731899999 108001.7289999984 20.79300000029616,
    481328.083999999 108009.2069999985 20.79300000029616,
    481328.083999999 108009.2069999985 58.66020000015851,
    481328.563000001 108008.2252000012 58.66020000015851
))'''

new_geom1 = clean_plane2(wkt_geom1)
new_geom2 = clean_plane2(wkt_geom2)

print(f"new_geom1: {new_geom1}")
print(f"new_geom2: {new_geom2}")