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feat: tessellation of multiple multi-triangle faces

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This commit is contained in:
s3lph 2024-12-17 03:22:16 +01:00
parent c51dcd6514
commit 4f0d3ce83d
Signed by: s3lph
GPG key ID: 0AA29A52FB33CFB5
1 changed files with 76 additions and 38 deletions
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114
map.py
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@ -4,6 +4,8 @@ import numpy as np
import sys
import json
from tqdm import tqdm, trange
EPS = sys.float_info.epsilon
@ -32,23 +34,30 @@ class Triangle:
self.v3p = self.plane_coords(self.v3)
def intersect(self, ray):
'''
:param ray: numpy.array(3) Ray cast from [0, 0, 0]
:return: A tuple of [bool, Optional[numpy.array(3)]]:
The first component is True if the ray intersects the triangle, False otherwise.
The second component marks the intersection of the triangle's plane (even if outside the triangle), or
None if the ray does not intersect the plane at all.
'''
# https://en.wikipedia.org/wiki/Möller–Trumbore_intersection_algorithm
ray_cross_e2 = np.cross(ray, self.e2)
dot = np.dot(self.e1, ray_cross_e2)
if abs(dot) < EPS:
return None
return False, None
s = -self.v1
u = np.dot(s, ray_cross_e2) / dot
if (u < 0 and abs(u) > EPS) or (u > 1 and abs(u - 1) > EPS):
return None
s_cross_e1 = np.cross(s, self.e1)
v = np.dot(ray, s_cross_e1) / dot
if (v < 0 and abs(v) > EPS) or (u + v > 1 and abs(u + v - 1) > EPS):
return None
t = np.dot(self.e2, s_cross_e1) / dot
if (u < 0 and abs(u) > EPS) or (u > 1 and abs(u - 1) > EPS):
return False, ray * t
if (v < 0 and abs(v) > EPS) or (u + v > 1 and abs(u + v - 1) > EPS):
return False, ray * t
if t <= EPS:
return None
return ray * t
return False, None
return True, ray * t
def plane_coords(self, v):
u = np.dot(self.e1 / self.e1n, v - self.v1)
@ -57,6 +66,16 @@ class Triangle:
return np.array([u, v])
class Face:
def __init__(self, vs):
self.vertices = vs
self.tris = []
for i in range(1, len(vs)-1):
self.tris.append(Triangle(vs[0], vs[i], vs[i+1]))
self.plane_coords = [self.tris[0].plane_coords(v) for v in self.vertices]
def convert_to_cartesian(lon, lat):
x = cos(lon*pi/180)
y = sin(lon*pi/180)
@ -65,52 +84,71 @@ def convert_to_cartesian(lon, lat):
return np.array([x/mag, y/mag, z/mag])
def map_poly(tri, poly):
def map_poly(tri, poly, ref=None):
if ref is None:
ref = tri
p0 = convert_to_cartesian(*poly[0])
p0i = tri.intersect(p0)
p0b, p0i = tri.intersect(p0)
mapped = []
new = True
for i in range(1, len(poly)):
p1 = convert_to_cartesian(*poly[i])
p1i = tri.intersect(p1)
if p0i is not None and p1i is not None:
p1b, p1i = tri.intersect(p1)
if p0b or p1b and p0i is not None and p1i is not None:
if new:
mapped.append([tri.plane_coords(p0i), tri.plane_coords(p1i)])
mapped.append([ref.plane_coords(p0i), ref.plane_coords(p1i)])
new = False
else:
mapped[-1].append(tri.plane_coords(p1i))
mapped[-1].append(ref.plane_coords(p1i))
else:
new = True
p0 = p1
p0i = p1i
p0b = p1b
return mapped
if __name__ == '__main__':
t = Triangle(np.array([5,0,0]), np.array([0,5,0]), np.array([0,0,5]))
countries = {}
fs = [Face([a, b, c, d]) for a, b, c, d in [
(np.array([1,1,1]), np.array([-1,1,1]), np.array([-1,-1,1]), np.array([1,-1,1])), # top
(np.array([1,1,-1]), np.array([-1,1,-1]), np.array([-1,-1,-1]), np.array([1,-1,-1])), # bottom
(np.array([-1,-1,-1]), np.array([-1,1,-1]), np.array([-1,1,1]), np.array([-1,-1,1])), # left
(np.array([1,-1,-1]), np.array([1,1,-1]), np.array([1,1,1]), np.array([1,-1,1])), # right
(np.array([-1,-1,-1]), np.array([1,-1,-1]), np.array([1,-1,1]), np.array([-1,-1,1])), # front
(np.array([-1,1,-1]), np.array([1,1,-1]), np.array([1,1,1]), np.array([-1,1,1])), # back
]]
with open('countries.geojson', 'r') as f:
j = json.load(f)
for f in j['features']:
cc = f['properties']['ADMIN']
if f['geometry']['type'] == 'MultiPolygon':
countries[cc] = []
for poly in f['geometry']['coordinates']:
countries[cc].extend(map_poly(t, poly[0]))
elif f['geometry']['type'] == 'Polygon':
countries[cc] = map_poly(tri, f['geometry']['coordinates'][0])
minx = min(t.v1p[0], t.v2p[0], t.v3p[0])
miny = min(t.v1p[1], t.v2p[1], t.v3p[1])
maxx = max(t.v1p[0], t.v2p[0], t.v3p[0])
maxy = max(t.v1p[1], t.v2p[1], t.v3p[1])
w = maxx - minx
h = maxy - miny
print(f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="{minx} {miny} {w} {h}" width="{w}" height="{h}">')
print(f'<path fill="none" stroke="black" stroke-width="0.01" d="M {t.v1p[0]} {t.v1p[1]} L {t.v2p[0]} {t.v2p[1]} L {t.v3p[0]} {t.v3p[1]} Z" />')
for c, l in countries.items():
for ls in l:
print(f'<path fill="none" stroke="red" stroke-width="0.01" d="M {ls[0][0]} {ls[0][1]}', end='')
for x, y in ls[1:]:
print(f' L {x} {y}', end='')
print('" />')
print('</svg>')
for i, face in tqdm(list(enumerate(fs)), desc='Faces '):
countries = {}
for t in face.tris:
for f in tqdm(j['features'], desc='Features', total=len(face.tris)*len(j['features'])):
cc = f['properties']['ADMIN']
if f['geometry']['type'] == 'MultiPolygon':
for poly in f['geometry']['coordinates']:
countries.setdefault(cc, []).extend(map_poly(t, poly[0], face.tris[0]))
elif f['geometry']['type'] == 'Polygon':
countries.setdefault(cc, []).extend(map_poly(t, f['geometry']['coordinates'][0], face.tris[0]))
minx = min(v[0] for v in face.plane_coords)
miny = min(v[1] for v in face.plane_coords)
maxx = max(v[0] for v in face.plane_coords)
maxy = max(v[1] for v in face.plane_coords)
w = maxx - minx
h = maxy - miny
with open(f'face{i}.svg', 'w') as svg:
svg.write(f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="{minx} {miny} {w} {h}" width="{w}" height="{h}" id="face{i}">\n')
svg.write(f' <g id="cut">\n <path id="outline" fill="none" stroke="black" stroke-width="0.01" d="M {face.plane_coords[0][0]} {face.plane_coords[0][1]}')
for v in face.plane_coords[1:]:
svg.write(f' L {v[0]} {v[1]}')
svg.write(' Z" />\n </g>\n <g id="engrave">\n')
for c, l in countries.items():
if l:
svg.write(f' <g id="{c}">\n')
for ls in l:
svg.write(f' <path fill="none" stroke="red" stroke-width="0.01" d="M {ls[0][0]} {ls[0][1]}')
for x, y in ls[1:]:
svg.write(f' L {x} {y}')
svg.write('" />\n')
svg.write(' </g>\n')
svg.write(' </g>\n</svg>\n')