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feat: tessellation of multiple multi-triangle faces

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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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96
map.py
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@ -4,6 +4,8 @@ import numpy as np
import sys import sys
import json import json
from tqdm import tqdm, trange
EPS = sys.float_info.epsilon EPS = sys.float_info.epsilon
@ -32,23 +34,30 @@ class Triangle:
self.v3p = self.plane_coords(self.v3) self.v3p = self.plane_coords(self.v3)
def intersect(self, ray): 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 # https://en.wikipedia.org/wiki/Möller–Trumbore_intersection_algorithm
ray_cross_e2 = np.cross(ray, self.e2) ray_cross_e2 = np.cross(ray, self.e2)
dot = np.dot(self.e1, ray_cross_e2) dot = np.dot(self.e1, ray_cross_e2)
if abs(dot) < EPS: if abs(dot) < EPS:
return None return False, None
s = -self.v1 s = -self.v1
u = np.dot(s, ray_cross_e2) / dot 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) s_cross_e1 = np.cross(s, self.e1)
v = np.dot(ray, s_cross_e1) / dot 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 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: if t <= EPS:
return None return False, None
return ray * t return True, ray * t
def plane_coords(self, v): def plane_coords(self, v):
u = np.dot(self.e1 / self.e1n, v - self.v1) u = np.dot(self.e1 / self.e1n, v - self.v1)
@ -57,6 +66,16 @@ class Triangle:
return np.array([u, v]) 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): def convert_to_cartesian(lon, lat):
x = cos(lon*pi/180) x = cos(lon*pi/180)
y = sin(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]) 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]) p0 = convert_to_cartesian(*poly[0])
p0i = tri.intersect(p0) p0b, p0i = tri.intersect(p0)
mapped = [] mapped = []
new = True new = True
for i in range(1, len(poly)): for i in range(1, len(poly)):
p1 = convert_to_cartesian(*poly[i]) p1 = convert_to_cartesian(*poly[i])
p1i = tri.intersect(p1) p1b, p1i = tri.intersect(p1)
if p0i is not None and p1i is not None: if p0b or p1b and p0i is not None and p1i is not None:
if new: if new:
mapped.append([tri.plane_coords(p0i), tri.plane_coords(p1i)]) mapped.append([ref.plane_coords(p0i), ref.plane_coords(p1i)])
new = False new = False
else: else:
mapped[-1].append(tri.plane_coords(p1i)) mapped[-1].append(ref.plane_coords(p1i))
else: else:
new = True new = True
p0 = p1 p0 = p1
p0i = p1i p0i = p1i
p0b = p1b
return mapped return mapped
if __name__ == '__main__': if __name__ == '__main__':
t = Triangle(np.array([5,0,0]), np.array([0,5,0]), np.array([0,0,5])) fs = [Face([a, b, c, d]) for a, b, c, d in [
countries = {} (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: with open('countries.geojson', 'r') as f:
j = json.load(f) j = json.load(f)
for f in j['features']:
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'] cc = f['properties']['ADMIN']
if f['geometry']['type'] == 'MultiPolygon': if f['geometry']['type'] == 'MultiPolygon':
countries[cc] = []
for poly in f['geometry']['coordinates']: for poly in f['geometry']['coordinates']:
countries[cc].extend(map_poly(t, poly[0])) countries.setdefault(cc, []).extend(map_poly(t, poly[0], face.tris[0]))
elif f['geometry']['type'] == 'Polygon': elif f['geometry']['type'] == 'Polygon':
countries[cc] = map_poly(tri, f['geometry']['coordinates'][0]) countries.setdefault(cc, []).extend(map_poly(t, f['geometry']['coordinates'][0], face.tris[0]))
minx = min(t.v1p[0], t.v2p[0], t.v3p[0]) minx = min(v[0] for v in face.plane_coords)
miny = min(t.v1p[1], t.v2p[1], t.v3p[1]) miny = min(v[1] for v in face.plane_coords)
maxx = max(t.v1p[0], t.v2p[0], t.v3p[0]) maxx = max(v[0] for v in face.plane_coords)
maxy = max(t.v1p[1], t.v2p[1], t.v3p[1]) maxy = max(v[1] for v in face.plane_coords)
w = maxx - minx w = maxx - minx
h = maxy - miny h = maxy - miny
print(f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="{minx} {miny} {w} {h}" width="{w}" height="{h}">') with open(f'face{i}.svg', 'w') as svg:
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" />') 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(): for c, l in countries.items():
if l:
svg.write(f' <g id="{c}">\n')
for ls in l: for ls in l:
print(f'<path fill="none" stroke="red" stroke-width="0.01" d="M {ls[0][0]} {ls[0][1]}', end='') 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:]: for x, y in ls[1:]:
print(f' L {x} {y}', end='') svg.write(f' L {x} {y}')
print('" />') svg.write('" />\n')
print('</svg>') svg.write(' </g>\n')
svg.write(' </g>\n</svg>\n')