feat: first experimental version

map.py

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+
+from math import *
+import numpy as np
+import sys
+import json
+
+
+EPS = sys.float_info.epsilon
+
+
+class Triangle:
+
+    def __init__(self, v1, v2, v3):
+        # Vertices
+        self.v1 = v1
+        self.v2 = v2
+        self.v3 = v3
+        # Edges of the origin vertex and their L2 norms
+        self.e1 = v2 - v1
+        self.e2 = v3 - v1
+        self.e1n = np.linalg.norm(self.e1)
+        self.e2n = np.linalg.norm(self.e2)
+        # Normal vector of the triangle's plane
+        self.n = np.cross(self.e1 / self.e1n, self.e2 / self.e2n)
+        # The vertex coordinates in plane coordinates
+        self.v1p = self.plane_coords(self.v1)
+        self.v2p = self.plane_coords(self.v2)
+        self.v3p = self.plane_coords(self.v3)
+
+    def intersect(self, ray):
+        # 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
+        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 t <= EPS:
+            return None
+        return ray * t
+
+    def plane_coords(self, v):
+        u = np.dot(self.e1, v - self.v1) / self.e1n
+        n = np.cross(self.n, self.e1 / self.e1n)
+        v = np.dot(n, v-self.v2)
+        return np.array([u, v])
+
+
+def convert_to_cartesian(lon, lat):
+    x = cos(lon*pi/180)
+    y = sin(lon*pi/180)
+    z = tan(lat*pi/180)
+    mag = sqrt(x**2 + y**2 + z**2)
+    return np.array([x/mag, y/mag, z/mag])
+
+
+def map_poly(tri, poly):
+    p0 = convert_to_cartesian(*poly[0])
+    p0i = tri.intersect(p0)
+    mapped = []
+    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:
+            mapped.append((tri.plane_coords(p0i), tri.plane_coords(p1i)))
+        p0 = p1
+        p0i = p1i
+    return mapped
+
+
+if __name__ == '__main__':
+    t = Triangle(np.array([5,0,0]), np.array([0,5,0]), np.array([0,0,5]))
+    countries = {}
+    with open('/tmp/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'][0]:
+                    countries[cc].extend(map_poly(t, poly))
+            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 a, b in l:
+            print(f'<path fill="none" stroke="red" stroke-width="0.01" d="M {a[0]} {a[1]} L {b[0]} {b[1]}" />')
+    print('</svg>')