def make_map( filename ): def _sphere_to_cart( theta, phi ): return vector_3d( \ s.sin( theta ) * s.cos( phi ), \ s.cos( theta ), \ s.sin( theta ) * s.sin( phi ) ) def _draw_this_circle( c, Circle ): pass def _draw_latitude_circle( c, latitude ): pass def _draw_longitude_circle( c, longitude ): pass # set up our triangle c = get_letter_canvas( filename ) # hex grid c.setStrokeColor( (0.75, 0.75, 1) ) # c.setLineWidth( 0.001 ) # draw_hexes( c, 2 ) c.setLineWidth( 0.0005 ) draw_hexes( c, 10 ) c.setStrokeColor( (0.75,0.75,0.75) ) d20 = Icosahedron( numeric = True ) d20.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) ) d20.make_faces() mappings = face_mappings( d20 ) face_plane = d20.faces[0].plane rot_mat = mappings.face_dict['a'][0] for lat in range( 0, 40, 5 ): if lat % 5: c.setLineWidth( 0.0005 ) else: c.setLineWidth( 0.001 ) lat_rad = to_rad( lat ).evalf() try: point = line_plane_intersect( two_point_line( zero_3d, _sphere_to_cart( lat_rad, 0 ) ), face_plane ) mp1 = point.multiply( rot_mat ) point = line_plane_intersect( two_point_line( zero_3d, _sphere_to_cart( lat_rad, _pi/2 ) ), face_plane ) mp2 = point.multiply( rot_mat ) point = line_plane_intersect( two_point_line( zero_3d, _sphere_to_cart( lat_rad, -_pi/2 ) ), face_plane ) mp3 = point.multiply( rot_mat ) the_circle = three_point_circle( mp1[0], mp1[1], mp2[0], mp2[1], mp3[0], mp3[1] ) c.circle( the_circle.x0, the_circle.y0, the_circle.radius, fill=0, stroke=1 ) except: pass for lon in range( 0, 360, 5 ): if lon % 5: c.setLineWidth( 0.0005 ) else: c.setLineWidth( 0.001 ) try: point = line_plane_intersect( two_point_line( _sphere_to_cart( _pi/4, to_rad( lon).evalf() ), zero_3d ), face_plane ) mp1 = point.multiply( rot_mat ) end_pt = _pi/9 if (lon % 5) == 0: end_pt = _pi/18 if (lon % 10) == 0: end_pt = _pi/36 if (lon % 30) == 0: end_pt = 0 point = line_plane_intersect( two_point_line( _sphere_to_cart( end_pt, to_rad( lon).evalf() ), zero_3d ), face_plane ) mp2 = point.multiply( rot_mat ) c.line( mp1[0], mp1[1], mp2[0], mp2[1] ) except: pass c.showPage() c.save()
def make_map( filename ): def _sphere_to_cart( theta, phi ): return vector_3d( \ s.sin( theta ) * s.cos( phi ), \ s.cos( theta ), \ s.sin( theta ) * s.sin( phi ) ) def _draw_this_circle( c, Circle ): pass def _draw_latitude_circle( c, latitude ): pass def _draw_longitude_circle( c, longitude ): pass # set up our triangle c = get_letter_canvas( filename ) # hex grid c.setStrokeColor( (0.75, 0.75, 1) ) # c.setLineWidth( 0.001 ) # draw_hexes( c, 2 ) c.setLineWidth( 0.0005 ) draw_hexes( c, 10 ) c.setStrokeColor( (0.75,0.75,0.75) ) d20 = Icosahedron( numeric = True ) d20.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) ) d20.make_faces() mappings = face_mappings( d20 ) face_plane = d20.faces[16].plane rot_mat = mappings.face_dict['q'][0] bag_o_points = dict() for lat in range( 90, 171, 5 ): for lon in range( 210, 331, 5 ): point = line_plane_intersect( two_point_line( \ _sphere_to_cart( to_rad( lat ).evalf(), to_rad( lon ).evalf() ), zero_3d), face_plane, ray=True ) mp = point.multiply( rot_mat ) # c.circle( mp[0],mp[1],0.002,fill=1,stroke=0) bag_o_points[(lat,lon)] = mp for lat in range( 90, 169, 5 ): for lon in range( 210, 330, 5 ): p0 = bag_o_points[(lat, lon)] p1 = bag_o_points[(lat+5,lon)] p2 = bag_o_points[(lat,lon+5)] if lon % 5: c.setLineWidth( 0.0005 ) else: c.setLineWidth( 0.001 ) c.line( p0[0],p0[1],p1[0],p1[1] ) if lat % 5: c.setLineWidth( 0.0005 ) else: c.setLineWidth( 0.001 ) c.line( p0[0],p0[1],p2[0],p2[1] ) c.showPage() c.save()
def make_map( filename ): # = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = # helpers # = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = def _map_point( point ): line = two_point_line( point, zero_3d ) for hit in d20.face_hit( line ): # print hit[0] mapped_point = mappings.map_point( hit[0], hit[1] ) if mapped_point: new_x, new_y = mapped_point c.circle( sx(new_x), sy(new_y), 0.5, stroke=0, fill=1 ) def _sphere_to_cart( theta, phi ): return vector_3d( \ s.sin( theta ) * s.cos( phi ), \ s.cos( theta ), \ s.sin( theta ) * s.sin( phi ) ) def _arc_azimuth( start_az, end_az, inclin, step ): for azimuth in range( start_az, end_az, step ): _map_point( _sphere_to_cart( to_rad( inclin ).evalf(), to_rad(azimuth).evalf() )) def _arc_inclin( start_inc, end_inc, azimuth, step ): for inclin in range( start_inc, end_inc, step ): _map_point( _sphere_to_cart( to_rad( inclin ).evalf(), to_rad(azimuth).evalf() )) def _plot_skeleton(): th = (s.sqrt(3)/2).evalf() c.line( sx(0), sy(2 * th) , sx(0.5), sy(3 * th) ) c.line( sx(0.5), sy(th) , sx(1.5), sy(3 * th) ) c.line( sx(1), sy(0) , sx(2.5), sy(3 * th) ) c.line( sx(2), sy(0) , sx(3.5), sy(3 * th) ) c.line( sx(3), sy(0) , sx(4.5), sy(3 * th) ) c.line( sx(4), sy(0) , sx(5), sy(2 * th) ) c.line( sx(5), sy(0) , sx(5.5), sy(th) ) c.line( sx(0), sy( 2 * th ), sx(1), sy(0) ) c.line( sx(0.5), sy( 3 * th ), sx(2), sy(0) ) c.line( sx(1.5), sy( 3 * th ), sx(3), sy(0) ) c.line( sx(2.5), sy( 3 * th ), sx(4), sy(0) ) c.line( sx(3.5), sy( 3 * th ), sx(5), sy(0) ) c.line( sx(4.5), sy( 3 * th ), sx(5.5), sy( th ) ) c.line( sx(0), sy( 2 * th), sx( 5 ), sy( 2*th ) ) c.line( sx(0.5), sy(th), sx( 5.5 ), sy( th ) ) # = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = # main # = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = c = canvas.Canvas( filename, pagesize=( 17*72, 11*72 ) ) d20 = Icosahedron( numeric = True ) d20.rotate_vertices( rot_x( -s.atan2( s.GoldenRatio-1, s.GoldenRatio ).evalf() ) ) d20.make_faces() mappings = face_mappings( d20 ) inc_factor = (s.pi/180).evalf() az_factor = (s.pi/180).evalf() c.setFillColorRGB( .5,.5, 1 ) for azimuth in range( 0, 360, 5 ): _arc_inclin( 20, 161, azimuth, 1 ) for inclin in range( 20, 161, 5 ): _arc_azimuth( 0, 360, inclin, 1 ) c.setStrokeColorRGB( .5,.5, .5 ) _plot_skeleton() c.showPage() c.save()