######################################################## # routines to set up, transform and manage weather tiles # Thorsten Renk, July 2010 ######################################################## # function purpose # # tile_management_loop to decide if a tile is created, removed or considered current # generate_tile to decide on orientation and type and set up all information for tile creation # remove_tile to delete a tile by index # change_active_tile to change the tile the aircraft is currently in and to generate neighbour info # copy_entry to copy tile information from one node to another # create_neighbour to set up information for a new neighbouring tile # create_neighbours to initialize the 8 neighbours of the initial tile # calc_geo to get local Cartesian geometry for latitude conversion # get_lat to get latitude from Cartesian coordinates # get_lon to get longitude from Cartesian coordinates ################################### # tile management loop ################################### var tile_management_loop = func { var tNode = props.globals.getNode(lw~"tiles", 1).getChildren("tile"); var viewpos = geo.aircraft_position(); # using viewpos here triggers massive tile ops for tower view... var code = getprop(lw~"tiles/tile[4]/code"); var i = 0; var d_min = 100000.0; var i_min = 0; var distance_to_load = getprop(lw~"config/distance-to-load-tile-m"); var distance_to_remove = getprop(lw~"config/distance-to-remove-tile-m"); var current_heading = getprop("orientation/heading-deg"); var loading_flag = getprop(lw~"tmp/asymmetric-tile-loading-flag"); var this_frame_generated_flag = 0; # use this flag to avoid overlapping tile generation calls foreach (var t; tNode) { var tpos = geo.Coord.new(); tpos.set_latlon(t.getNode("latitude-deg").getValue(),t.getNode("longitude-deg").getValue(),0.0); var d = viewpos.distance_to(tpos); if (d < d_min) {d_min = d; i_min = i;} var flag = t.getNode("generated-flag").getValue(); var dir = viewpos.course_to(tpos); var d_load = distance_to_load; var d_remove = distance_to_remove; if (loading_flag == 1) { if ((abs(dir-current_heading) > 135.0) and (abs(dir-current_heading) < 225.0)) { d_load = 0.7 * d_load; d_remove = 0.7 * d_remove; } } # the tile needs to be generated, unless it already has been # and if no other tile has been generated in this loop cycle # and the thread and convective system are idle # (we want to avoid overlapping tile generation) if ((d < distance_to_load) and (flag==0) and (this_frame_generated_flag == 0) and (getprop(lw~"tmp/thread-status") == "idle") and (getprop(lw~"tmp/convective-status") == "idle")) { setprop(lw~"tiles/tile-counter",getprop(lw~"tiles/tile-counter")+1); print("Building tile unique index ",getprop(lw~"tiles/tile-counter"), " in direction ",i); generate_tile(code, tpos.lat(), tpos.lon(),i); if (getprop(lw~"config/dynamics-flag") == 1) { var quadtree = []; weather_dynamics.generate_quadtree_structure(0, quadtree); append(weather_dynamics.cloudQuadtrees,quadtree); } t.getNode("generated-flag").setValue(1); t.getNode("timestamp-sec").setValue(weather_dynamics.time_lw); t.getNode("tile-index",1).setValue(getprop(lw~"tiles/tile-counter")); this_frame_generated_flag = 1; } if ((d > distance_to_remove) and (flag==1)) # the tile needs to be deleted if it exists { print("Removing tile, unique index ", t.getNode("tile-index").getValue()); remove_tile(t.getNode("tile-index").getValue()); t.getNode("generated-flag").setValue(0); } i = i + 1; } # end foreach #print("Minimum distance to: ",i_min); if (i_min != 4) # we've entered a different tile { print("Changing active tile to direction ", i_min); change_active_tile(i_min); } if (getprop(lw~"tile-loop-flag") ==1) {settimer(tile_management_loop, 5.0);} } ################################### # tile generation call ################################### var generate_tile = func (code, lat, lon, dir_index) { # make sure the last tile call has finished, otherwise put on hold #if ((getprop(lw~"tmp/thread-status") != "idle") or (getprop(lw~"tmp/convective-status") != "idle")) # { # print("Tile generation overlap, delaying..."); # settimer( func {generate_tile(code, lat, lon, dir_index);}, 1); # } setprop(lw~"tiles/tmp/latitude-deg", lat); setprop(lw~"tiles/tmp/longitude-deg",lon); setprop(lw~"tiles/tmp/code",code); # do windspeed and orientation before presampling check, but test not to do it again if (((getprop(lw~"tmp/presampling-flag") == 1) and (getprop(lw~"tmp/presampling-status") == "idle")) or (getprop(lw~"tmp/presampling-flag") == 0)) { var alpha = getprop(lw~"tmp/tile-orientation-deg"); if ((local_weather.wind_model_flag == 2) or (local_weather.wind_model_flag ==4)) { alpha = alpha + 2.0 * (rand()-0.5) * 10.0; # account for the systematic spin of weather systems around a low pressure # core dependent on hemisphere if (lat >0.0) {alpha = alpha -3.0;} else {alpha = alpha +3.0;} setprop(lw~"tmp/tile-orientation-deg",alpha); # compute the new windspeed var windspeed = getprop(lw~"tmp/windspeed-kt"); windspeed = windspeed + 2.0 * (rand()-0.5) * 2.0; if (windspeed < 0) {windspeed = rand();} setprop(lw~"tmp/windspeed-kt"); # store the tile orientation and wind strength in an array for fast processing append(weather_dynamics.tile_wind_direction, alpha); append(weather_dynamics.tile_wind_speed, windspeed); } else if (local_weather.wind_model_flag ==5) # alpha and windspeed are calculated { var res = local_weather.wind_interpolation(lat,lon,0.0); alpha = res[0]; setprop(lw~"tmp/tile-orientation-deg",alpha); var windspeed = res[1]; setprop(lw~"tmp/windspeed-kt",windspeed); append(weather_dynamics.tile_wind_direction,res[0]); append(weather_dynamics.tile_wind_speed,res[1]); } props.globals.getNode(lw~"tiles").getChild("tile",dir_index).getNode("orientation-deg").setValue(alpha); } # now see if we need to presample the terrain if ((getprop(lw~"tmp/presampling-flag") == 1) and (getprop(lw~"tmp/presampling-status") == "idle")) { local_weather.terrain_presampling_start(lat, lon, 1000, 40000, getprop(lw~"tmp/tile-orientation-deg")); setprop(lw~"tiles/tmp/dir-index",dir_index); return; } print("Current tile type: ", code); if (getprop(lw~"tmp/tile-management") == "repeat tile") { if (code == "altocumulus_sky"){weather_tiles.set_altocumulus_tile();} else if (code == "broken_layers") {weather_tiles.set_broken_layers_tile();} else if (code == "stratus") {weather_tiles.set_overcast_stratus_tile();} else if (code == "cumulus_sky") {weather_tiles.set_fair_weather_tile();} else if (code == "gliders_sky") {weather_tiles.set_gliders_sky_tile();} else if (code == "blue_thermals") {weather_tiles.set_blue_thermals_tile();} else if (code == "summer_rain") {weather_tiles.set_summer_rain_tile();} else if (code == "high_pressure_core") {weather_tiles.set_high_pressure_core_tile();} else if (code == "high_pressure") {weather_tiles.set_high_pressure_tile();} else if (code == "high_pressure_border") {weather_tiles.set_high_pressure_border_tile();} else if (code == "low_pressure_border") {weather_tiles.set_low_pressure_border_tile();} else if (code == "low_pressure") {weather_tiles.set_low_pressure_tile();} else if (code == "low_pressure_core") {weather_tiles.set_low_pressure_core_tile();} else if (code == "cold_sector") {weather_tiles.set_cold_sector_tile();} else if (code == "warm_sector") {weather_tiles.set_warm_sector_tile();} else if (code == "tropical_weather") {weather_tiles.set_tropical_weather_tile();} else {print("Repeat tile not implemented with this tile type!");} } else if (getprop(lw~"tmp/tile-management") == "realistic weather") { var rn = rand(); if (code == "low_pressure_core") { if (rn > 0.2) {weather_tiles.set_low_pressure_core_tile();} else {weather_tiles.set_low_pressure_tile();} } else if (code == "low_pressure") { if (rn > 0.2) {weather_tiles.set_low_pressure_tile();} else if (rn > 0.1) {weather_tiles.set_low_pressure_core_tile();} else {weather_tiles.set_low_pressure_border_tile();} } else if (code == "low_pressure_border") { if (rn > 0.4) {weather_tiles.set_low_pressure_border_tile();} else if (rn > 0.3) {weather_tiles.set_cold_sector_tile();} else if (rn > 0.2) {weather_tiles.set_warm_sector_tile();} else if (rn > 0.1) {weather_tiles.set_low_pressure_tile();} else {weather_tiles.set_high_pressure_border_tile();} } else if (code == "high_pressure_border") { if (rn > 0.4) {weather_tiles.set_high_pressure_border_tile();} else if (rn > 0.3) {weather_tiles.set_cold_sector_tile();} else if (rn > 0.2) {weather_tiles.set_warm_sector_tile();} else if (rn > 0.1) {weather_tiles.set_high_pressure_tile();} else {weather_tiles.set_low_pressure_border_tile();} } else if (code == "high_pressure") { if (rn > 0.2) {weather_tiles.set_high_pressure_tile();} else if (rn > 0.1) {weather_tiles.set_high_pressure_border_tile();} else {weather_tiles.set_high_pressure_core_tile();} } else if (code == "high_pressure_core") { if (rn > 0.2) {weather_tiles.set_high_pressure_core_tile();} else {weather_tiles.set_high_pressure_tile();} } else if (code == "cold_sector") { if (rn > 0.3) {weather_tiles.set_cold_sector_tile();} else if (rn > 0.2) { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_warmfront1_tile();} else if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_cold_sector_tile();} else if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_coldfront_tile();} } else if (rn > 0.1) {weather_tiles.set_low_pressure_border_tile();} else {weather_tiles.set_high_pressure_border_tile();} } else if (code == "warm_sector") { if (rn > 0.3) {weather_tiles.set_warm_sector_tile();} else if (rn > 0.2) { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_coldfront_tile();} else if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_warm_sector_tile();} else if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_warmfront4_tile();} } else if (rn > 0.1) {weather_tiles.set_low_pressure_border_tile();} else {weather_tiles.set_high_pressure_border_tile();} } else if (code == "warmfront1") { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_warmfront2_tile();} else if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_warmfront1_tile();} else if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_cold_sector_tile();} } else if (code == "warmfront2") { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_warmfront3_tile();} if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_warmfront2_tile();} if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_warmfront1_tile();} } else if (code == "warmfront3") { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_warmfront4_tile();} if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_warmfront3_tile();} if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_warmfront2_tile();} } else if (code == "warmfront4") { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_warm_sector_tile();} if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_warmfront4_tile();} if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_warmfront3_tile();} } else if (code == "coldfront") { if ((dir_index ==0) or (dir_index ==1) or (dir_index==2)) {weather_tiles.set_cold_sector_tile();} else if ((dir_index ==3) or (dir_index ==5)) {weather_tiles.set_coldfront_tile();} else if ((dir_index ==6) or (dir_index ==7) or (dir_index==8)) {weather_tiles.set_warm_sector_tile();} } else { print("Realistic weather not implemented with this tile type!"); } } # end if mode == realistic weather } ################################### # tile removal call ################################### var remove_tile = func (index) { compat_layer.remove_clouds(index); var effectNode = props.globals.getNode("local-weather/effect-volumes").getChildren("effect-volume"); var ecount = 0; foreach (var e; effectNode) { if (e.getNode("tile-index").getValue() == index) { e.remove(); ecount = ecount + 1; } } setprop(lw~"effect-volumes/number",getprop(lw~"effect-volumes/number")- ecount); # set placement indices to zero to reinitiate search for free positions setprop(lw~"clouds/placement-index",0); setprop(lw~"clouds/model-placement-index",0); setprop(lw~"effect-volumes/effect-placement-index",0); # remove quadtree structures if (getprop(lw~"config/dynamics-flag") ==1) { setsize(weather_dynamics.cloudQuadtrees[index-1],0); } # rebuild effect volume vector local_weather.assemble_effect_array(); } ################################### # active tile change and neighbour # recomputation ################################### var change_active_tile = func (index) { var t = props.globals.getNode(lw~"tiles").getChild("tile",index,0); var lat = t.getNode("latitude-deg").getValue(); var lon = t.getNode("longitude-deg").getValue(); var alpha = getprop(lw~"tmp/tile-orientation-deg"); if (index == 0) { copy_entry(4,8); copy_entry(3,7); copy_entry(1,5); copy_entry(0,4); create_neighbour(lat,lon,0,alpha); create_neighbour(lat,lon,1,alpha); create_neighbour(lat,lon,2,alpha); create_neighbour(lat,lon,3,alpha); create_neighbour(lat,lon,6,alpha); } else if (index == 1) { copy_entry(3,6); copy_entry(4,7); copy_entry(5,8); copy_entry(0,3); copy_entry(1,4); copy_entry(2,5); create_neighbour(lat,lon,0,alpha); create_neighbour(lat,lon,1,alpha); create_neighbour(lat,lon,2,alpha); } else if (index == 2) { copy_entry(4,6); copy_entry(1,3); copy_entry(2,4); copy_entry(5,7); create_neighbour(lat,lon,0,alpha); create_neighbour(lat,lon,1,alpha); create_neighbour(lat,lon,2,alpha); create_neighbour(lat,lon,5,alpha); create_neighbour(lat,lon,8,alpha); } else if (index == 3) { copy_entry(1,2); copy_entry(4,5); copy_entry(7,8); copy_entry(0,1); copy_entry(3,4); copy_entry(6,7); create_neighbour(lat,lon,0,alpha); create_neighbour(lat,lon,3,alpha); create_neighbour(lat,lon,6,alpha); } else if (index == 5) { copy_entry(1,0); copy_entry(4,3); copy_entry(7,6); copy_entry(2,1); copy_entry(5,4); copy_entry(8,7); create_neighbour(lat,lon,2,alpha); create_neighbour(lat,lon,5,alpha); create_neighbour(lat,lon,8,alpha); } else if (index == 6) { copy_entry(4,2); copy_entry(3,1); copy_entry(6,4); copy_entry(7,5); create_neighbour(lat,lon,0,alpha); create_neighbour(lat,lon,3,alpha); create_neighbour(lat,lon,6,alpha); create_neighbour(lat,lon,7,alpha); create_neighbour(lat,lon,8,alpha); } else if (index == 7) { copy_entry(3,0); copy_entry(4,1); copy_entry(5,2); copy_entry(6,3); copy_entry(7,4); copy_entry(8,5); create_neighbour(lat,lon,6,alpha); create_neighbour(lat,lon,7,alpha); create_neighbour(lat,lon,8,alpha); } else if (index == 8) { copy_entry(4,0); copy_entry(7,3); copy_entry(8,4); copy_entry(5,1); create_neighbour(lat,lon,2,alpha); create_neighbour(lat,lon,5,alpha); create_neighbour(lat,lon,6,alpha); create_neighbour(lat,lon,7,alpha); create_neighbour(lat,lon,8,alpha); } } ##################################### # copy tile info in neighbour matrix ##################################### var copy_entry = func (from_index, to_index) { var tNode = props.globals.getNode(lw~"tiles"); var f = tNode.getChild("tile",from_index,0); var t = tNode.getChild("tile",to_index,0); t.getNode("latitude-deg").setValue(f.getNode("latitude-deg").getValue()); t.getNode("longitude-deg").setValue(f.getNode("longitude-deg").getValue()); t.getNode("generated-flag").setValue(f.getNode("generated-flag").getValue()); t.getNode("tile-index").setValue(f.getNode("tile-index").getValue()); t.getNode("code").setValue(f.getNode("code").getValue()); t.getNode("timestamp-sec").setValue(f.getNode("timestamp-sec").getValue()); t.getNode("orientation-deg").setValue(f.getNode("orientation-deg").getValue()); } ##################################### # create adjacent tile coordinates ##################################### var create_neighbour = func (blat, blon, index, alpha) { var x = 0.0; var y = 0.0; var phi = alpha * math.pi/180.0; calc_geo(blat); if ((index == 0) or (index == 3) or (index == 6)) {x =-40000.0;} if ((index == 2) or (index == 5) or (index == 8)) {x = 40000.0;} if ((index == 0) or (index == 1) or (index == 2)) {y = 40000.0;} if ((index == 6) or (index == 7) or (index == 8)) {y = -40000.0;} var t = props.globals.getNode(lw~"tiles").getChild("tile",index,0); t.getNode("latitude-deg",1).setValue(blat + get_lat(x,y,phi)); t.getNode("longitude-deg",1).setValue(blon + get_lon(x,y,phi)); t.getNode("generated-flag",1).setValue(0); t.getNode("tile-index",1).setValue(-1); t.getNode("code",1).setValue(""); t.getNode("timestamp-sec",1).setValue(weather_dynamics.time_lw); t.getNode("orientation-deg",1).setValue(0.0); } ##################################### # find the 8 adjacent tile coordinates # after the initial setup call ##################################### var create_neighbours = func (blat, blon, alpha) { var x = 0.0; var y = 0.0; var phi = alpha * math.pi/180.0; calc_geo(blat); x = -40000.0; y = 40000.0; setprop(lw~"tiles/tile[0]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[0]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[0]/generated-flag",0); setprop(lw~"tiles/tile[0]/tile-index",-1); setprop(lw~"tiles/tile[0]/code",""); setprop(lw~"tiles/tile[0]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[0]/orientation-deg",0.0); x = 0.0; y = 40000.0; setprop(lw~"tiles/tile[1]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[1]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[1]/generated-flag",0); setprop(lw~"tiles/tile[1]/tile-index",-1); setprop(lw~"tiles/tile[1]/code",""); setprop(lw~"tiles/tile[1]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[1]/orientation-deg",0.0); x = 40000.0; y = 40000.0; setprop(lw~"tiles/tile[2]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[2]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[2]/generated-flag",0); setprop(lw~"tiles/tile[2]/tile-index",-1); setprop(lw~"tiles/tile[2]/code",""); setprop(lw~"tiles/tile[2]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[2]/orientation-deg",0.0); x = -40000.0; y = 0.0; setprop(lw~"tiles/tile[3]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[3]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[3]/generated-flag",0); setprop(lw~"tiles/tile[3]/tile-index",-1); setprop(lw~"tiles/tile[3]/code",""); setprop(lw~"tiles/tile[3]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[3]/orientation-deg",0.0); # this is the current tile x = 0.0; y = 0.0; setprop(lw~"tiles/tile[4]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[4]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[4]/generated-flag",1); setprop(lw~"tiles/tile[4]/tile-index",1); setprop(lw~"tiles/tile[4]/code",""); setprop(lw~"tiles/tile[4]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[4]/orientation-deg",getprop(lw~"tmp/tile-orientation-deg")); x = 40000.0; y = 0.0; setprop(lw~"tiles/tile[5]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[5]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[5]/generated-flag",0); setprop(lw~"tiles/tile[5]/tile-index",-1); setprop(lw~"tiles/tile[5]/code",""); setprop(lw~"tiles/tile[5]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[5]/orientation-deg",0.0); x = -40000.0; y = -40000.0; setprop(lw~"tiles/tile[6]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[6]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[6]/generated-flag",0); setprop(lw~"tiles/tile[6]/tile-index",-1); setprop(lw~"tiles/tile[6]/code",""); setprop(lw~"tiles/tile[6]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[6]/orientation-deg",0.0); x = 0.0; y = -40000.0; setprop(lw~"tiles/tile[7]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[7]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[7]/generated-flag",0); setprop(lw~"tiles/tile[7]/tile-index",-1); setprop(lw~"tiles/tile[7]/code",""); setprop(lw~"tiles/tile[7]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[7]/orientation-deg",0.0); x = 40000.0; y = -40000.0; setprop(lw~"tiles/tile[8]/latitude-deg",blat + get_lat(x,y,phi)); setprop(lw~"tiles/tile[8]/longitude-deg",blon + get_lon(x,y,phi)); setprop(lw~"tiles/tile[8]/generated-flag",0); setprop(lw~"tiles/tile[8]/tile-index",-1); setprop(lw~"tiles/tile[8]/code",""); setprop(lw~"tiles/tile[8]/timestamp-sec",weather_dynamics.time_lw); setprop(lw~"tiles/tile[8]/orientation-deg",0.0); } ################### # global variables ################### # these already exist in different namespace, but for ease of typing we define them here as well var lat_to_m = 110952.0; # latitude degrees to meters var m_to_lat = 9.01290648208234e-06; # meters to latitude degrees var ft_to_m = 0.30480; var m_to_ft = 1.0/ft_to_m; var inhg_to_hp = 33.76389; var hp_to_inhg = 1.0/inhg_to_hp; var lon_to_m = 0.0; #local_weather.lon_to_m; var m_to_lon = 0.0; # local_weather.m_to_lon; var lw = "/local-weather/"; var modelArrays = []; ################### # helper functions ################### var calc_geo = func(clat) { lon_to_m = math.cos(clat*math.pi/180.0) * lat_to_m; m_to_lon = 1.0/lon_to_m; } var get_lat = func (x,y,phi) { return (y * math.cos(phi) - x * math.sin(phi)) * m_to_lat; } var get_lon = func (x,y,phi) { return (x * math.cos(phi) + y * math.sin(phi)) * m_to_lon; }