1 class AmfController < ApplicationController
5 # RAILS_DEFAULT_LOGGER.error("Args: #{args[0]}, #{args[1]}, #{args[2]}, #{args[3]}")
7 # ====================================================================
10 # ---- talk process AMF request
13 req=StringIO.new(request.raw_post) # Get POST data as request
14 req.read(2) # Skip version indicator and client ID
15 results={} # Results of each body
20 headers=getint(req) # Read number of headers
22 headers.times do # Read each header
23 name=getstring(req) # |
24 req.getc # | skip boolean
25 value=getvalue(req) # |
26 header["name"]=value # |
29 bodies=getint(req) # Read number of bodies
30 bodies.times do # Read each body
31 message=getstring(req) # | get message name
32 index=getstring(req) # | get index in response sequence
33 bytes=getlong(req) # | get total size in bytes
34 args=getvalue(req) # | get response (probably an array)
37 when 'getpresets'; results[index]=putdata(index,getpresets)
38 when 'whichways'; results[index]=putdata(index,whichways(args))
39 when 'getway'; results[index]=putdata(index,getway(args))
40 when 'putway'; results[index]=putdata(index,putway(args))
41 when 'deleteway'; results[index]=putdata(index,deleteway(args))
48 RAILS_DEFAULT_LOGGER.info(" Response: start")
49 response.headers["Content-Type"]="application/x-amf"
50 a,b=results.length.divmod(256)
51 ans=0.chr+0.chr+0.chr+0.chr+a.chr+b.chr
53 RAILS_DEFAULT_LOGGER.info(" Response: encode #{k}")
56 RAILS_DEFAULT_LOGGER.info(" Response: end")
63 # ====================================================================
67 # return presets,presetmenus and presetnames arrays
71 presetmenus={}; presetmenus['point']=[]; presetmenus['way']=[]
72 presetnames={}; presetnames['point']={}; presetnames['way']={}
76 RAILS_DEFAULT_LOGGER.info(" Message: getpresets")
78 # File.open("config/potlatch/presets.txt") do |file|
80 # Temporary patch to get around filepath problem
81 # To remove this patch and make the code nice again:
82 # 1. uncomment above line
83 # 2. fix the path in the above line
84 # 3. delete this here document, and the following line (StringIO....)
88 motorway: highway=motorway,ref=(type road number)
89 trunk road: highway=trunk,ref=(type road number),name=(type road name)
90 primary road: highway=primary,ref=(type road number),name=(type road name)
91 secondary road: highway=secondary,ref=(type road number),name=(type road name)
92 residential road: highway=residential,name=(type road name)
93 unclassified road: highway=unclassified,name=(type road name)
96 footpath: highway=footway,foot=yes
97 bridleway: highway=bridleway,foot=yes,horse=yes,bicycle=yes
98 byway: highway=byway,foot=yes,horse=yes,bicycle=yes,motorcar=yes
99 permissive path: highway=footway,foot=permissive
102 cycle lane: highway=cycleway,cycleway=lane,ncn_ref=
103 cycle track: highway=cycleway,cycleway=track,ncn_ref=
104 cycle lane (NCN): highway=cycleway,cycleway=lane,name=(type name here),ncn_ref=(type route number)
105 cycle track (NCN): highway=cycleway,cycleway=track,name=(type name here),ncn_ref=(type route number)
108 canal: waterway=canal,name=(type name here)
109 navigable river: waterway=river,boat=yes,name=(type name here)
110 navigable drain: waterway=drain,boat=yes,name=(type name here)
111 derelict canal: waterway=derelict_canal,name=(type name here)
112 unnavigable river: waterway=river,boat=no,name=(type name here)
113 unnavigable drain: waterway=drain,boat=no,name=(type name here)
116 railway: railway=rail
117 tramway: railway=tram
118 light railway: railway=light_rail
119 preserved railway: railway=preserved
120 disused railway tracks: railway=disused
121 course of old railway: railway=abandoned
124 mini roundabout: highway=mini_roundabout
125 traffic lights: highway=traffic_signals
128 bridge: highway=bridge
131 cattle grid: highway=cattle_grid
137 lock gate: waterway=lock_gate
139 aqueduct: waterway=aqueduct
140 winding hole: waterway=turning_point
141 mooring: waterway=mooring
144 station: railway=station
145 viaduct: railway=viaduct
146 level crossing: railway=crossing
149 StringIO.open(txt) do |file|
150 file.each_line {|line|
152 if (t=~/(\w+)\/(\w+)/) then
155 presetmenus[presettype].push(presetcategory)
156 presetnames[presettype][presetcategory]=["(no preset)"]
157 elsif (t=~/^(.+):\s?(.+)$/) then
159 presetnames[presettype][presetcategory].push(pre)
161 kv.split(',').each {|a|
162 if (a=~/^(.+)=(.*)$/) then presets[pre][$1]=$2 end
167 return [presets,presetmenus,presetnames]
170 # ----- whichways(left,bottom,right,top)
171 # return array of ways in current bounding box
172 # at present, instead of using correct (=more complex) SQL to find
173 # corner-crossing ways, it simply enlarges the bounding box by +/- 0.01
176 xmin = args[0].to_f-0.01
177 ymin = args[1].to_f-0.01
178 xmax = args[2].to_f+0.01
179 ymax = args[3].to_f+0.01
181 RAILS_DEFAULT_LOGGER.info(" Message: whichways, bbox=#{xmin},#{ymin},#{xmax},#{ymax}")
183 waylist=WaySegment.find_by_sql("SELECT DISTINCT current_way_segments.id AS wayid"+
184 " FROM current_way_segments,current_segments,current_nodes,current_ways "+
185 " WHERE segment_id=current_segments.id "+
186 " AND current_segments.visible=1 "+
187 " AND node_a=current_nodes.id "+
188 " AND current_ways.id=current_way_segments.id "+
189 " AND current_ways.visible=1 "+
190 " AND (latitude BETWEEN "+ymin.to_s+" AND "+ymax.to_s+") "+
191 " AND (longitude BETWEEN "+xmin.to_s+" AND "+xmax.to_s+")")
193 ways = waylist.collect {|a| a.wayid.to_i } # get an array of way id's
195 pointlist =ActiveRecord::Base.connection.select_all("SELECT current_nodes.id,current_nodes.tags "+
196 " FROM current_nodes "+
197 " LEFT OUTER JOIN current_segments cs1 ON cs1.node_a=current_nodes.id "+
198 " LEFT OUTER JOIN current_segments cs2 ON cs2.node_b=current_nodes.id "+
199 " WHERE (latitude BETWEEN "+ymin.to_s+" AND "+ymax.to_s+") "+
200 " AND (longitude BETWEEN "+xmin.to_s+" AND "+xmax.to_s+") "+
201 " AND cs1.id IS NULL AND cs2.id IS NULL "+
202 " AND current_nodes.visible=1")
204 points = pointlist.collect {|a| [a['id'],tag2array(a['tags'])] } # get a list of node ids and their tags
209 # ----- getway (objectname, way, baselong, basey, masterscale)
210 # returns objectname, array of co-ordinates, attributes,
211 # xmin,xmax,ymin,ymax
214 objname,wayid,baselong,basey,masterscale=args
219 xmax = ymax = -999999
221 RAILS_DEFAULT_LOGGER.info(" Message: getway, id=#{wayid}")
223 readwayquery(wayid).each {|row|
224 xs1=long2coord(row['long1'].to_f,baselong,masterscale); ys1=lat2coord(row['lat1'].to_f,basey,masterscale)
225 xs2=long2coord(row['long2'].to_f,baselong,masterscale); ys2=lat2coord(row['lat2'].to_f,basey,masterscale)
226 points << [xs1,ys1,row['id1'].to_i,0,tag2array(row['tags1']),0] if (row['id1'].to_i!=lastid)
227 lastid = row['id2'].to_i
228 points << [xs2,ys2,row['id2'].to_i,1,tag2array(row['tags2']),row['segment_id'].to_i]
229 xmin = [xmin,row['long1'].to_f,row['long2'].to_f].min
230 xmax = [xmax,row['long1'].to_f,row['long2'].to_f].max
231 ymin = [ymin,row['lat1'].to_f,row['lat2'].to_f].min
232 ymax = [ymax,row['lat1'].to_f,row['lat2'].to_f].max
236 attrlist=ActiveRecord::Base.connection.select_all "SELECT k,v FROM current_way_tags WHERE id=#{wayid}"
237 attrlist.each {|a| attributes[a['k']]=a['v'] }
239 [objname,points,attributes,xmin,xmax,ymin,ymax]
242 # ----- putway (user token, way, array of co-ordinates, array of attributes,
243 # baselong, basey, masterscale)
244 # returns current way ID, new way ID, hash of renumbered nodes,
245 # xmin,xmax,ymin,ymax
248 usertoken,originalway,points,attributes,baselong,basey,masterscale=args
249 uid=getuserid(usertoken)
251 db_uqs='uniq'+uid.to_s+originalway.to_i.abs.to_s+Time.new.to_i.to_s # temp uniquesegments table name, typically 51 chars
252 db_uqn='unin'+uid.to_s+originalway.to_i.abs.to_s+Time.new.to_i.to_s # temp uniquenodes table name, typically 51 chars
253 db_now='@now'+uid.to_s+originalway.to_i.abs.to_s+Time.new.to_i.to_s # 'now' variable name, typically 51 chars
254 ActiveRecord::Base.connection.execute("SET #{db_now}=NOW()")
255 originalway=originalway.to_i
257 RAILS_DEFAULT_LOGGER.info(" Message: putway, id=#{way}")
259 # -- 3. read original way into memory
261 xc={}; yc={}; tagc={}; seg={}
264 readwayquery(way).each { |row|
265 id1=row['id1'].to_i; xc[id1]=row['long1'].to_f; yc[id1]=row['lat1'].to_f; tagc[id1]=row['tags1']
266 id2=row['id2'].to_i; xc[id2]=row['long2'].to_f; yc[id2]=row['lat2'].to_f; tagc[id2]=row['tags2']
267 seg[row['segment_id'].to_i]=id1.to_s+'-'+id2.to_s
269 ActiveRecord::Base.connection.update("UPDATE current_ways SET timestamp=#{db_now},user_id=#{uid},visible=1 WHERE id=#{way}")
271 way=ActiveRecord::Base.connection.insert("INSERT INTO current_ways (user_id,timestamp,visible) VALUES (#{uid},#{db_now},1)")
274 # -- 4. get version by inserting new row into ways
276 version=ActiveRecord::Base.connection.insert("INSERT INTO ways (id,user_id,timestamp,visible) VALUES (#{way},#{uid},#{db_now},1)")
278 # -- 5. compare nodes and update xmin,xmax,ymin,ymax
281 xmax = ymax = -999999
285 points.each_index do |i|
286 xs=coord2long(points[i][0],masterscale,baselong)
287 ys=coord2lat(points[i][1],masterscale,basey)
288 xmin=[xs,xmin].min; xmax=[xs,xmax].max
289 ymin=[ys,ymin].min; ymax=[ys,ymax].max
290 node=points[i][2].to_i
291 tagstr=array2tag(points[i][4])
292 tagsql="'"+sqlescape(tagstr)+"'"
297 newnode=ActiveRecord::Base.connection.insert("INSERT INTO current_nodes ( latitude,longitude,timestamp,user_id,visible,tags) VALUES ( #{ys},#{xs},#{db_now},#{uid},1,#{tagsql})")
298 ActiveRecord::Base.connection.insert("INSERT INTO nodes (id,latitude,longitude,timestamp,user_id,visible,tags) VALUES (#{newnode},#{ys},#{xs},#{db_now},#{uid},1,#{tagsql})")
300 renumberednodes[node.to_s]=newnode.to_s
302 elsif xc.has_key?(node)
303 # old node from original way - update
304 if (xs!=xc[node] or (ys/0.0000001).round!=(yc[node]/0.0000001).round or tagstr!=tagc[node])
305 ActiveRecord::Base.connection.insert("INSERT INTO nodes (id,latitude,longitude,timestamp,user_id,visible,tags) VALUES (#{node},#{ys},#{xs},#{db_now},#{uid},1,#{tagsql})")
306 ActiveRecord::Base.connection.update("UPDATE current_nodes SET latitude=#{ys},longitude=#{xs},timestamp=#{db_now},user_id=#{uid},tags=#{tagsql},visible=1 WHERE id=#{node}")
309 # old node, created in another way and now added to this way
315 # -- 6.i compare segments
318 seglist='' # list of existing segments that we want to keep
319 for i in (0..(points.length-2))
320 if (points[i+1][3].to_i==0) then next end
321 segid=points[i+1][5].to_i
322 from =points[i ][2].to_i
323 to =points[i+1][2].to_i
324 if seg.has_key?(segid)
325 if seg[segid]=="#{from}-#{to}" then
326 if (seglist!='') then seglist+=',' end; seglist+=segid.to_s
330 segid=ActiveRecord::Base.connection.insert("INSERT INTO current_segments ( node_a,node_b,timestamp,user_id,visible,tags) VALUES ( #{from},#{to},#{db_now},#{uid},1,'')")
331 ActiveRecord::Base.connection.insert("INSERT INTO segments (id,node_a,node_b,timestamp,user_id,visible,tags) VALUES (#{segid},#{from},#{to},#{db_now},#{uid},1,'')")
333 numberedsegments[(i+1).to_s]=segid.to_s
335 # numberedsegments.each{|a,b| RAILS_DEFAULT_LOGGER.error("Sending back: seg no. #{a} -> id #{b}") }
338 # -- 6.ii insert new way segments
340 createuniquesegments(way,db_uqs,seglist) # segments which appear in this way but no other
342 # delete segments from uniquesegments (and not in modified way)
345 INSERT INTO segments (id,node_a,node_b,timestamp,user_id,visible)
346 SELECT DISTINCT segment_id,node_a,node_b,#{db_now},#{uid},0
347 FROM current_segments AS cs, #{db_uqs} AS us
348 WHERE cs.id=us.segment_id AND cs.visible=1
350 ActiveRecord::Base.connection.insert(sql)
353 UPDATE current_segments AS cs, #{db_uqs} AS us
354 SET cs.timestamp=#{db_now},cs.visible=0,cs.user_id=#{uid}
355 WHERE cs.id=us.segment_id AND cs.visible=1
357 ActiveRecord::Base.connection.update(sql)
359 # delete nodes not in modified way or any other segments
361 createuniquenodes(db_uqs,db_uqn) # nodes which appear in this way but no other
364 INSERT INTO nodes (id,latitude,longitude,timestamp,user_id,visible)
365 SELECT DISTINCT cn.id,cn.latitude,cn.longitude,#{db_now},#{uid},0
366 FROM current_nodes AS cn,#{db_uqn}
369 ActiveRecord::Base.connection.insert(sql)
372 UPDATE current_nodes AS cn, #{db_uqn}
373 SET cn.timestamp=#{db_now},cn.visible=0,cn.user_id=#{uid}
376 ActiveRecord::Base.connection.update(sql)
378 ActiveRecord::Base.connection.execute("DROP TABLE #{db_uqs}")
379 ActiveRecord::Base.connection.execute("DROP TABLE #{db_uqn}")
381 # insert new version of route into way_segments
386 for i in (0..(points.length-2))
387 if (points[i+1][3].to_i==0) then next end
388 if insertsql !='' then insertsql +=',' end
389 if currentsql!='' then currentsql+=',' end
390 insertsql +="(#{way},#{points[i+1][5]},#{version})"
391 currentsql+="(#{way},#{points[i+1][5]},#{sequence})"
395 ActiveRecord::Base.connection.execute("DELETE FROM current_way_segments WHERE id=#{way}");
396 ActiveRecord::Base.connection.insert("INSERT INTO way_segments (id,segment_id,version ) VALUES #{insertsql}");
397 ActiveRecord::Base.connection.insert("INSERT INTO current_way_segments (id,segment_id,sequence_id) VALUES #{currentsql}");
399 # -- 7. insert new way tags
403 attributes.each do |k,v|
404 if v=='' then next end
405 if v[0,6]=='(type ' then next end
406 if insertsql !='' then insertsql +=',' end
407 if currentsql!='' then currentsql+=',' end
408 insertsql +="(#{way},'"+sqlescape(k)+"','"+sqlescape(v)+"',#{version})"
409 currentsql+="(#{way},'"+sqlescape(k)+"','"+sqlescape(v)+"')"
412 ActiveRecord::Base.connection.execute("DELETE FROM current_way_tags WHERE id=#{way}")
413 if (insertsql !='') then ActiveRecord::Base.connection.insert("INSERT INTO way_tags (id,k,v,version) VALUES #{insertsql}" ) end
414 if (currentsql!='') then ActiveRecord::Base.connection.insert("INSERT INTO current_way_tags (id,k,v) VALUES #{currentsql}") end
416 [originalway,way,renumberednodes,numberedsegments,xmin,xmax,ymin,ymax]
419 # ----- deleteway (user token, way)
420 # returns way ID only
425 RAILS_DEFAULT_LOGGER.info(" Message: deleteway, id=#{way}")
427 uid=getuserid(usertoken); if !uid then return end
430 db_uqs='uniq'+uid.to_s+way.to_i.abs.to_s+Time.new.to_i.to_s # temp uniquesegments table name, typically 51 chars
431 db_uqn='unin'+uid.to_s+way.to_i.abs.to_s+Time.new.to_i.to_s # temp uniquenodes table name, typically 51 chars
432 db_now='@now'+uid.to_s+way.to_i.abs.to_s+Time.new.to_i.to_s # 'now' variable name, typically 51 chars
433 ActiveRecord::Base.connection.execute("SET #{db_now}=NOW()")
434 createuniquesegments(way,db_uqs,'')
436 # - delete any otherwise unused segments
439 INSERT INTO segments (id,node_a,node_b,timestamp,user_id,visible)
440 SELECT DISTINCT segment_id,node_a,node_b,#{db_now},#{uid},0
441 FROM current_segments AS cs, #{db_uqs} AS us
442 WHERE cs.id=us.segment_id
444 ActiveRecord::Base.connection.insert(sql)
447 UPDATE current_segments AS cs, #{db_uqs} AS us
448 SET cs.timestamp=#{db_now},cs.visible=0,cs.user_id=#{uid}
449 WHERE cs.id=us.segment_id
451 ActiveRecord::Base.connection.update(sql)
453 # - delete any unused nodes
455 createuniquenodes(db_uqs,db_uqn)
458 INSERT INTO nodes (id,latitude,longitude,timestamp,user_id,visible)
459 SELECT DISTINCT cn.id,cn.latitude,cn.longitude,#{db_now},#{uid},0
460 FROM current_nodes AS cn,#{db_uqn}
463 ActiveRecord::Base.connection.insert(sql)
466 UPDATE current_nodes AS cn, #{db_uqn}
467 SET cn.timestamp=#{db_now},cn.visible=0,cn.user_id=#{uid}
470 ActiveRecord::Base.connection.update(sql)
472 ActiveRecord::Base.connection.execute("DROP TABLE #{db_uqs}")
473 ActiveRecord::Base.connection.execute("DROP TABLE #{db_uqn}")
477 ActiveRecord::Base.connection.insert("INSERT INTO ways (id,user_id,timestamp,visible) VALUES (#{way},#{uid},#{db_now},0)")
478 ActiveRecord::Base.connection.update("UPDATE current_ways SET user_id=#{uid},timestamp=#{db_now},visible=0 WHERE id=#{way}")
479 ActiveRecord::Base.connection.execute("DELETE FROM current_way_segments WHERE id=#{way}")
480 ActiveRecord::Base.connection.execute("DELETE FROM current_way_tags WHERE id=#{way}")
485 # ====================================================================
486 # Support functions for remote calls
489 ActiveRecord::Base.connection.select_all "SELECT n1.latitude AS lat1,n1.longitude AS long1,n1.id AS id1,n1.tags as tags1, "+
490 " n2.latitude AS lat2,n2.longitude AS long2,n2.id AS id2,n2.tags as tags2,segment_id "+
491 " FROM current_way_segments,current_segments,current_nodes AS n1,current_nodes AS n2 "+
492 " WHERE current_way_segments.id=#{id} "+
493 " AND segment_id=current_segments.id "+
494 " AND current_segments.visible=1 "+
495 " AND n1.id=node_a and n2.id=node_b "+
496 " AND n1.visible=1 AND n2.visible=1 "+
497 " ORDER BY sequence_id"
500 def createuniquesegments(way,uqs_name,seglist)
501 # Finds segments which appear in (previous version of) this way and no other
503 CREATE TEMPORARY TABLE #{uqs_name}
505 FROM (SELECT DISTINCT segment_id FROM current_way_segments
507 LEFT JOIN current_way_segments b
508 ON b.segment_id = a.segment_id
510 WHERE b.segment_id IS NULL
512 if (seglist!='') then sql+=" AND a.segment_id NOT IN (#{seglist})" end
513 ActiveRecord::Base.connection.execute(sql)
516 def createuniquenodes(uqs_name,uqn_name)
517 # Finds nodes which appear in uniquesegments but no other segments
519 CREATE TEMPORARY TABLE #{uqn_name}
520 SELECT DISTINCT node_id
521 FROM (SELECT cn.id AS node_id
522 FROM current_nodes AS cn,
523 current_segments AS cs,
525 WHERE cs.id=us.segment_id
526 AND (cn.id=cs.node_a OR cn.id=cs.node_b)) AS n
527 LEFT JOIN current_segments AS cs2 ON node_id=cs2.node_a AND cs2.visible=1
528 LEFT JOIN current_segments AS cs3 ON node_id=cs3.node_b AND cs3.visible=1
529 WHERE cs2.node_a IS NULL
530 AND cs3.node_b IS NULL
532 ActiveRecord::Base.connection.execute(sql)
536 a.gsub("'","''").gsub(92.chr,92.chr+92.chr)
541 a.gsub(';;;','#%').split(';').each do |b|
545 if k.nil? then k='' end
546 if v.nil? then v='' end
547 tags[k.gsub('#%','=')]=v.gsub('#%','=')
555 if v=='' then next end
556 if v[0,6]=='(type ' then next end
557 if str!='' then str+=';' end
558 str+=k.gsub(';',';;;').gsub('=','===')+'='+v.gsub(';',';;;').gsub('=','===')
564 token=sqlescape(token)
565 if (token=~/^(.+)\+(.+)$/) then
566 return ActiveRecord::Base.connection.select_value("SELECT id FROM users WHERE active=1 AND email='#{$1}' AND pass_crypt=MD5('#{$2}')")
568 return ActiveRecord::Base.connection.select_value("SELECT id FROM users WHERE active=1 AND token='#{token}'")
574 # ====================================================================
575 # AMF read subroutines
577 # ----- getint return two-byte integer
578 # ----- getlong return four-byte long
579 # ----- getstring return string with two-byte length
580 # ----- getdouble return eight-byte double-precision float
581 # ----- getobject return object/hash
582 # ----- getarray return numeric array
589 ((s.getc*256+s.getc)*256+s.getc)*256+s.getc
593 len=s.getc*256+s.getc
598 a=s.read(8).unpack('G') # G big-endian, E little-endian
613 while (key=getstring(s))
614 if (key=='') then break end
617 s.getc # skip the 9 'end of object' value
621 # ----- getvalue parse and get value
625 when 0; return getdouble(s) # number
626 when 1; return s.getc # boolean
627 when 2; return getstring(s) # string
628 when 3; return getobject(s) # object/hash
629 when 5; return nil # null
630 when 6; return nil # undefined
631 when 8; s.read(4) # mixedArray
632 return getobject(s) # |
633 when 10;return getarray(s) # array
634 else; return nil # error
638 # ====================================================================
639 # AMF write subroutines
641 # ----- putdata envelope data into AMF writeable form
642 # ----- encodevalue pack variables as AMF
645 d =encodestring(index+"/onResult")
646 d+=encodestring("null")
654 a=10.chr+encodelong(n.length)
662 a+=encodestring(k)+encodevalue(v)
666 2.chr+encodestring(n)
667 when 'Bignum','Fixnum','Float'
668 0.chr+encodedouble(n)
672 RAILS_DEFAULT_LOGGER.error("Unexpected Ruby type for AMF conversion: "+n.class.to_s)
676 # ----- encodestring encode string with two-byte length
677 # ----- encodedouble encode number as eight-byte double precision float
678 # ----- encodelong encode number as four-byte long
681 a,b=n.size.divmod(256)
693 # ====================================================================
694 # Co-ordinate conversion
696 def lat2coord(a,basey,masterscale)
697 -(lat2y(a)-basey)*masterscale+250
700 def long2coord(a,baselong,masterscale)
701 (a-baselong)*masterscale+350
705 180/Math::PI * Math.log(Math.tan(Math::PI/4+a*(Math::PI/180)/2))
708 def coord2lat(a,masterscale,basey)
709 y2lat((a-250)/-masterscale+basey)
712 def coord2long(a,masterscale,baselong)
713 (a-350)/masterscale+baselong
717 180/Math::PI * (2*Math.atan(Math.exp(a*Math::PI/180))-Math::PI/2)