File:Sonnenuhr-analemmatisch.png

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Description eine Analemmatische Sonnenuhr für Wien, selbst gezeichnet/programmiert
Date
Source made with GNU R, see source below
Author Thomas Steiner
Permission
(Reusing this file)
Thomas Steiner put it under the CC-by-SA 3.0.
I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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This chart was created with R.
Camera location48° 14′ 12″ N, 16° 22′ 10″ E  Heading=180° Kartographer map based on OpenStreetMap.View this and other nearby images on: OpenStreetMapinfo

R source code:

#gibt winkel der kugelkoordinaten zurück
coord2angle=function(coord) {
  diag=sqrt(coord[,1]^2+coord[,2]^2)
  psi=acos(coord[,1]/diag)
  psi[ ((coord[,1]>0)&(coord[,2]>0)) ] = -psi[ ((coord[,1]>0)&(coord[,2]>0)) ]
  phi=pi/2-atan(coord[,3]/diag)
  #phi[coord[,3]<0]=NA
  #psi[coord[,3]<0]=NA
  return( cbind(pi/2+psi, pi/2-phi) )
}

#gibt für einen zeitpunkt die koordinaten des stundenpunktes auf der ellipse zurück
anastundenskala=function(stunde,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA) {
  #TOOD: berechne frühesten sonnenauf- und spätesten sonnenuntergang
  ko=coords(t=4.545,S=stunde,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA,ignore=T) #datum ist 2.95, einfach so? längster tag!?... kein analemma!
  #an welchem tag ist 6h genau im osten?! dieses datum hier einsetzen!!!
  ang=coord2angle(ko)
  x=-sin(ang[,1])
  y=-sqrt(sin(phi)^2*(1-x^2))*sign(ko[,2])
  #x=-sin(ang[,1])
  #y=-sqrt(sin(phi)^2*(1-x^2))*sign(ko[,2])
  return( cbind(x,y) )
}

hoehenwinkel=function(datum,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA){ 
  ko=coords(t=datum,S=12,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA,ignore=T) #TODO: warum 12 mittags?!
  ang=coord2angle(ko)
  return( ang[,2] )
}

#für die analemmatische die markierung des datums
datumsmarkierung=function(datum,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA){
  alpha=hoehenwinkel(datum,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA)
  x=tan(alpha-pi/2+phi)
  return( x*cos(phi) )
}

lim=limits(RICHT=RICHT)
lim$xlim=c(-2.7,2.7)
lim$ylim=c(-2.7,2.7)
############################## wie im alten
if (OUT=="pdf") {
  CairoPDF(paste("sundial-",RICHT,"_",10*DIST,".pdf",sep=""),width=(DIST*(lim$xli[2]-lim$xli[1])+2)/2.54, height=(DIST* (lim$yli[2]-lim$yli[1])+2)/2.54, title=paste("Annalematische Sonnenuhr in",location))
} else if (OUT=="png") {
  CairoPNG(paste("sundial-",RICHT,"_",10*DIST,".png",sep=""),width=round(1200*sqrt(2)), height=1200)
}
par( mai=c(1,1,1,1)/2.54 )
#plot(c(-4.8,0.7),c(-5.3,0.2),type="n",xaxs="i",yaxs="i",xlim=lim$xli,ylim=lim$yli,asp=1,xaxt="n",yaxt="n",bty="n",ann=F)
##############################

plot(0,0,xlim=c(-1.1,1.1),ylim=c(-1.1,1.1),asp=1,xaxt="n",yaxt="n",type="n",bty="n",ann=F) 

stunden=seq(0,24,length=200)
sk=anastundenskala(stunden,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA)
lines(sk,col="gray")
stunden=seq(0,23,by=1)
sk=anastundenskala(stunden,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA)
lines(sk,type="p",col="blue",lwd=2)
text(sk[,1],sk[,2],stunden,col="skyblue",adj=c(1,0)) 

abline(h=0,v=0,col="lightgray") 

#180/pi*hoehenwinkel(seq(0,2*pi,length=12),phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA)
jaz=cumsum(c(0,31,28,31,30,31,30,31,31,30,31,30))/365*2*pi #eine linie pro monat
dm=datumsmarkierung(jaz,phi=phi,lambda=lambda,KAPPA=KAPPA,EPSILON=EPSILON,ALPHA=ALPHA)
text(0,dm[1:6],angle2date(jaz[1:6]),adj=1.1,col="blue",cex=0.8)
text(0,dm[7:12],angle2date(jaz[7:12]),adj=-0.1,col="blue",cex=0.8)
lines(rep(0,length(dm)),dm,type="b",col="blue")

text(0.66,-0.12,paste(location,",\n",round(lambda*180/pi,3),"° n.Br.\n",round(phi*180/pi,3),"°ö.L.\n","MESZ",sep=""),cex=0.75,col="orange")

if (OUT=="pdf" | OUT=="png" | OUT=="jpg") {
  dev.off()
}

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5 July 2009

48°14'12.001"N, 16°22'9.998"E

heading: 180 degree

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