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Three-Dimensional Geometry and Topology (Princeton Mathematical Series)

• 双曲線幾何
• ポアンカレ ディスク モデル

# hyperbolic disk 

t<-seq(from=0,to=1,length=100)*2*pi
xc<-cos(t)
yc<-sin(t)

#plot(xc,yc,type="l")


# straigt lines orthogonally crossing a point on the circle in hyperbolic geometic space 

#r<-seq(from=0,to=3,by=0.1)
r<-tan(seq(from=0,to=pi,length=10)/2)
Xcs<-Ycs<-matrix(0,length(r),length(t))
for(i in 1:length(r)){
	Xcs[i,]<-1+r[i]*cos(t)
	Ycs[i,]<-r[i]*sin(t)+r[i]
}
Xcs<-rbind(Xcs,Xcs)
Ycs<-rbind(Ycs,-Ycs)
xlim<-c(-1.5,3)
#xlim<-range(Xcs)
ylim<-xlim

plot(xc,yc,xlim=xlim,ylim=ylim,type="l",main="",xlab="",ylab="")
for(i in 1:length(Xcs[,1])){
	par(new=TRUE)
	plot(Xcs[i,],Ycs[i,],xlim=xlim,ylim=ylim,type="l",main="",xlab="",ylab="")
	
}
abline(h=0)

• 速くするためにはこちらを