ぱらぱらめくる『The algorithmic beauty of plants』３ ブッシュな木

• 昨日の続き
• ３次元でも
• 伸びるにしたがって、枝が短くなるように
• 葉を入れたり
• ３次元の座標はとれたけれど、描図技術が今一つなので。。。

[
[

#
# U,V :Ru
# M,N :Rl
# P,Q :Rh
# W   :pi


ResultTurtle3<-function(x,d=1,D=pi/2,initX=NULL,initA=NULL){
	Ru<-matrix(c(cos(D),sin(D),0,-sin(D),cos(D),0,0,0,1),3,3,byrow=TRUE)
	Rl<-matrix(c(cos(D),0,-sin(D),0,1,0,sin(D),0,cos(D)),3,3,byrow=TRUE)
	Rh<-matrix(c(1,0,0,0,cos(D),-sin(D),0,sin(D),cos(D)),3,3,byrow=TRUE)
	Ru2<-matrix(c(cos(-D),sin(-D),0,-sin(-D),cos(-D),0,0,0,1),3,3,byrow=TRUE)
	Rl2<-matrix(c(cos(-D),0,-sin(-D),0,1,0,sin(-D),0,cos(-D)),3,3,byrow=TRUE)
	Rh2<-matrix(c(1,0,0,0,cos(-D),-sin(-D),0,sin(-D),cos(-D)),3,3,byrow=TRUE)
	Rw<-matrix(c(-1,0,0,0,-1,0,0,0,1),3,3,byrow=TRUE)
	Niter<-length(x)
	X<-matrix(0,Niter+1,3)
	T<-diag(rep(1,3))
	Ts<-NULL
	Ts[[1]]<-T
	Y<-X
	L<-rep(0,Niter)
	K<-rep(0,Niter)
	K[1]<-d
	if(is.null(initX)){
		initX<-c(0,0)
	}
	if(is.null(initA)){
		initA<-0
	}
	X[1,]<-c(initX,initA)
	Stocker<-c()
	for(i in 1:length(x)){
		X[i+1,]<-X[i,]
		Ts[[i+1]]<-Ts[[i]]
		K[i+1]<-K[i]
		if(x[i]=="F"){
			X[i+1,1]<-X[i+1,1]+K[i]*cos(X[i,3])
			X[i+1,2]<-X[i+1,2]+K[i]*sin(X[i,3])
			L[i]<-1
		}else if(x[i]=="f"){
			X[i+1,1]<-X[i+1,1]+K[i]*cos(X[i,3])
			X[i+1,2]<-X[i+1,2]+K[i]*sin(X[i,3])
			L[i]<-0
		}else if(x[i]=="A"){
			L[i]<-2
		}else if(x[i]=="S"){
			L[i]<-3
		}else if(x[i]=="L"){
			L[i]<-4
		}else if(x[i]=="U"){
			Ts[[i+1]]<-Ru%*%Ts[[i+1]]
		}else if(x[i]=="V"){
			Ts[[i+1]]<-Ru2%*%Ts[[i+1]]
		}else if(x[i]=="M"){
			Ts[[i+1]]<-Rl%*%Ts[[i+1]]

		}else if(x[i]=="N"){
			Ts[[i+1]]<-Rl2%*%Ts[[i+1]]

		}else if(x[i]=="P"){
			Ts[[i+1]]<-Rh%*%Ts[[i+1]]

		}else if(x[i]=="Q"){
			Ts[[i+1]]<-Rh2%*%Ts[[i+1]]

		}else if(x[i]=="W"){
			Ts[[i+1]]<-Rw%*%Ts[[i+1]]

		}else if(x[i]=="!"){
			K[i+1]<-K[i]*0.9
		}else if(x[i]=="'"){
			X[i+1,3]<-X[i+1,3]+D
			L[i]<-1

		}else if(x[i]=="{"){
			X[i+1,3]<-X[i+1,3]+D
			L[i]<-1

		}else if(x[i]=="}"){
			X[i+1,3]<-X[i+1,3]+D
			L[i]<-1

		}else if(x[i]=="["){
			Stocker<-c(Stocker,i+1)
			L[i]<-1

		}else if(x[i]=="]"){
			X[i+1,]<-X[Stocker[length(Stocker)],]
			L[i]<-1
			K[i+1]<-K[Stocker[length(Stocker)]]
			Stocker<-Stocker[1:(length(Stocker)-1)]
		}
		Y[i,]<-X[i+1,]
	}
	list(X=X,Y=Y,L=L,x=x)
}
DrawTurtle3<-function(ttl,col=FALSE){
	library(rgl)
	if(col){
		plot3d(ttl$X[,1],ttl$X[,2],ttl$X[,3],col=ttl$L,cex=ttl$L,cex=0.1)
	}else{
		plot3d(ttl$X[,1],ttl$X[,2],ttl$X[,3],cex=0.1)
	}
	
	#xlim<-ylim<-range(ttl$X[,1:2])
	#plot(ttl$X[,1],ttl$X[,2],cex=0.1,xlim=xlim,ylim=ylim)
XY<-cbind(ttl$X,ttl$Y)
XYc<-c(t(XY))
XY2<-matrix(XYc,ncol=3,byrow=TRUE)
	segments3d(XY2,col=c(1,ttl$L))
	#for(i in 1:length(ttl$L)){
		#if(ttl$L[i]==1){
			#c<-1
			#if(col)c<-ttl$L[i]
			#segments3d(ttl$X[i,],ttl$Y[i,],col=c)
		#}
	#}
	
}


elem<-c("A","S","[","]","L","!","'","U","V","M","N","P","Q","W","{","}")


initX<-c("A")
replacer<-hash(elem,elem)
replacer[["A"]]<-"[MFL!A]QQQQQ'[&FL!A]QQQQQQQ'[MFL!A]"

replacer[["F"]]<-"SQQQQQF"
replacer[["S"]]<-"FL"
replacer[["L"]]<-"['''NN{VfUfUfVWVfUfUf}]"
Nstep<-5

X<-MakeSequence2(initX,Nstep,replacer)
X[[Nstep+1]]


D<-22.5/180*pi
ttl<-ResultTurtle3(X[[Nstep+1]],D=D)
DrawTurtle3(ttl,col=TRUE)
DrawTurtle2(ttl)