単位円（Unit Circle=半径１の円弧）そのものの統計学的特性、特にヒストグラム（histogram）上への現れ方の描画結果はかなりの衝撃です。
要するに式に表すと(e^θi)t=(cos(θ)+sin(θi))となる図形を引き渡してみたのですが…
直交座標上には綺麗な三面図が出現…
X-Y座標(円弧面)
X-Z座標（Cos波面）フーリエ変換における「偶数系波形の顕現面」。
Y-Z座標（Sin波面）フーリエ変換における「奇数系波形の顕現面」。
一方、ある種の線微分的観点から「長さ1の半径の集合体」と見ると…
| class | frequency | |
|---|---|---|
| 1 | 0 ～ 1 | 60 |
かかる徹底的なまでの「沈黙」が「あらゆる波形を正弦波の重ね合わせによって合成する」フーリエ解析（Fourier analysis）によって破られる訳です。果たしてどんな景色が広がる事になるのでしょう？
例えば有名な「三角波（Triangular wave）」合成…
実は複素数空間（complex n-space）からはこんな風に見えるんです。
「偶数系」なので実数部を正面にすると確かに三角波が合成されています。
これくらい「揺らぎ」があれば、何とか相応に意味ある統計データが得られますね。
X-Y座標（円弧面）…２周期分描画されているが、よく分からない。
library(gplots)
FATW_xy<-function(x){
switch(x,
"0"= f0<-function(x) {pi/4*x/x},
"1"= f0<-function(x) {pi/4-2*pi/pi^2*exp(2*pi*x/pi*(0+1i))},
"2"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2)},
"3"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2)},
"4"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2+exp(14*pi*x/pi*(0+1i))/7^2)},
"5"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2+exp(14*pi*x/pi*(0+1i))/7^2+exp(18*pi*x/pi*(0+1i))/9^2)}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Y, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="y",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5")
saveGIF({
for (i in Time_Code){
FATW_xy(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
X-Z座標（Cos波面）…フーリエ変換における「奇数系波形の顕現面」。ここでは「三角波の合成（周期２回分）」が見て取れる。
library(gplots)
FATW_xz<-function(x){
switch(x,
"0"= f0<-function(x) {pi/4*x/x},
"1"= f0<-function(x) {pi/4-2*pi/pi^2*exp(2*pi*x/pi*(0+1i))},
"2"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2)},
"3"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2)},
"4"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2+exp(14*pi*x/pi*(0+1i))/7^2)},
"5"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2+exp(14*pi*x/pi*(0+1i))/7^2+exp(18*pi*x/pi*(0+1i))/9^2)}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5")
saveGIF({
for (i in Time_Code){
FATW_xz(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
Y-Z座標（Sin波面）…周期２回分描画されている。
library(gplots)
FATW_yz<-function(x){
switch(x,
"0"= f0<-function(x) {pi/4*x/x},
"1"= f0<-function(x) {pi/4-2*pi/pi^2*exp(2*pi*x/pi*(0+1i))},
"2"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2)},
"3"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2)},
"4"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2+exp(14*pi*x/pi*(0+1i))/7^2)},
"5"= f0<-function(x) {pi/4-2*pi/pi^2*(exp(2*pi*x/pi*(0+1i))+exp(6*pi*x/pi*(0+1i))/3^2+exp(10*pi*x/pi*(0+1i))/5^2+exp(14*pi*x/pi*(0+1i))/7^2+exp(18*pi*x/pi*(0+1i))/9^2)}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$Y, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="y",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5")
saveGIF({
for (i in Time_Code){
FATW_yz(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
放物線（Parabola）
複素数空間（complex n-space）における全体像。
「偶数系」なので実数部を正面にすると確かに放物線が合成されています。
X-Y座標（円弧面）…大きさの増大が目盛りに逃がされている？
library(gplots)
FAPB_xy<-function(x){
switch(x,
"0"= f0<-function(x) {pi^2/3*x/x},
"1"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i)))},
"2"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2)},
"3"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2)},
"4"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2)},
"5"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2)},
"6"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2)},
"7"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2)},
"8"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2+exp(x*8*(0+1i))/8^2)},
"9"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2+exp(x*8*(0+1i))/8^2)-exp(x*9*(0+1i))/9^2}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Y, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="y",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9")
saveGIF({
for (i in Time_Code){
FAPB_xy(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
X-Z座標（Cos波面）…フーリエ変換における「偶数系波形の顕現面」。ここでは「波放物線の合成」が見て取れる。周期幅が極端に狭まっている？
library(gplots)
FAPB_xy<-function(x){
switch(x,
"0"= f0<-function(x) {pi^2/3*x/x},
"1"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i)))},
"2"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2)},
"3"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2)},
"4"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2)},
"5"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2)},
"6"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2)},
"7"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2)},
"8"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2+exp(x*8*(0+1i))/8^2)},
"9"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2+exp(x*8*(0+1i))/8^2)-exp(x*9*(0+1i))/9^2}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9")
saveGIF({
for (i in Time_Code){
FAPB_xy(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
Y-Z座標（Sin波面）…周期幅が極端に狭まっている？
library(gplots)
FAPB_xy<-function(x){
switch(x,
"0"= f0<-function(x) {pi^2/3*x/x},
"1"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i)))},
"2"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2)},
"3"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2)},
"4"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2)},
"5"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2)},
"6"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2)},
"7"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2)},
"8"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2+exp(x*8*(0+1i))/8^2)},
"9"= f0<-function(x) {pi^2/3+4*(-exp(x*(0+1i))+exp(x*2*(0+1i))/2^2-exp(x*3*(0+1i))/3^2+exp(x*4*(0+1i))/4^2-exp(x*5*(0+1i))/5^2+exp(x*6*(0+1i))/6^2-exp(x*7*(0+1i))/7^2+exp(x*8*(0+1i))/8^2)-exp(x*9*(0+1i))/9^2}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$Y, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="y",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9")
saveGIF({
for (i in Time_Code){
FAPB_xy(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
ノコギリ波（Sawtooth wave）
複素数空間（complex n-space）における全体像。
虚数部を正面に向けると確かにノコギリ波が合成されています。
X-Y座標(円弧面)…バラツキが激しくなる。
library(gplots)
FASW_xy<-function(x){
switch(x,
"0"= f0<-function(x) {pi/2*x/x},
"1"= f0<-function(x) {pi/2-exp(x*2*(0+1i))},
"2"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2},
"3"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3},
"4"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4},
"5"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5},
"6"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6},
"7"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7},
"8"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8},
"9"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9},
"10"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10},
"11"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12},
"12"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14},
"13"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16},
"14"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16-exp(x*34*(0+1i))/17-exp(x*36*(0+1i))/18},
"15"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16-exp(x*34*(0+1i))/17-exp(x*36*(0+1i))/18-exp(x*38*(0+1i))/19-exp(x*40*(0+1i))/20}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Y, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="y",zlab="counts")}
#アニメーション
library("animation")
Time_Code=Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9","10","11","12","13","14","15")
saveGIF({
for (i in Time_Code){
FASW_xy(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
X-Z座標（Cos波面）…周期１回分？（波形の乱れが酷い）
library(gplots)
FASW_xz<-function(x){
switch(x,
"0"= f0<-function(x) {pi/2*x/x},
"1"= f0<-function(x) {pi/2-exp(x*2*(0+1i))},
"2"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2},
"3"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3},
"4"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4},
"5"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5},
"6"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6},
"7"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7},
"8"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8},
"9"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9},
"10"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10},
"11"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12},
"12"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14},
"13"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16},
"14"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16-exp(x*34*(0+1i))/17-exp(x*36*(0+1i))/18},
"15"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16-exp(x*34*(0+1i))/17-exp(x*36*(0+1i))/18-exp(x*38*(0+1i))/19-exp(x*40*(0+1i))/20}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9","10","11","12","13","14","15")
saveGIF({
for (i in Time_Code){
FASW_xz(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
Y-Z座標（Sin波面）…フーリエ変換における「奇数系波形の顕現面」。ここでは「ノコギリ波の合成（周期１回分）」が見て取れる。
library(gplots)
FASW_yz<-function(x){
switch(x,
"0"= f0<-function(x) {pi/2*x/x},
"1"= f0<-function(x) {pi/2-exp(x*2*(0+1i))},
"2"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2},
"3"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3},
"4"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4},
"5"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5},
"6"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6},
"7"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7},
"8"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8},
"9"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9},
"10"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10},
"11"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12},
"12"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14},
"13"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16},
"14"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16-exp(x*34*(0+1i))/17-exp(x*36*(0+1i))/18},
"15"= f0<-function(x) {pi/2-exp(x*2*(0+1i))-exp(x*4*(0+1i))/2-exp(x*6*(0+1i))/3-exp(x*8*(0+1i))/4-exp(x*10*(0+1i))/5-exp(x*12*(0+1i))/6-exp(x*14*(0+1i))/7-exp(x*16*(0+1i))/8-exp(x*18*(0+1i))/9-exp(x*20*(0+1i))/10-exp(x*22*(0+1i))/11-exp(x*24*(0+1i))/12-exp(x*26*(0+1i))/13-exp(x*28*(0+1i))/14-exp(x*30*(0+1i))/15-exp(x*32*(0+1i))/16-exp(x*34*(0+1i))/17-exp(x*36*(0+1i))/18-exp(x*38*(0+1i))/19-exp(x*40*(0+1i))/20}
)z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$Y, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="y",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9","10","11","12","13","14","15")
saveGIF({
for (i in Time_Code){
FASW_yz(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
矩形波（Square wave）
複素数空間（complex n-space）における全体像。
「奇数系」なので虚数部を正面にすると確かに矩形波が合成されています。
X-Y座標（円弧面）…周期１回分。
library(gplots)
FASqW_xy<-function(x){
switch(x,
"0"= f0<-function(x) {1/2*x/x},
"1"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))},
"2"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))},
"3"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))},
"4"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))},
"5"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))},
"6"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))},
"7"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))},
"8"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))+2/(15*pi)*exp(x*15*(0+1i))},
"9"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))+2/(15*pi)*exp(x*15*(0+1i))+2/(17*pi)*exp(x*17*(0+1i))}
)
z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Y, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="y",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9")
saveGIF({
for (i in Time_Code){
FASqW_xy(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
X-Z座標（Cos波面）…周期１回分。
library(gplots)
FASqW_xz<-function(x){
switch(x,
"0"= f0<-function(x) {1/2*x/x},
"1"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))},
"2"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))},
"3"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))},
"4"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))},
"5"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))},
"6"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))},
"7"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))},
"8"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))+2/(15*pi)*exp(x*15*(0+1i))},
"9"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))+2/(15*pi)*exp(x*15*(0+1i))+2/(17*pi)*exp(x*17*(0+1i))}
)
z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$X, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="x",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9")
saveGIF({
for (i in Time_Code){
FASqW_xz(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
Y-Z座標（Sin波面）…フーリエ変換における「奇数系波形の顕現面」。ここでは「矩形波の合成（周期１回分）」が見て取れる。
library(gplots)
FASqW_yz<-function(x){
switch(x,
"0"= f0<-function(x) {1/2*x/x},
"1"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))},
"2"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))},
"3"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))},
"4"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))},
"5"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))},
"6"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))},
"7"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))},
"8"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))+2/(15*pi)*exp(x*15*(0+1i))},
"9"= f0<-function(x) {1/2+2/pi*exp(x*(0+1i))+2/(3*pi)*exp(x*3*(0+1i))+2/(5*pi)*exp(x*5*(0+1i))+2/(7*pi)*exp(x*7*(0+1i))+2/(9*pi)*exp(x*9*(0+1i))+2/(11*pi)*exp(x*11*(0+1i))+2/(13*pi)*exp(x*13*(0+1i))+2/(15*pi)*exp(x*15*(0+1i))+2/(17*pi)*exp(x*17*(0+1i))}
)
z_axis<-seq(1,-1,length=60)
radian_axis<-seq(0,2*pi,length=60)
x_axis<-Re(f0(radian_axis))
y_axis<-Im(f0(radian_axis))
polygon_60 <- data.frame(X=x_axis, Y=y_axis,Z=z_axis)#3Dヒストグラム。遠近法プロット (persp)用データをhist2d() を使用して作成
h2d <- hist2d(polygon_60$Y, polygon_60$Z, show=FALSE, same.scale=TRUE, nbins=c(20,30))
# 遠近法プロット (persp) 描画
persp( h2d$x, h2d$y, h2d$counts,
ticktype="detailed", theta=60, phi=30,
expand=0.5, shade=0.5, col="cyan", ltheta=-30,main="polygon 60 with hist2d()",xlab="y",ylab="z",zlab="counts")}
#アニメーション
library("animation")
Time_Code=c("0","0","0","0","0","1","1","1","2","2","2","3","3","3","4","4","4","5","5","6","7","8","9")
saveGIF({
for (i in Time_Code){
FASqW_yz(i)
}
}, interval = 0.1, movie.name = "polygon_60_hist2d.gif")
詳細な考察については、とりあえず以下に続く…
