Information Visualization (5) - R 그래픽 기초 (사각형을 이용한 나선형 그리기 Spiral Squares)

Spiral Squares

이번에는 사각형을 이용한 나선 그리기입니다.

> plot.new()

> plot.window(xlim = c(-1, 1), ylim = c(-1, 1), asp = 1)

> square = seq(0, 2 * pi, length = 5)[1:4] // 0에서 2π 사이를 5등분한 후 그 중 0에서부터 4개의 값만 취합니다

> n = 51 // 사각형 갯수

> r = rep(1.12, n) // 1.12를 n 만큼 반복

> r = cumprod(r) // cumprod() function returns the cumulative multiplication results.

> r = r/r[n]

> theta = seq(0, 2*pi, length = n)

> for (i in n:1) {

x = r[i] * cos(theta[i] + square)

y = r[i] * sin(theta[i] + square)

polygon(x, y, col = "gray")

}

이해가 쉽도록 각각의 과정을 떼어서 실행해보면 다음과 같습니다. 

> n=51

> r=rep(1.12,n)

> r

 [1] 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12

[15] 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12

[29] 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12

[43] 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12

> r=cumprod(r)

> r

 [1]   1.120000   1.254400   1.404928   1.573519   1.762342   1.973823

 [7]   2.210681   2.475963   2.773079   3.105848   3.478550   3.895976

[13]   4.363493   4.887112   5.473566   6.130394   6.866041   7.689966

[19]   8.612762   9.646293  10.803848  12.100310  13.552347  15.178629

[25]  17.000064  19.040072  21.324881  23.883866  26.749930  29.959922

[31]  33.555113  37.581726  42.091533  47.142517  52.799620  59.135574

[37]  66.231843  74.179664  83.081224  93.050970 104.217087 116.723137

[43] 130.729914 146.417503 163.987604 183.666116 205.706050 230.390776

[49] 258.037669 289.002190 323.682453

> r=r/r[n]

> r

 [1] 0.003460181 0.003875403 0.004340452 0.004861306 0.005444662 0.006098022

 [7] 0.006829785 0.007649359 0.008567282 0.009595356 0.010746798 0.012036414

[13] 0.013480784 0.015098478 0.016910295 0.018939530 0.021212274 0.023757747

[19] 0.026608677 0.029801718 0.033377924 0.037383275 0.041869268 0.046893580

[25] 0.052520809 0.058823307 0.065882103 0.073787956 0.082642510 0.092559612

[31] 0.103666765 0.116106777 0.130039590 0.145644341 0.163121662 0.182696261

[37] 0.204619813 0.229174190 0.256675093 0.287476104 0.321973237 0.360610025

[43] 0.403883228 0.452349215 0.506631121 0.567426856 0.635518078 0.711780248

[49] 0.797193878 0.892857143 1.000000000

> 

> theta = seq(0, 2*pi, length=n)

> theta

 [1] 0.0000000 0.1256637 0.2513274 0.3769911 0.5026548 0.6283185 0.7539822

 [8] 0.8796459 1.0053096 1.1309734 1.2566371 1.3823008 1.5079645 1.6336282

[15] 1.7592919 1.8849556 2.0106193 2.1362830 2.2619467 2.3876104 2.5132741

[22] 2.6389378 2.7646015 2.8902652 3.0159289 3.1415927 3.2672564 3.3929201

[29] 3.5185838 3.6442475 3.7699112 3.8955749 4.0212386 4.1469023 4.2725660

[36] 4.3982297 4.5238934 4.6495571 4.7752208 4.9008845 5.0265482 5.1522120

[43] 5.2778757 5.4035394 5.5292031 5.6548668 5.7805305 5.9061942 6.0318579

[50] 6.1575216 6.2831853

> 

엑셀을 이용해 그 과정을 살펴보면 다음과 같다.

pi	3.141592654
n	51
#	square=seq(0, 2*pi, length=5)
0	0
1	1.570796327
2	3.141592654
3	4.71238898
4	6.283185307

	x	y	x	y	x	y	x	y	x	y
i	1	1	2	2	3	3	4	4	5	5
theta=seq(0, 2*pi, length=n)	0.125663706	0.125663706	0.251327412	0.251327412	0.376991118	0.376991118	0.502654825	0.502654825	0.628318531	0.628318531
r	0.003460181	0.003460181	0.003875403	0.003875403	0.004340452	0.004340452	0.004861306	0.004861306	0.005444662	0.005444662
1	0.003432897	0.000433676	0.00375365	0.000963774	0.00403565	0.001597827	0.004259995	0.002341952	0.004404824	0.003200292
2	-0.000433676	0.003432897	-0.00096377	0.00375365	-0.00159783	0.00403565	-0.00234195	0.004259995	-0.00320029	0.004404824
3	-0.003432897	-0.000433676	-0.00375365	-0.00096377	-0.00403565	-0.00159783	-0.00425999	-0.00234195	-0.00440482	-0.00320029
4	0.000433676	-0.003432897	0.000963774	-0.00375365	0.001597827	-0.00403565	0.002341952	-0.00425999	0.003200292	-0.00440482
	x=r[i]*cos(theta[i]+square)	y = r[i]*sin(theta[i]+square)

엑셀로 그려보면 다음과 같다