# 3D Sine Wave

September 16, 2014
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Had a headache last night, so decided to take things easy and just read posts Google+. Then I came across this post which seems interesting so I thought I would play around before I head to bed.

First of all, I thought generating a square base would be much easier in R compare to hexagons. Starting with 2 numeric vectors and then expand them by expand.grid() would do the job. The next step is to provide the rotation, this is also rather simple since it can be achieved by multiplying the following matrix.

[ R = begin{bmatrix} cos theta & -sin theta \ sin theta & cos theta \ end{bmatrix} ]

Finally, the last step is to define the wave. This is done by a sine function with the phase being the distance away from the center.

[ d = sqrt{x^2 + y^2}\ y_t = y_t + 10 times sin(t + d) ]

And here is the code, enjoy....

library(animation)## Create the square to start withx = seq(-5, 5, length = 50)y = seq(-5, 5, length = 50)square = as.matrix(expand.grid(x, y))## Create the rotation matrixangle = pi/180rotation =    matrix(c(cos(angle), -sin(angle), sin(angle), cos(angle)), ncol = 2)## PlotsaveGIF(    {        init = square        for(i in seq(0, 2 * pi, length = 360)){            tmp = init            distFromCenter = sqrt(tmp[, 1]^2 + tmp[, 2]^2)            tmp[, 2] = tmp[, 2] + 10 * sin(i - distFromCenter)            colIntensity = (tmp[, 2] + abs(min(tmp[, 2])))/                max((tmp[, 2] + abs(min(tmp[, 2]))))            plot(tmp[, c(1, 2)], xlim = c(-10, 10), ylim = c(-20, 20),                 pch = ".", cex = 3, axes = FALSE, xlab = "", ylab = "",                 col = rgb(colIntensity, 0, 0))                        init = init %*% rotation        }    },    movie.name = "./wave.gif", interval = 0.005,    nmax = 30, ani.width = 800,  ani.height = 800    )

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