Tuesday, September 16, 2014

3D Sine Wave

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 with
x = seq(-5, 5, length = 50)
y = seq(-5, 5, length = 50)
square = as.matrix(expand.grid(x, y))

## Create the rotation matrix
angle = pi/180
rotation =
    matrix(c(cos(angle), -sin(angle), sin(angle), cos(angle)), ncol = 2)

## Plot
saveGIF(
    {
        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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