Pygame water ripple effect

Question

I have Googled for it but there are no ready scripts - as opposed to the same effect on Flash. I have checked the algorithm on The Water Effect Explained and also tested an imp

Answer 1

The following using numpy might get you started. It should be fast enough as it is though you could get much faster even in python (have a look here to see how http://www.scipy.org/PerformancePython).

By the way there are several drawbacks in the method described :

1. you cannot control the speed of the ripples - to do that you would have to modify the equations used in the ripple function (if you figure out how it relates to the wave equation http://en.wikipedia.org/wiki/Wave_equation then you are done)
2. the "depth" of the "pool" is fixed (and probably too shallow). I added a depth parameter to magnify the effect
3. the article reads integer pixel offsets - you would get a much nicer result with interpolated values (i guess you can do that with opengl, but my knowledge in that area is nil)

code:

import numpy

def ripple(w1, w2, damp, n = 1):
    for _ in xrange(n):
        w2 *= -2
        w2[1:-1,1:-1] += w1[0:-2, 1: -1]
        w2[1:-1,1:-1] += w1[2:  , 1: -1]
        w2[1:-1,1:-1] += w1[1:-1, 0: -2]
        w2[1:-1,1:-1] += w1[1:-1, 2:   ]
        w2 *= .5 * (1. - 1./damp)
        w1, w2 = w2, w1

def refract(x, y, w, rindex, depth = 10):
    sx = x[0,1] - x[0,0]
    sy = y[1,0] - y[0,0]

    dw_dx = (w[2: ,1:-1] - w[:-2,1:-1]) / sx * .5
    dw_dy = (w[1:-1,2: ] - w[1:-1,:-2]) / sy * .5

    xang = numpy.arctan(dw_dx)
    xrefract = numpy.arcsin(sin(xang) / rindex)
    dx = numpy.tan(xrefract) * dw_dx * depth

    yang = numpy.arctan(dw_dy)
    yrefract = numpy.arcsin(sin(yang) / rindex)
    dy = numpy.tan(yrefract) * dw_dy * depth

    dx *= numpy.sign(dw_dx)
    dy *= numpy.sign(dw_dy)

    xmin = x[0,0]
    xmax = x[0,-1]
    x[1:-1,1:-1] += dx
    x[:,:] = numpy.where(x < xmin, xmin, x)
    x[:,:] = numpy.where(x > xmax, xmax, x)

    ymin = y[0,0]
    ymax = y[-1,0]
    y[1:-1,1:-1] += dy
    y[:,:] = numpy.where(y < ymin, ymin, y)
    y[:,:] = numpy.where(y > ymax, ymax, y)

x and y should be grids from a numpy.meshgrid call : here's a sample usage:

    x,y = meshgrid(x,y)
    w = 10 * exp(- (x*x + y*y))
    w1 = w.copy()
    x1,y1 = meshgrid(r_[0:len(x):1.0], r_[0:len(y):1.0])
    ripple(w, w1, 16) # w1 will be modified
    refract(x1, y1, w1, rindex=2, depth=10) # x1 and y1 will be modified
    numpy.around(x1, out=x1) # but you will get better results with interpolate
    numpy.around(y1, out=y1) #