import numpy as np

import cv2

from scipy import interpolate

from scipy import ndimage

from scipy import sparse

import scipy.sparse.linalg as linalg # import spsolve

#ffmpeg -i ./%06d.jpg will.mp4

### Setup

dt = 0.01

img = cv2.imread('fajar-2.jpg')

# make image smaller to make run faster if you want

#img = cv2.pyrDown(img)

#img = cv2.pyrDown(img)

Nx = img.shape[0]

Ny = img.shape[1]

v = np.zeros((Nx,Ny,2))

x = np.linspace(0,1,Nx, endpoint=False)

y = np.linspace(0,1,Ny, endpoint=False)

X, Y = np.meshgrid(x,y, indexing='ij')

#v[:,:,0] = -Y + 0.5

#v[:,:,1] = X - 0.5

#### Build necessary derivative and interpolation matrices

def build_grad(N):

# builds N-1 x N finite difference matrix

data = np.array([-np.ones(N), np.ones(N-1)])

return sparse.diags(data, np.array([0, 1]), shape= (N-1,N))

# gradient operators

gradx = sparse.kron(build_grad(Nx), sparse.identity(Ny-1))

grady = sparse.kron(sparse.identity(Nx-1), build_grad(Ny))

def build_K(N):

return sparse.diags(data, diags )

# Laplacian operator . Zero dirichlet boundary conditions

# why the hell is this reversed? Sigh.

K = sparse.kronsum(build_K(Ny),build_K(Nx))

Ksolve = linalg.factorized(K)

def build_interp(N):

data = np.array([np.ones(N)/2., np.ones(N-1)/2.])

diags = np.array([0, 1])

return sparse.diags(data, diags, shape= (N-1,N))

interpy = sparse.kron(sparse.identity(Nx), build_interp(Ny))

interpx = sparse.kron(build_interp(Nx), sparse.identity(Ny))

def projection_pass(vx,vy):

return gradx.T.dot(w).reshape(Nx,Ny-1), grady.T.dot(w).reshape(Nx-1,Ny)

for i in range(600):

#while True: #

v[:,:,0] += np.linalg.norm(img,axis=2) * dt * 0.001 # gravity force

# interpolate onto edges

vx = interpy.dot(v[:,:,0].flatten()).reshape(Nx,Ny-1)

vy = interpx.dot(v[:,:,1].flatten()).reshape(Nx-1,Ny)

# project incomperessible

dvx, dvy = projection_pass(vx,vy)

#interpolate change back to original grid

v[:,:,0] -= interpy.T.dot(dvx.flatten()).reshape(Nx,Ny)

v[:,:,1] -= interpx.T.dot(dvy.flatten()).reshape(Nx,Ny)

#advect everything

coords = np.stack( [(X - v[:,:,0]*dt)*Nx, (Y - v[:,:,1]*dt)*Ny], axis=0)

print(coords.shape)

print(v.shape)

for j in range(3):

img[:,:,j] = ndimage.map_coordinates(img[:,:,j], coords, order=5, mode='wrap')

v[:,:,0] = ndimage.map_coordinates(v[:,:,0], coords, order=5, mode='wrap')

v[:,:,1] = ndimage.map_coordinates(v[:,:,1], coords, order=5, mode='wrap')

cv2.imshow('image',img)

cv2.imwrite(f'fajar-2/{i:06}.jpg',img)

k = cv2.waitKey(30) & 0xFF

if k == ord(' '):

break

cv2.destroyAllWindows()