levelset 3d
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@ -5,12 +5,71 @@ import imageio.v2 as imageio
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import perlin_noise
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# X, Y, Z = np.mgrid[:100, :100, :100]
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# V = np.sqrt((X - 50)**2 + (Y - 50)**2 + (Z - 50)**2)
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def generate_perlin_noise_3d(shape, res):
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def f(t):
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return 6*t**5 - 15*t**4 + 10*t**3
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delta = (res[0] / shape[0], res[1] / shape[1], res[2] / shape[2])
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d = (shape[0] // res[0], shape[1] // res[1], shape[2] // res[2])
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grid = np.mgrid[0:res[0]:delta[0],0:res[1]:delta[1],0:res[2]:delta[2]]
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grid = grid.transpose(1, 2, 3, 0) % 1
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# Gradients
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theta = 2*np.pi*np.random.rand(res[0]+1, res[1]+1, res[2]+1)
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phi = 2*np.pi*np.random.rand(res[0]+1, res[1]+1, res[2]+1)
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gradients = np.stack((np.sin(phi)*np.cos(theta), np.sin(phi)*np.sin(theta), np.cos(phi)), axis=3)
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gradients[-1] = gradients[0]
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g000 = gradients[0:-1,0:-1,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g100 = gradients[1: ,0:-1,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g010 = gradients[0:-1,1: ,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g110 = gradients[1: ,1: ,0:-1].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g001 = gradients[0:-1,0:-1,1: ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g101 = gradients[1: ,0:-1,1: ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g011 = gradients[0:-1,1: ,1: ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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g111 = gradients[1: ,1: ,1: ].repeat(d[0], 0).repeat(d[1], 1).repeat(d[2], 2)
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# Ramps
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n000 = np.sum(np.stack((grid[:,:,:,0] , grid[:,:,:,1] , grid[:,:,:,2] ), axis=3) * g000, 3)
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n100 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1] , grid[:,:,:,2] ), axis=3) * g100, 3)
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n010 = np.sum(np.stack((grid[:,:,:,0] , grid[:,:,:,1]-1, grid[:,:,:,2] ), axis=3) * g010, 3)
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n110 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1]-1, grid[:,:,:,2] ), axis=3) * g110, 3)
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n001 = np.sum(np.stack((grid[:,:,:,0] , grid[:,:,:,1] , grid[:,:,:,2]-1), axis=3) * g001, 3)
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n101 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1] , grid[:,:,:,2]-1), axis=3) * g101, 3)
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n011 = np.sum(np.stack((grid[:,:,:,0] , grid[:,:,:,1]-1, grid[:,:,:,2]-1), axis=3) * g011, 3)
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n111 = np.sum(np.stack((grid[:,:,:,0]-1, grid[:,:,:,1]-1, grid[:,:,:,2]-1), axis=3) * g111, 3)
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# Interpolation
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t = f(grid)
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n00 = n000*(1-t[:,:,:,0]) + t[:,:,:,0]*n100
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n10 = n010*(1-t[:,:,:,0]) + t[:,:,:,0]*n110
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n01 = n001*(1-t[:,:,:,0]) + t[:,:,:,0]*n101
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n11 = n011*(1-t[:,:,:,0]) + t[:,:,:,0]*n111
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n0 = (1-t[:,:,:,1])*n00 + t[:,:,:,1]*n10
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n1 = (1-t[:,:,:,1])*n01 + t[:,:,:,1]*n11
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return ((1-t[:,:,:,2])*n0 + t[:,:,:,2]*n1)
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V = 10 * generate_perlin_noise_3d((100, 100, 100), (10, 10, 10))
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X, Y, Z = np.mgrid[:100, :100, :100]
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V += np.sqrt((X-50)**2 + (Y-50)**2 + (Z-50)**2)
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V = (V - V.min()) / (V.max() - V.min())
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frame_list = []
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fig = plt.figure()
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ax = fig.add_subplot(111, projection='3d')
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for i in np.linspace(0.05, 0.5, 100):
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ax.clear()
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vertices, triangles = mcubes.marching_cubes(V, i)
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ax.plot_trisurf(vertices[:,0], vertices[:,1], vertices[:,2], triangles=triangles)
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ax.set_xlim(0, 100)
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ax.set_ylim(0, 100)
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ax.set_zlim(0, 100)
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ax.set_xticklabels([])
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ax.set_yticklabels([])
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ax.set_zticklabels([])
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plt.savefig(f"/tmp/frame.png", bbox_inches='tight', pad_inches=0, dpi=300, transparent=True)
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frame_list.append(imageio.imread(f"/tmp/frame.png"))
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imageio.mimsave('picture.gif', frame_list + frame_list[::-1], fps=60)
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# for i in range(5, 45):
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# vertices, triangles = mcubes.marching_cubes(V, i)
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# mcubes.export_obj(vertices, triangles, f"cube_{i}.obj")
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noise = perlin_noise.PerlinNoise(octaves=6, seed=1)
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