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Includes 30 custom nodes committed directly, 7 Civitai-exclusive loras stored via Git LFS, and a setup script that installs all dependencies and downloads HuggingFace-hosted models on vast.ai. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
67 lines
2.8 KiB
Python
67 lines
2.8 KiB
Python
import numpy as np
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from scipy.ndimage import map_coordinates, spline_filter
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from scipy.sparse.linalg import factorized
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from .numerical import difference, operator
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class Fluid:
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def __init__(self, shape, *quantities, pressure_order=1, advect_order=3):
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self.shape = shape
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self.dimensions = len(shape)
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# Prototyping is simplified by dynamically
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# creating advected quantities as needed.
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self.quantities = quantities
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for q in quantities:
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setattr(self, q, np.zeros(shape))
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self.indices = np.indices(shape)
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self.velocity = np.zeros((self.dimensions, *shape))
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laplacian = operator(shape, difference(2, pressure_order))
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self.pressure_solver = factorized(laplacian)
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self.advect_order = advect_order
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def step(self):
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# Advection is computed backwards in time as described in Stable Fluids.
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advection_map = self.indices - self.velocity
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# SciPy's spline filter introduces checkerboard divergence.
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# A linear blend of the filtered and unfiltered fields based
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# on some value epsilon eliminates this error.
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def advect(field, filter_epsilon=10e-2, mode='constant'):
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filtered = spline_filter(field, order=self.advect_order, mode=mode)
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field = filtered * (1 - filter_epsilon) + field * filter_epsilon
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return map_coordinates(field, advection_map, prefilter=False, order=self.advect_order, mode=mode)
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# Apply advection to each axis of the
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# velocity field and each user-defined quantity.
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for d in range(self.dimensions):
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self.velocity[d] = advect(self.velocity[d])
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for q in self.quantities:
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setattr(self, q, advect(getattr(self, q)))
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# Compute the jacobian at each point in the
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# velocity field to extract curl and divergence.
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jacobian_shape = (self.dimensions,) * 2
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partials = tuple(np.gradient(d) for d in self.velocity)
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jacobian = np.stack(partials).reshape(*jacobian_shape, *self.shape)
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divergence = jacobian.trace()
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# If this curl calculation is extended to 3D, the y-axis value must be negated.
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# This corresponds to the coefficients of the levi-civita symbol in that dimension.
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# Higher dimensions do not have a vector -> scalar, or vector -> vector,
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# correspondence between velocity and curl due to differing isomorphisms
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# between exterior powers in dimensions != 2 or 3 respectively.
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curl_mask = np.triu(np.ones(jacobian_shape, dtype=bool), k=1)
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curl = (jacobian[curl_mask] - jacobian[curl_mask.T]).squeeze()
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# Apply the pressure correction to the fluid's velocity field.
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pressure = self.pressure_solver(divergence.flatten()).reshape(self.shape)
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self.velocity -= np.gradient(pressure)
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return divergence, curl, pressure |