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import warp as wp
from .geometry import Geometry
from warp.fem.types import Sample, ElementIndex, Coords, make_free_sample
from warp.fem import cache
_mat32 = wp.mat(shape=(3, 2), dtype=float)
class DeformedGeometry(Geometry):
def __init__(self, field):
"""Constructs a Deformed Geometry from a displacement field defined over a base geometry"""
from warp.fem.field import DiscreteField
self.field: DiscreteField = field
self.base = self.field.space.geometry
self.dimension = self.base.dimension
if not wp.types.type_is_vector(field.dtype) or wp.types.type_length(field.dtype) != self.dimension:
raise ValueError("Invalid value type for position field")
self.CellArg = self.field.ElementEvalArg
self.field_trace = field.trace()
self.SideArg = self._make_side_arg()
self.SideIndexArg = self.base.SideIndexArg
self.cell_count = self.base.cell_count
self.vertex_count = self.base.vertex_count
self.side_count = self.base.side_count
self.boundary_side_count = self.base.boundary_side_count
self.reference_cell = self.base.reference_cell
self.reference_side = self.base.reference_side
self.side_index_arg_value = self.base.side_index_arg_value
self.cell_position = self._make_cell_position()
self.cell_deformation_gradient = self._make_cell_deformation_gradient()
self.cell_inverse_deformation_gradient = self._make_cell_inverse_deformation_gradient()
self.cell_measure = self._make_cell_measure()
self.boundary_side_index = self.base.boundary_side_index
self.side_to_cell_arg = self._make_side_to_cell_arg()
self.side_position = self._make_side_position()
self.side_deformation_gradient = self._make_side_deformation_gradient()
self.side_inner_cell_index = self._make_side_inner_cell_index()
self.side_outer_cell_index = self._make_side_outer_cell_index()
self.side_inner_cell_coords = self._make_side_inner_cell_coords()
self.side_outer_cell_coords = self._make_side_outer_cell_coords()
self.side_from_cell_coords = self._make_side_from_cell_coords()
self.side_inner_inverse_deformation_gradient = self._make_side_inner_inverse_deformation_gradient()
self.side_outer_inverse_deformation_gradient = self._make_side_outer_inverse_deformation_gradient()
self.side_measure = self._make_side_measure()
self.side_measure_ratio = self._make_side_measure_ratio()
self.side_normal = self._make_side_normal()
@property
def name(self):
return f"DefGeo_{self.field.name}"
# Geometry device interface
@cache.cached_arg_value
def cell_arg_value(self, device) -> "DeformedGeometry.CellArg":
args = self.CellArg()
args.elt_arg = self.base.cell_arg_value(device)
args.eval_arg = self.field.eval_arg_value(device)
return args
def _make_cell_position(self):
@cache.dynamic_func(suffix=self.name)
def cell_position(cell_arg: self.CellArg, s: Sample):
return self.field.eval_inner(cell_arg, s) + self.base.cell_position(cell_arg.elt_arg, s)
return cell_position
def _make_cell_deformation_gradient(self):
@cache.dynamic_func(suffix=self.name)
def cell_deformation_gradient(cell_arg: self.CellArg, s: Sample):
return self.field.eval_reference_grad_inner(cell_arg, s) + self.base.cell_deformation_gradient(
cell_arg.elt_arg, s
)
return cell_deformation_gradient
def _make_cell_inverse_deformation_gradient(self):
@cache.dynamic_func(suffix=self.name)
def cell_inverse_deformation_gradient(cell_arg: self.CellArg, s: Sample):
return wp.inverse(self.cell_deformation_gradient(cell_arg, s))
return cell_inverse_deformation_gradient
def _make_cell_measure(self):
REF_MEASURE = wp.constant(self.reference_cell().measure())
@cache.dynamic_func(suffix=self.name)
def cell_measure(args: self.CellArg, s: Sample):
return wp.abs(wp.determinant(self.cell_deformation_gradient(args, s))) * REF_MEASURE
return cell_measure
@wp.func
def cell_normal(args: Any, s: Sample):
return wp.vec2(0.0)
def _make_side_arg(self):
@cache.dynamic_struct(suffix=self.name)
class SideArg:
base_arg: self.base.SideArg
trace_arg: self.field_trace.EvalArg
field_arg: self.field.EvalArg
return SideArg
@cache.cached_arg_value
def side_arg_value(self, device) -> "DeformedGeometry.SideArg":
args = self.SideArg()
args.base_arg = self.base.side_arg_value(device)
args.field_arg = self.field.eval_arg_value(device)
args.trace_arg = self.field_trace.eval_arg_value(device)
return args
def _make_side_position(self):
@cache.dynamic_func(suffix=self.name)
def side_position(args: self.SideArg, s: Sample):
trace_arg = self.field_trace.ElementEvalArg(args.base_arg, args.trace_arg)
return self.field_trace.eval_inner(trace_arg, s) + self.base.side_position(args.base_arg, s)
return side_position
def _make_side_deformation_gradient(self):
@cache.dynamic_func(suffix=self.name)
def side_deformation_gradient(args: self.SideArg, s: Sample):
base_def_grad = self.base.side_deformation_gradient(args.base_arg, s)
trace_arg = self.field_trace.ElementEvalArg(args.base_arg, args.trace_arg)
Du = self.field_trace.eval_grad_inner(trace_arg, s)
return base_def_grad + Du * base_def_grad
return side_deformation_gradient
def _make_side_inner_inverse_deformation_gradient(self):
@cache.dynamic_func(suffix=self.name)
def side_inner_inverse_deformation_gradient(args: self.SideArg, s: Sample):
cell_index = self.side_inner_cell_index(args, s.element_index)
cell_coords = self.side_inner_cell_coords(args, s.element_index, s.element_coords)
cell_arg = self.side_to_cell_arg(args)
return self.cell_inverse_deformation_gradient(cell_arg, make_free_sample(cell_index, cell_coords))
def _make_side_outer_inverse_deformation_gradient(self):
@cache.dynamic_func(suffix=self.name)
def side_outer_inverse_deformation_gradient(args: self.SideArg, s: Sample):
cell_index = self.side_outer_cell_index(args, s.element_index)
cell_coords = self.side_outer_cell_coords(args, s.element_index, s.element_coords)
cell_arg = self.side_to_cell_arg(args)
return self.cell_inverse_deformation_gradient(cell_arg, make_free_sample(cell_index, cell_coords))
@wp.func
def _side_measure(F: wp.vec2):
return wp.length(F)
@wp.func
def _side_measure(F: _mat32):
Fcross = wp.vec3(
F[1, 0] * F[2, 1] - F[2, 0] * F[1, 1],
F[2, 0] * F[0, 1] - F[0, 0] * F[2, 1],
F[0, 0] * F[1, 1] - F[1, 0] * F[0, 1],
)
return wp.length(Fcross)
@wp.func
def _side_normal(F: wp.vec2):
return wp.normalize(wp.vec2(-F[1], F[0]))
@wp.func
def _side_normal(F: _mat32):
Fcross = wp.vec3(
F[1, 0] * F[2, 1] - F[2, 0] * F[1, 1],
F[2, 0] * F[0, 1] - F[0, 0] * F[2, 1],
F[0, 0] * F[1, 1] - F[1, 0] * F[0, 1],
)
return wp.normalize(Fcross)
def _make_side_measure(self):
REF_MEASURE = wp.constant(self.reference_side().measure())
@cache.dynamic_func(suffix=self.name)
def side_measure(args: self.SideArg, s: Sample):
F = self.side_deformation_gradient(args, s)
return DeformedGeometry._side_measure(F) * REF_MEASURE
return side_measure
def _make_side_measure_ratio(self):
@cache.dynamic_func(suffix=self.name)
def side_measure_ratio(args: self.SideArg, s: Sample):
inner = self.side_inner_cell_index(args, s.element_index)
outer = self.side_outer_cell_index(args, s.element_index)
inner_coords = self.side_inner_cell_coords(args, s.element_index, s.element_coords)
outer_coords = self.side_outer_cell_coords(args, s.element_index, s.element_coords)
cell_arg = self.side_to_cell_arg(args)
return self.side_measure(args, s) / wp.min(
self.cell_measure(cell_arg, make_free_sample(inner, inner_coords)),
self.cell_measure(cell_arg, make_free_sample(outer, outer_coords)),
)
return side_measure_ratio
def _make_side_normal(self):
@cache.dynamic_func(suffix=self.name)
def side_normal(args: self.SideArg, s: Sample):
F = self.side_deformation_gradient(args, s)
return DeformedGeometry._side_normal(F)
return side_normal
def _make_side_inner_cell_index(self):
@cache.dynamic_func(suffix=self.name)
def side_inner_cell_index(args: self.SideArg, side_index: ElementIndex):
return self.base.side_inner_cell_index(args.base_arg, side_index)
return side_inner_cell_index
def _make_side_outer_cell_index(self):
@cache.dynamic_func(suffix=self.name)
def side_outer_cell_index(args: self.SideArg, side_index: ElementIndex):
return self.base.side_outer_cell_index(args.base_arg, side_index)
return side_outer_cell_index
def _make_side_inner_cell_coords(self):
@cache.dynamic_func(suffix=self.name)
def side_inner_cell_coords(args: self.SideArg, side_index: ElementIndex, side_coords: Coords):
return self.base.side_inner_cell_coords(args.base_arg, side_index, side_coords)
return side_inner_cell_coords
def _make_side_outer_cell_coords(self):
@cache.dynamic_func(suffix=self.name)
def side_outer_cell_coords(args: self.SideArg, side_index: ElementIndex, side_coords: Coords):
return self.base.side_outer_cell_coords(args.base_arg, side_index, side_coords)
return side_outer_cell_coords
def _make_side_from_cell_coords(self):
@cache.dynamic_func(suffix=self.name)
def side_from_cell_coords(
args: self.SideArg,
side_index: ElementIndex,
cell_index: ElementIndex,
cell_coords: Coords,
):
return self.base.side_from_cell_coords(args.base_arg, side_index, cell_index, cell_coords)
return side_from_cell_coords
def _make_side_to_cell_arg(self):
@cache.dynamic_func(suffix=self.name)
def side_to_cell_arg(side_arg: self.SideArg):
return self.CellArg(self.base.side_to_cell_arg(side_arg.base_arg), side_arg.field_arg)
return side_to_cell_arg
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