380 lines
15 KiB
Python
380 lines
15 KiB
Python
"""
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Drawing-related methods for Grid class
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"""
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from typing import List, Optional, Union, Sequence, Callable
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import numpy # type: ignore
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from numpy import diff, floor, ceil, zeros, hstack, newaxis
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from float_raster import raster
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from . import GridError, Direction
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from ._helpers import is_scalar
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eps_callable_t = Callable[[numpy.ndarray, numpy.ndarray, numpy.ndarray], numpy.ndarray]
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def draw_polygons(self,
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surface_normal: Union[Direction, int],
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center: numpy.ndarray,
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polygons: Sequence[numpy.ndarray],
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thickness: float,
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eps: Union[Sequence[Union[float, eps_callable_t]], float, eps_callable_t],
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) -> None:
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"""
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Draw polygons on an axis-aligned plane.
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Args:
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surface_normal: Axis normal to the plane we're drawing on. Can be a `Direction` or
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integer in `range(3)`
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center: 3-element ndarray or list specifying an offset applied to all the polygons
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polygons: List of Nx2 or Nx3 ndarrays, each specifying the vertices of a polygon
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(non-closed, clockwise). If Nx3, the surface_normal coordinate is ignored. Each
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polygon must have at least 3 vertices.
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thickness: Thickness of the layer to draw
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eps: Value to draw with ('epsilon'). Can be scalar, callable, or a list
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of any of these (1 per grid). Callable values should take an ndarray the shape of the
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grid and return an ndarray of equal shape containing the eps value at the given x, y,
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and z (natural, not grid coordinates).
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Raises:
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GridError
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"""
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# Turn surface_normal into its integer representation
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if isinstance(surface_normal, Direction):
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surface_normal = surface_normal.value
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assert(isinstance(surface_normal, int))
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if surface_normal not in range(3):
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raise GridError('Invalid surface_normal direction')
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center = numpy.squeeze(center)
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# Check polygons, and remove redundant coordinates
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surface = numpy.delete(range(3), surface_normal)
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for i, polygon in enumerate(polygons):
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malformed = 'Malformed polygon: (%i)' % i
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if polygon.shape[1] not in (2, 3):
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raise GridError(malformed + 'must be a Nx2 or Nx3 ndarray')
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if polygon.shape[1] == 3:
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polygon = polygon[surface, :]
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if not polygon.shape[0] > 2:
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raise GridError(malformed + 'must consist of more than 2 points')
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if polygon.ndim > 2 and not numpy.unique(polygon[:, surface_normal]).size == 1:
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raise GridError(malformed + 'must be in plane with surface normal %s'
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% 'xyz'[surface_normal])
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# Broadcast eps where necessary
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if is_scalar(eps):
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eps = [eps] * len(self.grids)
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elif isinstance(eps, numpy.ndarray):
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raise GridError('ndarray not supported for eps')
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# ## Compute sub-domain of the grid occupied by polygons
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# 1) Compute outer bounds (bd) of polygons
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bd_2d_min = [0, 0]
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bd_2d_max = [0, 0]
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for polygon in polygons:
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bd_2d_min = numpy.minimum(bd_2d_min, polygon.min(axis=0))
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bd_2d_max = numpy.maximum(bd_2d_max, polygon.max(axis=0))
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bd_min = numpy.insert(bd_2d_min, surface_normal, -thickness / 2.0) + center
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bd_max = numpy.insert(bd_2d_max, surface_normal, +thickness / 2.0) + center
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# 2) Find indices (bdi) just outside bd elements
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buf = 2 # size of safety buffer
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# Use s_min and s_max with unshifted pos2ind to get absolute limits on
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# the indices the polygons might affect
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s_min = self.shifts.min(axis=0)
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s_max = self.shifts.max(axis=0)
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bdi_min = self.pos2ind(bd_min + s_min, None, round_ind=False, check_bounds=False) - buf
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bdi_max = self.pos2ind(bd_max + s_max, None, round_ind=False, check_bounds=False) + buf
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bdi_min = numpy.maximum(floor(bdi_min), 0).astype(int)
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bdi_max = numpy.minimum(ceil(bdi_max), self.shape - 1).astype(int)
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# 3) Adjust polygons for center
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polygons = [poly + center[surface] for poly in polygons]
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# ## Generate weighing function
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def to_3d(vector: numpy.ndarray, val: float = 0.0) -> numpy.ndarray:
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v_2d = numpy.array(vector, dtype=float)
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return numpy.insert(v_2d, surface_normal, (val,))
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# iterate over grids
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for i, grid in enumerate(self.grids):
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# ## Evaluate or expand eps[i]
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if callable(eps[i]):
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# meshgrid over the (shifted) domain
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domain = [self.shifted_xyz(i)[k][bdi_min[k]:bdi_max[k]+1] for k in range(3)]
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(x0, y0, z0) = numpy.meshgrid(*domain, indexing='ij')
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# evaluate on the meshgrid
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eps_i = eps[i](x0, y0, z0)
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if not numpy.isfinite(eps_i).all():
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raise GridError('Non-finite values in eps[%u]' % i)
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elif not is_scalar(eps[i]):
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raise GridError('Unsupported eps[{}]: {}'.format(i, type(eps[i])))
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else:
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# eps[i] is scalar non-callable
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eps_i = eps[i]
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w_xy = zeros((bdi_max - bdi_min + 1)[surface].astype(int))
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# Draw each polygon separately
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for polygon in polygons:
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# Get the boundaries of the polygon
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pbd_min = polygon.min(axis=0)
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pbd_max = polygon.max(axis=0)
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# Find indices in w_xy just outside polygon
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# using per-grid xy-weights (self.shifted_xyz())
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corner_min = self.pos2ind(to_3d(pbd_min), i,
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check_bounds=False)[surface].astype(int)
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corner_max = self.pos2ind(to_3d(pbd_max), i,
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check_bounds=False)[surface].astype(int)
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# Find indices in w_xy which are modified by polygon
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# First for the edge coordinates (+1 since we're indexing edges)
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edge_slices = [numpy.s_[i:f + 2] for i, f in zip(corner_min, corner_max)]
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# Then for the pixel centers (-bdi_min since we're
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# calculating weights within a subspace)
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centers_slice = tuple(numpy.s_[i:f + 1] for i, f in zip(corner_min - bdi_min[surface],
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corner_max - bdi_min[surface]))
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aa_x, aa_y = (self.shifted_exyz(i)[a][s] for a, s in zip(surface, edge_slices))
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w_xy[centers_slice] += raster(polygon.T, aa_x, aa_y)
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# Clamp overlapping polygons to 1
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w_xy = numpy.minimum(w_xy, 1.0)
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# 2) Generate weights in z-direction
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w_z = numpy.zeros(((bdi_max - bdi_min + 1)[surface_normal], ))
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def get_zi(offset, i=i, w_z=w_z):
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edges = self.shifted_exyz(i)[surface_normal]
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point = center[surface_normal] + offset
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grid_coord = numpy.digitize(point, edges) - 1
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w_coord = grid_coord - bdi_min[surface_normal]
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if w_coord < 0:
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w_coord = 0
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f = 0
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elif w_coord >= w_z.size:
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w_coord = w_z.size - 1
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f = 1
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else:
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dz = self.shifted_dxyz(i)[surface_normal][grid_coord]
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f = (point - edges[grid_coord]) / dz
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return f, w_coord
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zi_top_f, zi_top = get_zi(+thickness / 2.0)
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zi_bot_f, zi_bot = get_zi(-thickness / 2.0)
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w_z[zi_bot + 1:zi_top] = 1
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if zi_bot < zi_top:
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w_z[zi_top] = zi_top_f
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w_z[zi_bot] = 1 - zi_bot_f
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else:
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w_z[zi_bot] = zi_top_f - zi_bot_f
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# 3) Generate total weight function
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w = (w_xy[:, :, newaxis] * w_z).transpose(numpy.insert([0, 1], surface_normal, (2,)))
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# ## Modify the grid
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g_slice = (i,) + tuple(numpy.s_[bdi_min[a]:bdi_max[a] + 1] for a in range(3))
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self.grids[g_slice] = (1 - w) * self.grids[g_slice] + w * eps_i
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def draw_polygon(self,
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surface_normal: Union[Direction, int],
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center: numpy.ndarray,
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polygon: numpy.ndarray,
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thickness: float,
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eps: Union[Sequence[Union[float, eps_callable_t]], float, eps_callable_t],
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) -> None:
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"""
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Draw a polygon on an axis-aligned plane.
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Args:
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surface_normal: Axis normal to the plane we're drawing on. Can be a Direction or
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integer in range(3)
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center: 3-element ndarray or list specifying an offset applied to the polygon
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polygon: Nx2 or Nx3 ndarray specifying the vertices of a polygon (non-closed,
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clockwise). If Nx3, the surface_normal coordinate is ignored. Must have at
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least 3 vertices.
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thickness: Thickness of the layer to draw
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eps: Value to draw with ('epsilon'). See `draw_polygons()` for details.
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"""
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self.draw_polygons(surface_normal, center, [polygon], thickness, eps)
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def draw_slab(self,
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surface_normal: Union[Direction, int],
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center: numpy.ndarray,
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thickness: float,
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eps: Union[List[Union[float, eps_callable_t]], float, eps_callable_t],
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) -> None:
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"""
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Draw an axis-aligned infinite slab.
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Args:
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surface_normal: Axis normal to the plane we're drawing on. Can be a `Direction` or
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integer in `range(3)`
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center: Surface_normal coordinate at the center of the slab
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thickness: Thickness of the layer to draw
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eps: Value to draw with ('epsilon'). See `draw_polygons()` for details.
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"""
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# Turn surface_normal into its integer representation
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if isinstance(surface_normal, Direction):
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surface_normal = surface_normal.value
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if surface_normal not in range(3):
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raise GridError('Invalid surface_normal direction')
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if not is_scalar(center):
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center = numpy.squeeze(center)
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if len(center) == 3:
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center = center[surface_normal]
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else:
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raise GridError('Bad center: {}'.format(center))
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# Find center of slab
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center_shift = self.center
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center_shift[surface_normal] = center
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surface = numpy.delete(range(3), surface_normal)
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xyz_min = numpy.array([self.xyz[a][0] for a in range(3)], dtype=float)[surface]
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xyz_max = numpy.array([self.xyz[a][-1] for a in range(3)], dtype=float)[surface]
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dxyz = numpy.array([max(self.dxyz[i]) for i in surface], dtype=float)
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xyz_min -= 4 * dxyz
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xyz_max += 4 * dxyz
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p = numpy.array([[xyz_min[0], xyz_max[1]],
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[xyz_max[0], xyz_max[1]],
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[xyz_max[0], xyz_min[1]],
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[xyz_min[0], xyz_min[1]]], dtype=float)
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self.draw_polygon(surface_normal, center_shift, p, thickness, eps)
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def draw_cuboid(self,
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center: numpy.ndarray,
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dimensions: numpy.ndarray,
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eps: Union[List[Union[float, eps_callable_t]], float, eps_callable_t],
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) -> None:
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"""
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Draw an axis-aligned cuboid
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Args:
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center: 3-element ndarray or list specifying the cuboid's center
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dimensions: 3-element list or ndarray containing the x, y, and z edge-to-edge
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sizes of the cuboid
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eps: Value to draw with ('epsilon'). See `draw_polygons()` for details.
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"""
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p = numpy.array([[-dimensions[0], +dimensions[1]],
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[+dimensions[0], +dimensions[1]],
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[+dimensions[0], -dimensions[1]],
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[-dimensions[0], -dimensions[1]]], dtype=float) / 2.0
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thickness = dimensions[2]
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self.draw_polygon(Direction.z, center, p, thickness, eps)
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def draw_cylinder(self,
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surface_normal: Union[Direction, int],
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center: numpy.ndarray,
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radius: float,
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thickness: float,
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num_points: int,
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eps: Union[List[Union[float, eps_callable_t]], float, eps_callable_t],
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) -> None:
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"""
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Draw an axis-aligned cylinder. Approximated by a num_points-gon
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Args:
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surface_normal: Axis normal to the plane we're drawing on. Can be a `Direction` or
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integer in `range(3)`
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center: 3-element ndarray or list specifying the cylinder's center
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radius: cylinder radius
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thickness: Thickness of the layer to draw
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num_points: The circle is approximated by a polygon with `num_points` vertices
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eps: Value to draw with ('epsilon'). See `draw_polygons()` for details.
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"""
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theta = numpy.linspace(0, 2*numpy.pi, num_points, endpoint=False)
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x = radius * numpy.sin(theta)
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y = radius * numpy.cos(theta)
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polygon = hstack((x[:, newaxis], y[:, newaxis]))
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self.draw_polygon(surface_normal, center, polygon, thickness, eps)
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def draw_extrude_rectangle(self,
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rectangle: numpy.ndarray,
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direction: Union[Direction, int],
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polarity: int,
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distance: float,
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) -> None:
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"""
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Extrude a rectangle of a previously-drawn structure along an axis.
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Args:
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rectangle: 2x3 ndarray or list specifying the rectangle's corners
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direction: Direction to extrude in. Direction enum or int in range(3)
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polarity: +1 or -1, direction along axis to extrude in
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distance: How far to extrude
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"""
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# Turn extrude_direction into its integer representation
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if isinstance(direction, Direction):
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direction = direction.value
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assert(isinstance(direction, int))
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s = numpy.sign(polarity)
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rectangle = numpy.array(rectangle, dtype=float)
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if s == 0:
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raise GridError('0 is not a valid polarity')
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if direction not in range(3):
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raise GridError('Invalid direction: {}'.format(direction))
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if rectangle[0, direction] != rectangle[1, direction]:
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raise GridError('Rectangle entries along extrusion direction do not match.')
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center = rectangle.sum(axis=0) / 2.0
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center[direction] += s * distance / 2.0
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surface = numpy.delete(range(3), direction)
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dim = numpy.fabs(diff(rectangle, axis=0).T)[surface]
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p = numpy.vstack((numpy.array([-1, -1, 1, 1], dtype=float) * dim[0]/2.0,
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numpy.array([-1, 1, 1, -1], dtype=float) * dim[1]/2.0)).T
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thickness = distance
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eps_func = []
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for i, grid in enumerate(self.grids):
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z = self.pos2ind(rectangle[0, :], i, round_ind=False, check_bounds=False)[direction]
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ind = [int(floor(z)) if i == direction else slice(None) for i in range(3)]
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fpart = z - floor(z)
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mult = [1-fpart, fpart][::s] # reverses if s negative
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eps = mult[0] * grid[ind]
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ind[direction] += 1
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eps += mult[1] * grid[ind]
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def f_eps(xs, ys, zs, i=i, eps=eps) -> numpy.ndarray:
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# transform from natural position to index
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xyzi = numpy.array([self.pos2ind(qrs, which_shifts=i)
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for qrs in zip(xs.flat, ys.flat, zs.flat)], dtype=int)
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# reshape to original shape and keep only in-plane components
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qi, ri = (numpy.reshape(xyzi[:, k], xs.shape) for k in surface)
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return eps[qi, ri]
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eps_func.append(f_eps)
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self.draw_polygon(direction, center, p, thickness, eps_func)
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