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426 lines
15 KiB
Python
426 lines
15 KiB
Python
from typing import Sequence, Any, cast
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import copy
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from enum import Enum
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import numpy
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from numpy import pi, inf
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from numpy.typing import NDArray, ArrayLike
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from . import Shape, normalized_shape_tuple, Polygon, Circle
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from ..error import PatternError
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from ..repetition import Repetition
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from ..utils import is_scalar, rotation_matrix_2d
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from ..utils import remove_colinear_vertices, remove_duplicate_vertices, annotations_t
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class PathCap(Enum):
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Flush = 0 # Path ends at final vertices
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Circle = 1 # Path extends past final vertices with a semicircle of radius width/2
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Square = 2 # Path extends past final vertices with a width-by-width/2 rectangle
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SquareCustom = 4 # Path extends past final vertices with a rectangle of length
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# # defined by path.cap_extensions
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class Path(Shape):
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"""
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A path, consisting of a bunch of vertices (Nx2 ndarray), a width, an end-cap shape,
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and an offset.
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Note that the setter for `Path.vertices` may (but may not) create a copy of the
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passed vertex coordinates. See `numpy.array(..., copy=False)` for details.
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A normalized_form(...) is available, but can be quite slow with lots of vertices.
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"""
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__slots__ = (
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'_vertices', '_width', '_cap', '_cap_extensions',
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# Inherited
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'_offset', '_repetition', '_annotations',
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)
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_vertices: NDArray[numpy.float64]
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_width: float
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_cap: PathCap
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_cap_extensions: NDArray[numpy.float64] | None
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Cap = PathCap
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# width property
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@property
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def width(self) -> float:
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"""
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Path width (float, >= 0)
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"""
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return self._width
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@width.setter
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def width(self, val: float) -> None:
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if not is_scalar(val):
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raise PatternError('Width must be a scalar')
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if not val >= 0:
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raise PatternError('Width must be non-negative')
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self._width = val
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# cap property
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@property
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def cap(self) -> PathCap:
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"""
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Path end-cap
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Note that `cap_extensions` will be reset to default values if
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`cap` is changed away from `PathCap.SquareCustom`.
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"""
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return self._cap
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@cap.setter
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def cap(self, val: PathCap) -> None:
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self._cap = PathCap(val)
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if self.cap != PathCap.SquareCustom:
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self.cap_extensions = None
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elif self.cap_extensions is None:
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# just got set to SquareCustom
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self.cap_extensions = numpy.zeros(2)
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# cap_extensions property
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@property
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def cap_extensions(self) -> Any | None: # mypy#3004 NDArray[numpy.float64]]:
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"""
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Path end-cap extension
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Note that `cap_extensions` will be reset to default values if
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`cap` is changed away from `PathCap.SquareCustom`.
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Returns:
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2-element ndarray or `None`
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"""
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return self._cap_extensions
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@cap_extensions.setter
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def cap_extensions(self, vals: ArrayLike | None) -> None:
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custom_caps = (PathCap.SquareCustom,)
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if self.cap in custom_caps:
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if vals is None:
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raise Exception('Tried to set cap extensions to None on path with custom cap type')
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self._cap_extensions = numpy.array(vals, dtype=float)
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else:
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if vals is not None:
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raise Exception('Tried to set custom cap extensions on path with non-custom cap type')
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self._cap_extensions = vals
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# vertices property
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@property
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def vertices(self) -> Any: # mypy#3004 NDArray[numpy.float64]]:
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"""
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Vertices of the path (Nx2 ndarray: `[[x0, y0], [x1, y1], ...]`
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When setting, note that a copy of the provided vertices may or may not be made,
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following the rules from `numpy.array(.., copy=False)`.
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"""
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return self._vertices
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@vertices.setter
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def vertices(self, val: ArrayLike) -> None:
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val = numpy.array(val, dtype=float)
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if len(val.shape) < 2 or val.shape[1] != 2:
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raise PatternError('Vertices must be an Nx2 array')
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if val.shape[0] < 2:
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raise PatternError('Must have at least 2 vertices (Nx2 where N>1)')
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self._vertices = val
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# xs property
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@property
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def xs(self) -> NDArray[numpy.float64]:
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"""
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All vertex x coords as a 1D ndarray
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"""
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return self.vertices[:, 0]
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@xs.setter
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def xs(self, val: ArrayLike) -> None:
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val = numpy.array(val, dtype=float).flatten()
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if val.size != self.vertices.shape[0]:
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raise PatternError('Wrong number of vertices')
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self.vertices[:, 0] = val
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# ys property
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@property
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def ys(self) -> NDArray[numpy.float64]:
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"""
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All vertex y coords as a 1D ndarray
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"""
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return self.vertices[:, 1]
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@ys.setter
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def ys(self, val: ArrayLike) -> None:
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val = numpy.array(val, dtype=float).flatten()
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if val.size != self.vertices.shape[0]:
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raise PatternError('Wrong number of vertices')
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self.vertices[:, 1] = val
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def __init__(
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self,
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vertices: ArrayLike,
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width: float = 0.0,
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*,
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cap: PathCap = PathCap.Flush,
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cap_extensions: ArrayLike | None = None,
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offset: ArrayLike = (0.0, 0.0),
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rotation: float = 0,
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repetition: Repetition | None = None,
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annotations: annotations_t | None = None,
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raw: bool = False,
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) -> None:
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self._cap_extensions = None # Since .cap setter might access it
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if raw:
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assert isinstance(vertices, numpy.ndarray)
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assert isinstance(offset, numpy.ndarray)
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assert isinstance(cap_extensions, numpy.ndarray) or cap_extensions is None
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self._vertices = vertices
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self._offset = offset
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self._repetition = repetition
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self._annotations = annotations if annotations is not None else {}
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self._width = width
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self._cap = cap
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self._cap_extensions = cap_extensions
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else:
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self.vertices = vertices
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self.offset = offset
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self.repetition = repetition
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self.annotations = annotations if annotations is not None else {}
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self.width = width
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self.cap = cap
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self.cap_extensions = cap_extensions
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self.rotate(rotation)
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def __deepcopy__(self, memo: dict | None = None) -> 'Path':
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memo = {} if memo is None else memo
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new = copy.copy(self)
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new._offset = self._offset.copy()
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new._vertices = self._vertices.copy()
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new._cap = copy.deepcopy(self._cap, memo)
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new._cap_extensions = copy.deepcopy(self._cap_extensions, memo)
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new._annotations = copy.deepcopy(self._annotations)
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return new
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@staticmethod
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def travel(
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travel_pairs: Sequence[tuple[float, float]],
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width: float = 0.0,
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cap: PathCap = PathCap.Flush,
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cap_extensions: tuple[float, float] | None = None,
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offset: ArrayLike = (0.0, 0.0),
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rotation: float = 0,
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) -> 'Path':
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"""
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Build a path by specifying the turn angles and travel distances
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rather than setting the distances directly.
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Args:
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travel_pairs: A list of (angle, distance) pairs that define
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the path. Angles are counterclockwise, in radians, and are relative
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to the previous segment's direction (the initial angle is relative
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to the +x axis).
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width: Path width, default `0`
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cap: End-cap type, default `Path.Cap.Flush` (no end-cap)
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cap_extensions: End-cap extension distances, when using `Path.Cap.CustomSquare`.
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Default `(0, 0)` or `None`, depending on cap type
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offset: Offset, default `(0, 0)`
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rotation: Rotation counterclockwise, in radians. Default `0`
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Returns:
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The resulting Path object
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"""
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# TODO: Path.travel() needs testing
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direction = numpy.array([1, 0])
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verts = [numpy.zeros(2)]
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for angle, distance in travel_pairs:
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direction = numpy.dot(rotation_matrix_2d(angle), direction.T).T
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verts.append(verts[-1] + direction * distance)
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return Path(vertices=verts, width=width, cap=cap, cap_extensions=cap_extensions,
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offset=offset, rotation=rotation)
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def to_polygons(
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self,
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num_vertices: int | None = None,
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max_arclen: float | None = None,
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) -> list['Polygon']:
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extensions = self._calculate_cap_extensions()
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v = remove_colinear_vertices(self.vertices, closed_path=False)
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dv = numpy.diff(v, axis=0)
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dvdir = dv / numpy.sqrt((dv * dv).sum(axis=1))[:, None]
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if self.width == 0:
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verts = numpy.vstack((v, v[::-1]))
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return [Polygon(offset=self.offset, vertices=verts)]
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perp = dvdir[:, ::-1] * [[1, -1]] * self.width / 2
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# add extensions
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if (extensions != 0).any():
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v[0] -= dvdir[0] * extensions[0]
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v[-1] += dvdir[-1] * extensions[1]
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dv = numpy.diff(v, axis=0) # recalculate dv; dvdir and perp should stay the same
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# Find intersections of expanded sides
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As = numpy.stack((dv[:-1], -dv[1:]), axis=2)
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bs = v[1:-1] - v[:-2] + perp[1:] - perp[:-1]
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ds = v[1:-1] - v[:-2] - perp[1:] + perp[:-1]
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rp = numpy.linalg.solve(As, bs)[:, 0, None]
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rn = numpy.linalg.solve(As, ds)[:, 0, None]
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intersection_p = v[:-2] + rp * dv[:-1] + perp[:-1]
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intersection_n = v[:-2] + rn * dv[:-1] - perp[:-1]
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towards_perp = (dv[1:] * perp[:-1]).sum(axis=1) > 0 # path bends towards previous perp?
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# straight = (dv[1:] * perp[:-1]).sum(axis=1) == 0 # path is straight
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acute = (dv[1:] * dv[:-1]).sum(axis=1) < 0 # angle is acute?
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# Build vertices
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o0 = [v[0] + perp[0]]
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o1 = [v[0] - perp[0]]
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for i in range(dv.shape[0] - 1):
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if towards_perp[i]:
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o0.append(intersection_p[i])
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if acute[i]:
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# Opposite is >270
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pt0 = v[i + 1] - perp[i + 0] + dvdir[i + 0] * self.width / 2
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pt1 = v[i + 1] - perp[i + 1] - dvdir[i + 1] * self.width / 2
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o1 += [pt0, pt1]
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else:
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o1.append(intersection_n[i])
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else:
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o1.append(intersection_n[i])
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if acute[i]:
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# > 270
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pt0 = v[i + 1] + perp[i + 0] + dvdir[i + 0] * self.width / 2
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pt1 = v[i + 1] + perp[i + 1] - dvdir[i + 1] * self.width / 2
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o0 += [pt0, pt1]
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else:
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o0.append(intersection_p[i])
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o0.append(v[-1] + perp[-1])
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o1.append(v[-1] - perp[-1])
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verts = numpy.vstack((o0, o1[::-1]))
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polys = [Polygon(offset=self.offset, vertices=verts)]
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if self.cap == PathCap.Circle:
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#for vert in v: # not sure if every vertex, or just ends?
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for vert in [v[0], v[-1]]:
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circ = Circle(offset=vert, radius=self.width / 2)
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polys += circ.to_polygons(num_vertices=num_vertices, max_arclen=max_arclen)
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return polys
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def get_bounds_single(self) -> NDArray[numpy.float64]:
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if self.cap == PathCap.Circle:
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bounds = self.offset + numpy.vstack((numpy.min(self.vertices, axis=0) - self.width / 2,
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numpy.max(self.vertices, axis=0) + self.width / 2))
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elif self.cap in (
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PathCap.Flush,
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PathCap.Square,
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PathCap.SquareCustom,
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):
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bounds = numpy.array([[+inf, +inf], [-inf, -inf]])
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polys = self.to_polygons()
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for poly in polys:
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poly_bounds = poly.get_bounds_single_nonempty()
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bounds[0, :] = numpy.minimum(bounds[0, :], poly_bounds[0, :])
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bounds[1, :] = numpy.maximum(bounds[1, :], poly_bounds[1, :])
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else:
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raise PatternError(f'get_bounds_single() not implemented for endcaps: {self.cap}')
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return bounds
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def rotate(self, theta: float) -> 'Path':
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if theta != 0:
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self.vertices = numpy.dot(rotation_matrix_2d(theta), self.vertices.T).T
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return self
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def mirror(self, axis: int = 0) -> 'Path':
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self.vertices[:, axis - 1] *= -1
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return self
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def scale_by(self, c: float) -> 'Path':
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self.vertices *= c
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self.width *= c
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return self
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def normalized_form(self, norm_value: float) -> normalized_shape_tuple:
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# Note: this function is going to be pretty slow for many-vertexed paths, relative to
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# other shapes
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offset = self.vertices.mean(axis=0) + self.offset
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zeroed_vertices = self.vertices - offset
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scale = zeroed_vertices.std()
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normed_vertices = zeroed_vertices / scale
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_, _, vertex_axis = numpy.linalg.svd(zeroed_vertices)
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rotation = numpy.arctan2(vertex_axis[0][1], vertex_axis[0][0]) % (2 * pi)
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rotated_vertices = numpy.vstack([numpy.dot(rotation_matrix_2d(-rotation), v)
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for v in normed_vertices])
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# Reorder the vertices so that the one with lowest x, then y, comes first.
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x_min = rotated_vertices[:, 0].argmin()
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if not is_scalar(x_min):
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y_min = rotated_vertices[x_min, 1].argmin()
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x_min = cast(Sequence, x_min)[y_min]
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reordered_vertices = numpy.roll(rotated_vertices, -x_min, axis=0)
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width0 = self.width / norm_value
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return ((type(self), reordered_vertices.data.tobytes(), width0, self.cap),
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(offset, scale / norm_value, rotation, False),
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lambda: Path(
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reordered_vertices * norm_value,
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width=self.width * norm_value,
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cap=self.cap,
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))
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def clean_vertices(self) -> 'Path':
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"""
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Removes duplicate, co-linear and otherwise redundant vertices.
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Returns:
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self
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"""
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self.remove_colinear_vertices()
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return self
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def remove_duplicate_vertices(self) -> 'Path':
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'''
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Removes all consecutive duplicate (repeated) vertices.
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Returns:
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self
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'''
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self.vertices = remove_duplicate_vertices(self.vertices, closed_path=False)
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return self
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def remove_colinear_vertices(self) -> 'Path':
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'''
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Removes consecutive co-linear vertices.
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Returns:
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self
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'''
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self.vertices = remove_colinear_vertices(self.vertices, closed_path=False)
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return self
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def _calculate_cap_extensions(self) -> NDArray[numpy.float64]:
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if self.cap == PathCap.Square:
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extensions = numpy.full(2, self.width / 2)
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elif self.cap == PathCap.SquareCustom:
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assert isinstance(self.cap_extensions, numpy.ndarray)
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extensions = self.cap_extensions
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else:
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# Flush or Circle
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extensions = numpy.zeros(2)
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return extensions
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def __repr__(self) -> str:
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centroid = self.offset + self.vertices.mean(axis=0)
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return f'<Path centroid {centroid} v{len(self.vertices)} w{self.width} c{self.cap}>'
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