538 lines
18 KiB
Python
538 lines
18 KiB
Python
# Copyright (c) 2018-2024 Manfred Moitzi
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# License: MIT License
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from __future__ import annotations
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from typing import TYPE_CHECKING, Iterable, Sequence, Iterator, Optional
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import math
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import numpy as np
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from ezdxf.math import Vec2, UVec
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from .bbox import BoundingBox2d
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from .construct2d import enclosing_angles
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from .circle import ConstructionCircle
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from .line import ConstructionRay, ConstructionLine
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from .ucs import UCS
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if TYPE_CHECKING:
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from ezdxf.entities import Arc
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from ezdxf.layouts import BaseLayout
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__all__ = ["ConstructionArc", "arc_chord_length", "arc_segment_count"]
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QUARTER_ANGLES = [0, math.pi * 0.5, math.pi, math.pi * 1.5]
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class ConstructionArc:
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"""Construction tool for 2D arcs.
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:class:`ConstructionArc` represents a 2D arc in the xy-plane, use an
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:class:`UCS` to place a DXF :class:`~ezdxf.entities.Arc` entity in 3D space,
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see method :meth:`add_to_layout`.
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Implements the 2D transformation tools: :meth:`translate`,
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:meth:`scale_uniform` and :meth:`rotate_z`
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Args:
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center: center point as :class:`Vec2` compatible object
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radius: radius
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start_angle: start angle in degrees
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end_angle: end angle in degrees
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is_counter_clockwise: swaps start- and end angle if ``False``
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"""
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def __init__(
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self,
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center: UVec = (0, 0),
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radius: float = 1.0,
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start_angle: float = 0.0,
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end_angle: float = 360.0,
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is_counter_clockwise: Optional[bool] = True,
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):
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self.center = Vec2(center)
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self.radius = radius
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if is_counter_clockwise:
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self.start_angle = start_angle
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self.end_angle = end_angle
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else:
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self.start_angle = end_angle
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self.end_angle = start_angle
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@property
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def start_point(self) -> Vec2:
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"""start point of arc as :class:`Vec2`."""
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return self.center + Vec2.from_deg_angle(self.start_angle, self.radius)
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@property
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def end_point(self) -> Vec2:
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"""end point of arc as :class:`Vec2`."""
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return self.center + Vec2.from_deg_angle(self.end_angle, self.radius)
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@property
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def is_passing_zero(self) -> bool:
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"""Returns ``True`` if the arc passes the x-axis (== 0 degree)."""
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return self.start_angle > self.end_angle
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@property
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def circle(self) -> ConstructionCircle:
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return ConstructionCircle(self.center, self.radius)
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@property
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def bounding_box(self) -> BoundingBox2d:
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"""bounding box of arc as :class:`BoundingBox2d`."""
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bbox = BoundingBox2d((self.start_point, self.end_point))
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bbox.extend(self.main_axis_points())
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return bbox
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def angles(self, num: int) -> Iterable[float]:
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"""Returns `num` angles from start- to end angle in degrees in
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counter-clockwise order.
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All angles are normalized in the range from [0, 360).
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"""
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if num < 2:
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raise ValueError("num >= 2")
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start: float = self.start_angle % 360
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stop: float = self.end_angle % 360
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if stop <= start:
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stop += 360
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for angle in np.linspace(start, stop, num=num, endpoint=True):
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yield angle % 360
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@property
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def angle_span(self) -> float:
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"""Returns angle span of arc from start- to end param."""
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end: float = self.end_angle
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if end < self.start_angle:
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end += 360.0
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return end - self.start_angle
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def vertices(self, a: Iterable[float]) -> Iterable[Vec2]:
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"""Yields vertices on arc for angles in iterable `a` in WCS as location
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vectors.
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Args:
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a: angles in the range from 0 to 360 in degrees, arc goes
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counter clockwise around the z-axis, WCS x-axis = 0 deg.
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"""
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center = self.center
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radius = self.radius
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for angle in a:
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yield center + Vec2.from_deg_angle(angle, radius)
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def flattening(self, sagitta: float) -> Iterable[Vec2]:
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"""Approximate the arc by vertices in WCS, argument `sagitta` is the
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max. distance from the center of an arc segment to the center of its
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chord.
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"""
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radius: float = abs(self.radius)
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if radius > 0:
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start: float = self.start_angle
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stop: float = self.end_angle
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if math.isclose(start, stop):
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return
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start %= 360
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stop %= 360
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if stop <= start:
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stop += 360
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angle_span: float = math.radians(stop - start)
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count = arc_segment_count(radius, angle_span, sagitta)
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yield from self.vertices(np.linspace(start, stop, count + 1))
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def tangents(self, a: Iterable[float]) -> Iterable[Vec2]:
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"""Yields tangents on arc for angles in iterable `a` in WCS as
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direction vectors.
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Args:
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a: angles in the range from 0 to 360 in degrees, arc goes
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counter-clockwise around the z-axis, WCS x-axis = 0 deg.
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"""
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for angle in a:
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r: float = math.radians(angle)
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yield Vec2((-math.sin(r), math.cos(r)))
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def main_axis_points(self) -> Iterator[Vec2]:
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center: Vec2 = self.center
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radius: float = self.radius
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start: float = math.radians(self.start_angle)
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end: float = math.radians(self.end_angle)
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for angle in QUARTER_ANGLES:
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if enclosing_angles(angle, start, end):
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yield center + Vec2.from_angle(angle, radius)
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def translate(self, dx: float, dy: float) -> ConstructionArc:
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"""Move arc about `dx` in x-axis and about `dy` in y-axis, returns
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`self` (floating interface).
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Args:
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dx: translation in x-axis
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dy: translation in y-axis
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"""
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self.center += Vec2(dx, dy)
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return self
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def scale_uniform(self, s: float) -> ConstructionArc:
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"""Scale arc inplace uniform about `s` in x- and y-axis, returns
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`self` (floating interface).
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"""
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self.radius *= float(s)
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return self
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def rotate_z(self, angle: float) -> ConstructionArc:
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"""Rotate arc inplace about z-axis, returns `self`
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(floating interface).
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Args:
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angle: rotation angle in degrees
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"""
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self.start_angle += angle
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self.end_angle += angle
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return self
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@property
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def start_angle_rad(self) -> float:
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"""Returns the start angle in radians."""
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return math.radians(self.start_angle)
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@property
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def end_angle_rad(self) -> float:
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"""Returns the end angle in radians."""
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return math.radians(self.end_angle)
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@staticmethod
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def validate_start_and_end_point(
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start_point: UVec, end_point: UVec
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) -> tuple[Vec2, Vec2]:
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start_point = Vec2(start_point)
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end_point = Vec2(end_point)
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if start_point == end_point:
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raise ValueError(
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"Start- and end point have to be different points."
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)
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return start_point, end_point
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@classmethod
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def from_2p_angle(
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cls,
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start_point: UVec,
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end_point: UVec,
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angle: float,
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ccw: bool = True,
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) -> ConstructionArc:
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"""Create arc from two points and enclosing angle. Additional
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precondition: arc goes by default in counter-clockwise orientation from
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`start_point` to `end_point`, can be changed by `ccw` = ``False``.
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Args:
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start_point: start point as :class:`Vec2` compatible object
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end_point: end point as :class:`Vec2` compatible object
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angle: enclosing angle in degrees
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ccw: counter-clockwise direction if ``True``
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"""
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_start_point, _end_point = cls.validate_start_and_end_point(
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start_point, end_point
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)
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angle = math.radians(angle)
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if angle == 0:
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raise ValueError("Angle can not be 0.")
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if ccw is False:
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_start_point, _end_point = _end_point, _start_point
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alpha2: float = angle / 2.0
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distance: float = _end_point.distance(_start_point)
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distance2: float = distance / 2.0
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radius: float = distance2 / math.sin(alpha2)
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height: float = distance2 / math.tan(alpha2)
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mid_point: Vec2 = _end_point.lerp(_start_point, factor=0.5)
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distance_vector: Vec2 = _end_point - _start_point
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height_vector: Vec2 = distance_vector.orthogonal().normalize(height)
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center: Vec2 = mid_point + height_vector
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return ConstructionArc(
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center=center,
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radius=radius,
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start_angle=(_start_point - center).angle_deg,
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end_angle=(_end_point - center).angle_deg,
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is_counter_clockwise=True,
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)
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@classmethod
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def from_2p_radius(
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cls,
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start_point: UVec,
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end_point: UVec,
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radius: float,
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ccw: bool = True,
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center_is_left: bool = True,
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) -> ConstructionArc:
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"""Create arc from two points and arc radius.
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Additional precondition: arc goes by default in counter-clockwise
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orientation from `start_point` to `end_point` can be changed
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by `ccw` = ``False``.
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The parameter `center_is_left` defines if the center of the arc is
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left or right of the line from `start_point` to `end_point`.
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Parameter `ccw` = ``False`` swaps start- and end point, which also
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inverts the meaning of ``center_is_left``.
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Args:
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start_point: start point as :class:`Vec2` compatible object
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end_point: end point as :class:`Vec2` compatible object
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radius: arc radius
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ccw: counter-clockwise direction if ``True``
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center_is_left: center point of arc is left of line from start- to
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end point if ``True``
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"""
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_start_point, _end_point = cls.validate_start_and_end_point(
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start_point, end_point
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)
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radius = float(radius)
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if radius <= 0:
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raise ValueError("Radius has to be > 0.")
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if ccw is False:
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_start_point, _end_point = _end_point, _start_point
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mid_point: Vec2 = _end_point.lerp(_start_point, factor=0.5)
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distance: float = _end_point.distance(_start_point)
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distance2: float = distance / 2.0
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height: float = math.sqrt(radius ** 2 - distance2 ** 2)
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center: Vec2 = mid_point + (_end_point - _start_point).orthogonal(
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ccw=center_is_left
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).normalize(height)
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return ConstructionArc(
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center=center,
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radius=radius,
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start_angle=(_start_point - center).angle_deg,
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end_angle=(_end_point - center).angle_deg,
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is_counter_clockwise=True,
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)
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@classmethod
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def from_3p(
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cls,
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start_point: UVec,
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end_point: UVec,
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def_point: UVec,
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ccw: bool = True,
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) -> ConstructionArc:
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"""Create arc from three points.
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Additional precondition: arc goes in counter-clockwise
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orientation from `start_point` to `end_point`.
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Args:
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start_point: start point as :class:`Vec2` compatible object
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end_point: end point as :class:`Vec2` compatible object
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def_point: additional definition point as :class:`Vec2` compatible
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object
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ccw: counter-clockwise direction if ``True``
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"""
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start_point, end_point = cls.validate_start_and_end_point(
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start_point, end_point
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)
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def_point = Vec2(def_point)
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if def_point == start_point or def_point == end_point:
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raise ValueError(
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"def_point has to be different to start- and end point"
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)
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circle = ConstructionCircle.from_3p(start_point, end_point, def_point)
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center = Vec2(circle.center)
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return ConstructionArc(
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center=center,
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radius=circle.radius,
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start_angle=(start_point - center).angle_deg,
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end_angle=(end_point - center).angle_deg,
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is_counter_clockwise=ccw,
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)
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def add_to_layout(
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self, layout: BaseLayout, ucs: Optional[UCS] = None, dxfattribs=None
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) -> Arc:
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"""Add arc as DXF :class:`~ezdxf.entities.Arc` entity to a layout.
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Supports 3D arcs by using an :ref:`UCS`. An :class:`ConstructionArc` is
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always defined in the xy-plane, but by using an arbitrary UCS, the arc
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can be placed in 3D space, automatically OCS transformation included.
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Args:
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layout: destination layout as :class:`~ezdxf.layouts.BaseLayout`
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object
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ucs: place arc in 3D space by :class:`~ezdxf.math.UCS` object
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dxfattribs: additional DXF attributes for the ARC entity
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"""
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arc = layout.add_arc(
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center=self.center,
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radius=self.radius,
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start_angle=self.start_angle,
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end_angle=self.end_angle,
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dxfattribs=dxfattribs,
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)
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return arc if ucs is None else arc.transform(ucs.matrix)
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def intersect_ray(
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self, ray: ConstructionRay, abs_tol: float = 1e-10
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) -> Sequence[Vec2]:
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"""Returns intersection points of arc and `ray` as sequence of
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:class:`Vec2` objects.
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Args:
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ray: intersection ray
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abs_tol: absolute tolerance for tests (e.g. test for tangents)
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Returns:
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tuple of :class:`Vec2` objects
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=========== ==================================
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tuple size Description
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=========== ==================================
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0 no intersection
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1 line intersects or touches the arc at one point
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2 line intersects the arc at two points
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=========== ==================================
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"""
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assert isinstance(ray, ConstructionRay)
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return [
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point
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for point in self.circle.intersect_ray(ray, abs_tol)
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if self._is_point_in_arc_range(point)
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]
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def intersect_line(
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self, line: ConstructionLine, abs_tol: float = 1e-10
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) -> Sequence[Vec2]:
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"""Returns intersection points of arc and `line` as sequence of
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:class:`Vec2` objects.
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Args:
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line: intersection line
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abs_tol: absolute tolerance for tests (e.g. test for tangents)
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Returns:
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tuple of :class:`Vec2` objects
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=========== ==================================
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tuple size Description
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=========== ==================================
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0 no intersection
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1 line intersects or touches the arc at one point
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2 line intersects the arc at two points
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=========== ==================================
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"""
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assert isinstance(line, ConstructionLine)
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return [
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point
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for point in self.circle.intersect_line(line, abs_tol)
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if self._is_point_in_arc_range(point)
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]
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def intersect_circle(
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self, circle: ConstructionCircle, abs_tol: float = 1e-10
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) -> Sequence[Vec2]:
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"""Returns intersection points of arc and `circle` as sequence of
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:class:`Vec2` objects.
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Args:
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circle: intersection circle
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abs_tol: absolute tolerance for tests
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Returns:
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tuple of :class:`Vec2` objects
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=========== ==================================
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tuple size Description
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=========== ==================================
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0 no intersection
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1 circle intersects or touches the arc at one point
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2 circle intersects the arc at two points
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=========== ==================================
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"""
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assert isinstance(circle, ConstructionCircle)
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return [
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point
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for point in self.circle.intersect_circle(circle, abs_tol)
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if self._is_point_in_arc_range(point)
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]
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def intersect_arc(
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self, other: ConstructionArc, abs_tol: float = 1e-10
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) -> Sequence[Vec2]:
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"""Returns intersection points of two arcs as sequence of
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:class:`Vec2` objects.
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Args:
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other: other intersection arc
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abs_tol: absolute tolerance for tests
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Returns:
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tuple of :class:`Vec2` objects
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=========== ==================================
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tuple size Description
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=========== ==================================
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0 no intersection
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1 other arc intersects or touches the arc at one point
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2 other arc intersects the arc at two points
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=========== ==================================
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"""
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assert isinstance(other, ConstructionArc)
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return [
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point
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for point in self.circle.intersect_circle(other.circle, abs_tol)
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if self._is_point_in_arc_range(point)
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and other._is_point_in_arc_range(point)
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]
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def _is_point_in_arc_range(self, point: Vec2) -> bool:
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# The point has to be on the circle defined by the arc, this is not
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# tested here! Helper tools to check intersections.
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start: float = self.start_angle % 360.0
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end: float = self.end_angle % 360.0
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angle: float = (point - self.center).angle_deg % 360.0
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if start > end: # arc passes 0 degree
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return angle >= start or angle <= end
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return start <= angle <= end
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def arc_chord_length(radius: float, sagitta: float) -> float:
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"""Returns the chord length for an arc defined by `radius` and
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the `sagitta`_.
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Args:
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radius: arc radius
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sagitta: distance from the center of the arc to the center of its base
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"""
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return 2.0 * math.sqrt(2.0 * radius * sagitta - sagitta * sagitta)
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def arc_segment_count(radius: float, angle: float, sagitta: float) -> int:
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"""Returns the count of required segments for the approximation
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of an arc for a given maximum `sagitta`_.
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Args:
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radius: arc radius
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angle: angle span of the arc in radians
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sagitta: max. distance from the center of an arc segment to the
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center of its chord
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"""
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chord_length: float = arc_chord_length(radius, sagitta)
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alpha: float = math.asin(chord_length / 2.0 / radius) * 2.0
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return math.ceil(angle / alpha)
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