315 lines
9.4 KiB
Python
315 lines
9.4 KiB
Python
from math import isclose
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from sympy import symbols, solve
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from loguru import logger
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from ..cgal_bindings.plane import Point_2, Segment_2, Line_2, squared_distance
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def point_maker(pre_point):
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if isinstance(pre_point, Point2D):
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return pre_point
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elif isinstance(pre_point, tuple):
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return Point2D(pre_point[0], pre_point[1])
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else:
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print(type(pre_point))
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raise ValueError("Invalid input for Point2D")
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class Shape2D(object):
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def __init__(self, **kwargs):
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self.color = kwargs.get("color", "white")
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class Point2D(Shape2D, Point_2):
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def __init__(self, x: float, y: float, **kwargs):
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Point_2.__init__(self, x, y)
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Shape2D.__init__(self, **kwargs)
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# 计算点到另一点的距离
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def distance_to_point(self, point):
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point = point_maker(point)
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return (squared_distance(self, point)) ** 0.5
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# 重载==运算符，判断两个Point2D实例是否为同一点
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def __eq__(self, other):
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self.point == point_maker(other)
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def __repr__(self):
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return f"Point2D(x: {self.x}, y: {self.y})"
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class Segment2D(Shape2D, Segment_2):
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def __init__(self, point1, point2, **kwargs):
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point1 = point_maker(point1)
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point2 = point_maker(point2)
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super(Shape2D, self).__init__(**kwargs)
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super(Segment_2, self).__init__(point1, point2)
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# 计算线段的长度
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def length(self):
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return self.squared_length() ** 0.5
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# 重载==运算符，判断两个Segment2D实例是否为同一条线段
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def __eq__(self, other) -> bool:
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return self == other
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# 重载`in`运算符，判断点是否在线段上
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def __contains__(self, point) -> bool:
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return self.has_on(point)
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# 重载`repr`方法，返回Segment2D的字符串表示
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def __repr__(self) -> str:
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return f"Segment2D({self.point1}, {self.point2})"
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# 线段的起点`source`
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@property
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def source(self):
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return self._source()
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# 线段的终点`target`
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@property
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def target(self):
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return self._target()
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# 直线类
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class Line(Shape2D, Line_2):
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def __init__(self, point1, point2, **kwargs):
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super(Line, self).__init__(**kwargs)
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self.point1 = point_maker(point1)
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self.point2 = point_maker(point2)
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if self.point1 == self.point2:
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raise ValueError("Invalid input for Line: point1 == point2")
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self._a = self.point2.y - self.point1.y
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self._b = self.point1.x - self.point2.x
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self._c = self.point2.x * self.point1.y - self.point1.x * self.point2.y
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if isclose(self.point1.x, self.point2.x):
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self._slope = float("inf")
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self._y_intercept = float("inf")
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else:
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self._slope = -self._a / self._b
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self._y_intercept = -self._c / self._b
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self._x, self._y = symbols("x y")
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self._expression = self._a * self._x + self._b * self._y + self._c
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self._length = (
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(self.point1.x - self.point2.x) ** 2 + (self.point1.y - self.point2.y) ** 2
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) ** 0.5
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def contains(self, point, allow_on_extended=False):
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""""""判断点`point`是否在线段上
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Args:
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point (Point2D or tuple): 需要判断的点
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allow_on_extended (bool, optional): 是否允许点在线段的延长线上. Defaults to False.
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Returns:
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_type_: boolean
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""""""
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point = point_maker(point)
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f = self.function
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if allow_on_extended:
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if isclose(self._b, 0.0):
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return isclose(point.x, self.point1.x)
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return isclose(f(point.x), point.y)
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if isclose(self._b, 0.0):
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return isclose(point.x, self.point1.x) and (
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point.y >= min(self.point1.y, self.point2.y)
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and point.y <= max(self.point1.y, self.point2.y)
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)
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return isclose(f(point.x), point.y) and (
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(
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point.x >= min(self.point1.x, self.point2.x)
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and point.x <= max(self.point1.x, self.point2.x)
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)
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)
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# 通过关键字`in`判断点是否在线段上
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def __contains__(self, point):
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return self.contains(point)
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# 计算点`point`到线段的垂足
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def foot_point(self, point):
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point = point_maker(point)
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if self.contains(point, allow_on_extended=True):
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return point
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else:
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denominator = self._a**2 + self._b**2
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x = (
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(self._b**2) * point.x
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- self._a * self._b * point.y
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- self._a * self._c
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) / denominator
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y = (
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(self._a**2) * point.y
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- self._a * self._b * point.x
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- self._b * self._c
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) / denominator
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return Point2D(x, y)
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# 计算点`point`到线段的距离
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def point_distance(self, point, is_to_line=False):
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point = point_maker(point)
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if self.contains(point):
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return 0
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else:
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dis_to_line = (
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abs(self._expression.evalf(subs={self._x: point.x, self._y: point.y}))
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/ (self._a**2 + self._b**2) ** 0.5
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)
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if is_to_line:
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return dis_to_line
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if self.foot_point(point) not in self:
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return min(
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self.point1.distance_to_point(point),
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self.point2.distance_to_point(point),
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)
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return dis_to_line
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# 该线段所在直线的纵截距
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@property
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def y_intercept(self):
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return self._y_intercept
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# 该线段的斜率
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@property
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def slope(self):
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return self._slope
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# 该线段所在直线的函数方程
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@property
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def function(self):
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def f(x):
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expr = self._expression.subs(self._x, x)
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res = solve(expr, self._y)
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if len(res) == 1:
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return res[0].evalf()
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else:
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return None
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return f
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# 该线段的函数式
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@property
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def expression(self):
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return f"{str(self._expression)} = 0"
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@property
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# 该线段的长度
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def length(self):
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return self._length
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""""""
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# 该线段与另一线段的交点
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def intersection(self, other):
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if isinstance(other, Line):
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if self.slope() == other.slope():
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return None
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else:
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x = (
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self.slope() * other.point1.x
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- self.point1.y
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+ other.slope() * self.point1.x
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- other.point1.y
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) / (self.slope() - other.slope())
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y = self.slope() * (x - self.point1.x) + self.point1.y
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return Point2D(x, y)
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else:
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raise ValueError("Invalid input for Line")
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""""""
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"""
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class Rectangle(Shape2D):
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def __init__(self, point1, point2, **kwargs):
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super(Rectangle, self).__init__(**kwargs)
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p1 = point_maker(point1)
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p2 = point_maker(point2)
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self.point1 = point_maker(p1)
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self.point2 = point_maker((point1.x, point2.y))
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self.point3 = point_maker(point2)
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self.point4 = point_maker((point2.x, point1.y))
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# 该矩形的四条边
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def sides(self):
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return [
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Line(self.point1, self.point2),
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Line(self.point2, self.point3),
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Line(self.point3, self.point4),
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Line(self.point4, self.point1),
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]
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# 该矩形的边长
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def side_lengths(self):
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return [line.length() for line in self.sides()]
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# 该矩形是否包含点`point`
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def contains(self, point):
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point = point_maker(point)
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lines = self.sides()
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return isclose(
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sum([line.point_distance(point) for line in lines]),
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sum(self.side_lengths()),
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)
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# 通过关键字`in`判断点是否在矩形内
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def __contains__(self, point):
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return self.contains(point)
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# 该矩形的面积
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def area(self):
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return self.side_lengths()[0] * self.side_lengths()[1]
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# 该矩形的周长
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def perimeter(self):
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return sum(self.side_lengths())
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# 该矩形的中心点
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@property
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def center(self):
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return Point2D(
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(self.point1.x + self.point3.x) / 2, (self.point1.y + self.point2.y) / 2
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)
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# 该矩形的四个顶点
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@property
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def vertices(self):
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return [self.point1, self.point2, self.point3, self.point4]
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# 该矩形的外接圆
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@property
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def circumcircle(self):
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pass
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class Polygon(Shape2D):
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def __init__(self, points, **kwargs):
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super(Polygon, self).__init__(**kwargs)
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self._points = [point_maker(point) for point in points]
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self._lines = [Line(self.points[i], self.points[(i + 1) % len(self.points)]) for i in range(len(self.points))]
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self._sides = [line.length() for line in self.lines]
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self._perimeter = sum(self.sides)
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self._center = Point2D(sum([point.x for point in self.points]) / len(self.points), sum([point.y for point in self.points]) / len(self.points))
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@property
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def points(self):
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return self._points
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@property
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def lines(self):
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return self._lines
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@property
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def sides(self):
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return self._sides
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@property
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def perimeter(self):
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return self._perimeter
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@property
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def center(self):
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return self._center
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""" |