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🐛 fix line.cal_intersection

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This commit is contained in:
远野千束
2024-08-28 01:26:59 +08:00
parent 04d7c82783
commit 5f4adbb75f
12 changed files with 374 additions and 106 deletions
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55
mbcp/mp_math/angle.py
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@@ -8,6 +8,7 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@File : angle.py
@Software: PyCharm
"""
import math
from typing import overload
from .const import PI # type: ignore
@@ -71,6 +72,60 @@ class AnyAngle:
"""
return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float:
"""
正弦值。
Returns:
正弦值
"""
return math.sin(self.radian)
@property
def cos(self) -> float:
"""
余弦值。
Returns:
余弦值
"""
return math.cos(self.radian)
@property
def tan(self) -> float:
"""
正切值。
Returns:
正切值
"""
return math.tan(self.radian)
@property
def cot(self) -> float:
"""
余切值。
Returns:
余切值
"""
return 1 / math.tan(self.radian)
@property
def sec(self) -> float:
"""
正割值。
Returns:
正割值
"""
return 1 / math.cos(self.radian)
@property
def csc(self) -> float:
"""
余割值。
Returns:
余割值
"""
return 1 / math.sin(self.radian)
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
return AnyAngle(self.radian + other.radian, is_radian=True)

4
mbcp/mp_math/const.py
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@@ -16,4 +16,6 @@ E = math.e
GOLDEN_RATIO = (1 + math.sqrt(5)) / 2
GAMMA = 0.57721566490153286060651209008240243104215933593992
EPSILON = 0.0001
"""ε"""
APPROX = 0.001
"""约等于误差"""

76
mbcp/mp_math/line.py
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@@ -8,8 +8,10 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@File : other.py
@Software: PyCharm
"""
import math
from typing import TYPE_CHECKING
from .const import APPROX
from .mp_math_typing import OneSingleVarFunc, RealNumber
from .utils import sign_format
from .vector import Vector3
@@ -30,6 +32,17 @@ class Line3:
self.point = point
self.direction = direction
def approx(self, other: 'Line3', epsilon: float = APPROX) -> bool:
"""
判断两条直线是否近似相等。
Args:
other: 另一条直线
epsilon: 误差
Returns:
是否近似相等
"""
return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
"""
计算直线和直线之间的夹角。
@@ -42,6 +55,28 @@ class Line3:
"""
return self.direction.cal_angle(other.direction)
def cal_distance(self, other: 'Line3 | Point3') -> float:
"""
计算直线和直线或点之间的距离。
Args:
other: 平行直线或点
Returns:
距离
Raises:
ValueError: 直线不平行
TypeError: 不支持的类型
"""
if isinstance(other, Line3):
if self.is_parallel(other):
return (self.point - other.point).cross(self.direction).length / self.direction.length
else:
raise ValueError("Lines are not parallel.")
elif isinstance(other, Point3):
return (other - self.point).cross(self.direction).length / self.direction.length
else:
raise TypeError("Unsupported type.")
def cal_intersection(self, other: 'Line3') -> 'Point3':
"""
计算两条直线的交点。
@@ -49,12 +84,16 @@ class Line3:
other: 另一条直线
Returns:
交点
Raises:
ValueError: 直线平行
ValueError: 直线不共面
"""
if self.is_parallel(other):
raise ValueError("Lines are parallel and do not intersect.")
if not self.is_coplanar(other):
raise ValueError("Lines are not coplanar and do not intersect.")
return self.point + self.direction.cross(other.direction)
return (self.point + (self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point)) /
self.direction.cross(other.direction).length ** 2 * self.direction)
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
"""
@@ -86,6 +125,17 @@ class Line3:
lambda t: self.point.y + self.direction.y * t,
lambda t: self.point.z + self.direction.z * t)
def is_approx_parallel(self, other: 'Line3', epsilon: float = 1e-6) -> bool:
"""
判断两条直线是否近似平行。
Args:
other: 另一条直线
epsilon: 误差
Returns:
是否近似平行
"""
return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: 'Line3') -> bool:
"""
判断两条直线是否平行。
@@ -106,15 +156,26 @@ class Line3:
"""
return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: 'Point3') -> bool:
"""
判断点是否在直线上。
Args:
point: 点
Returns:
是否在直线上
"""
return (point - self.point).is_parallel(self.direction)
def is_coplanar(self, other: 'Line3') -> bool:
"""
判断两条直线是否共面。
充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Args:
other: 另一条直线
Returns:
是否共面
"""
return self.direction.cross(other.direction).is_parallel(self.direction)
return self.direction.cross(other.direction) @ (self.point - other.point) == 0
def simplify(self):
"""
@@ -147,15 +208,20 @@ class Line3:
direction = p2 - p1
return cls(p1, direction)
def __and__(self, other: 'Line3') -> 'Point3':
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
"""
计算两条直线点集合的交集。交点
计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Args:
other: 另一条直线
Returns:
交点
"""
return self.cal_intersection(other)
if self.is_collinear(other):
return self
elif self.is_parallel(other) or not self.is_coplanar(other):
return None
else:
return self.cal_intersection(other)
def __eq__(self, other) -> bool:
"""

40
mbcp/mp_math/plane.py
View File

@@ -7,10 +7,11 @@ from typing import TYPE_CHECKING, overload
import numpy as np
from .const import APPROX
from .vector import Vector3, zero_vector3
from .line import Line3
from .point import Point3
from .utils import sign
from .utils import approx, sign
if TYPE_CHECKING:
from .angle import AnyAngle
@@ -31,6 +32,28 @@ class Plane3:
self.c = c
self.d = d
def approx(self, other: 'Plane3', epsilon: float = APPROX) -> bool:
"""
判断两个平面是否近似相等。
Args:
other:
epsilon:
Returns:
是否近似相等
"""
if self.a != 0:
k = other.a / self.a
return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
elif self.b != 0:
k = other.b / self.b
return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
elif self.c != 0:
k = other.c / self.c
return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
else:
return False
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
"""
计算平面与平面之间的夹角。
@@ -126,6 +149,16 @@ class Plane3:
"""
return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: 'Plane3') -> bool:
"""
判断两个平面是否平行。
Args:
other: 另一个平面
Returns:
是否平行
"""
return self.normal.is_parallel(other.normal)
@property
def normal(self) -> 'Vector3':
"""
@@ -237,5 +270,10 @@ class Plane3:
else:
raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool:
return self.approx(other)
def __rand__(self, other: 'Line3') -> 'Point3':
return self.cal_intersection_point3(other)

17
mbcp/mp_math/point.py
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@@ -1,5 +1,8 @@
from typing import TYPE_CHECKING, overload
from .const import APPROX
from .utils import approx
if TYPE_CHECKING:
from .vector import Vector3 # type: ignore
@@ -17,6 +20,18 @@ class Point3:
self.y = y
self.z = z
def approx(self, other: "Point3", epsilon: float = APPROX) -> bool:
"""
判断两个点是否近似相等。
Args:
other:
epsilon:
Returns:
是否近似相等
"""
return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def __str__(self):
return f"Point3({self.x}, {self.y}, {self.z})"
@@ -45,7 +60,7 @@ class Point3:
other:
Returns:
"""
return self.x == other.x and self.y == other.y and self.z == other.z
return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def __sub__(self, other: "Point3") -> "Vector3":
"""

68
mbcp/mp_math/segment.py
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@@ -23,68 +23,18 @@ class Segment3:
:param p1:
:param p2:
"""
self._start = p1
self._end = p2
self.p1 = p1
self.p2 = p2
"""方向向量"""
self._direction = self._end - self._start
self.direction = self.p2 - self.p1
"""长度"""
self._length = self._direction.length
self.length = self.direction.length
"""中心点"""
self._midpoint = (self._start + self._end) / 2
self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
def __repr__(self):
return f"Segment3({self.p1}, {self.p2})"
def __str__(self):
return f"Segment3({self._start}, {self._end})"
def _unset_properties(self):
self._length = None
self._direction = None
self._midpoint = None
@property
def start(self) -> "Point3":
return self._start
@start.setter
def start(self, value: "Point3"):
self._start = value
self._unset_properties()
@property
def end(self) -> "Point3":
return self._end
@end.setter
def end(self, value: "Point3"):
self._end = value
self._unset_properties()
@property
def length(self) -> float:
"""
线段的长度。
:return:
"""
if self._length is None:
self._length = (self._end - self._start).length
return self._length
@property
def direction(self) -> "Vector3":
"""
线段的方向向量。
:return:
"""
if self._direction is None:
self._direction = self._end - self._start
return self._direction
@property
def midpoint(self) -> "Point3":
"""
线段的中点。
:return:
"""
if self._midpoint is None:
self._midpoint = (self._start + self._end) / 2
return self._midpoint
return f"Segment3({self.p1} -> {self.p2})"

41
mbcp/mp_math/utils.py
View File

@@ -8,9 +8,16 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@File : utils.py
@Software: PyCharm
"""
from typing import overload
from typing import overload, TYPE_CHECKING
from mbcp.mp_math.mp_math_typing import RealNumber
from .mp_math_typing import RealNumber
from .const import APPROX
if TYPE_CHECKING:
from .vector import Vector3
from .point import Point3
from .plane import Plane3
from .line import Line3
def clamp(x: float, min_: float, max_: float) -> float:
@@ -27,24 +34,36 @@ def clamp(x: float, min_: float, max_: float) -> float:
return max(min(x, max_), min_)
class Approx(float):
class Approx:
"""
用于近似比较浮点数的类。
"""
epsilon = 0.001
"""全局近似值。"""
用于近似比较对象
def __new__(cls, x: RealNumber):
return super().__new__(cls, x)
已实现对象 实数 Vector3 Point3 Plane3 Line3
"""
def __init__(self, value: RealNumber):
self.value = value
def __eq__(self, other):
return abs(self - other) < Approx.epsilon
if isinstance(self.value, (float, int)):
if isinstance(other, (float, int)):
return abs(self.value - other) < APPROX
else:
self.raise_type_error(other)
elif isinstance(self.value, Vector3):
if isinstance(other, (Vector3, Point3, Plane3, Line3)):
return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
else:
self.raise_type_error(other)
def raise_type_error(self, other):
raise TypeError(f"Unsupported type: {type(self.value)} and {type(other)}")
def __ne__(self, other):
return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = 0.0001) -> bool:
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool:
"""
判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Args:

63
mbcp/mp_math/vector.py
View File

@@ -1,8 +1,12 @@
import math
from typing import overload, TYPE_CHECKING
import numpy as np
from .const import APPROX
from .mp_math_typing import RealNumber
from .point import Point3
from .utils import approx
if TYPE_CHECKING:
from .angle import AnyAngle
@@ -21,6 +25,18 @@ class Vector3:
self.y = y
self.z = z
def approx(self, other: 'Vector3', epsilon: float = APPROX) -> bool:
"""
判断两个向量是否近似相等。
Args:
other:
epsilon:
Returns:
是否近似相等
"""
return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
"""
计算两个向量之间的夹角。
@@ -31,16 +47,6 @@ class Vector3:
"""
return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def is_parallel(self, other: 'Vector3') -> bool:
"""
判断两个向量是否平行。
Args:
other: 另一个向量
Returns:
是否平行
"""
return self.cross(other) == Vector3(0, 0, 0)
def cross(self, other: 'Vector3') -> 'Vector3':
"""
向量积 叉乘：v1 cross v2 -> v3
@@ -61,6 +67,27 @@ class Vector3:
self.z * other.x - self.x * other.z,
self.x * other.y - self.y * other.x)
def is_approx_parallel(self, other: 'Vector3', epsilon: float = APPROX) -> bool:
"""
判断两个向量是否近似平行。
Args:
other: 另一个向量
epsilon: 允许的误差
Returns:
是否近似平行
"""
return self.cross(other).length < epsilon
def is_parallel(self, other: 'Vector3') -> bool:
"""
判断两个向量是否平行。
Args:
other: 另一个向量
Returns:
是否平行
"""
return self.cross(other).approx(zero_vector3)
def normalize(self):
"""
将向量归一化。
@@ -72,6 +99,15 @@ class Vector3:
self.y /= length
self.z /= length
@property
def np_array(self) -> 'np.ndarray':
"""
返回numpy数组
Returns:
"""
return np.array([self.x, self.y, self.z])
@property
def length(self) -> float:
"""
@@ -90,6 +126,9 @@ class Vector3:
"""
return self / self.length
def __abs__(self):
return self.length
@overload
def __add__(self, other: 'Vector3') -> 'Vector3':
...
@@ -122,7 +161,7 @@ class Vector3:
Returns:
是否相等
"""
return self.x == other.x and self.y == other.y and self.z == other.z
return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def __radd__(self, other: 'Point3') -> 'Point3':
"""
@@ -197,7 +236,7 @@ class Vector3:
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
return self.__mul__(other)
def __matmul__(self, other: 'Vector3') -> float:
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
"""
点乘。
Args: