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🐛 fix ε accuracy

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远野千束 2024-08-27 09:08:27 +08:00
parent a74811291f
commit 5a0e2f189c
14 changed files with 734 additions and 149 deletions
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143
main.py
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@ -8,3 +8,146 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@File : main.py
@Software: PyCharm
"""
import logging
from mbcp.mp_math.line import Line3
from mbcp.mp_math.plane import Plane3
from mbcp.mp_math.point import Point3
# def ac8s4e4():
# """
# 第八章第四节例4
# 问题：求与两平面x-4z-3=0和2x-y-5z-1=0的交线平行且过点(-3, 2, 5)的直线方程。
# """
# correct_ans = Line3(4, 3, 1, 1)
#
# pl1 = Plane3(1, 0, -4, -3)
# pl2 = Plane3(2, -1, -5, -1)
# p = Point3(-3, 2, 5)
# """解法1"""
# # 求直线方向向量s
# s = pl1.normal @ pl2.normal
# actual_ans = Line3.from_point_and_direction(p, s)
#
# logging.info(f"正确答案：{correct_ans} 实际答案：{actual_ans}")
# assert actual_ans == correct_ans
#
# """解法2"""
# # 过点p且与pl1平行的平面pl3
# pl3 = pl1.cal_parallel_plane3(p)
# # 过点p且与pl2平行的平面pl4
# pl4 = pl2.cal_parallel_plane3(p)
# # 求pl3和pl4的交线
# actual_ans = pl3.cal_intersection_line3(pl4)
# print(pl3, pl4, actual_ans)
#
# logging.info(f"正确答案：{correct_ans} 实际答案：{actual_ans}")
# assert actual_ans == correct_ans
#
#
# ac8s4e4()
import logging
from mbcp.mp_math.mp_math_typing import RealNumber
from mbcp.mp_math.utils import Approx
def three_var_func(x: RealNumber, y: RealNumber) -> RealNumber:
return x ** 3 * y ** 2 - 3 * x * y ** 3 - x * y + 1
class TestPartialDerivative:
# 样例来源：同济大学《高等数学》第八版下册 第九章第二节 例6
def test_2v_1o_1v(self):
"""测试二元函数关于第一个变量(x)的一阶偏导 df/dx"""
from mbcp.mp_math.utils import Approx
from mbcp.mp_math.equation import get_partial_derivative_func
partial_derivative_func = get_partial_derivative_func(three_var_func, 0)
# assert partial_derivative_func(1, 2, 3) == 4.0
def df_dx(x, y):
"""原函数关于x的偏导"""
return 3 * (x ** 2) * (y ** 2) - 3 * (y ** 3) - y
logging.info(f"Expected: {df_dx(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
assert Approx(partial_derivative_func(1, 2)) == df_dx(1, 2)
def test_2v_1o_2v(self):
"""测试二元函数关于第二个变量(y)的一阶偏导 df/dy"""
from mbcp.mp_math.utils import Approx
from mbcp.mp_math.equation import get_partial_derivative_func
partial_derivative_func = get_partial_derivative_func(three_var_func, 1)
def df_dy(x, y):
"""原函数关于y的偏导"""
return 2 * (x ** 3) * y - 9 * x * (y ** 2) - x
logging.info(f"Expected: {df_dy(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
assert Approx(partial_derivative_func(1, 2)) == df_dy(1, 2)
def test_2v_2o_12v(self):
"""高阶偏导d^2f/(dxdy)"""
from mbcp.mp_math.utils import Approx
from mbcp.mp_math.equation import get_partial_derivative_func
partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 1))
def df_dxdy(x, y):
"""原函数关于y和x的偏导"""
return 6 * x ** 2 * y - 9 * y ** 2 - 1
logging.info(f"Expected: {df_dxdy(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
assert Approx(partial_derivative_func(1, 2)) == df_dxdy(1, 2)
def test_2v_2o_1v2(self):
"""二阶偏导d^2f/(dx^2)"""
from mbcp.mp_math.utils import Approx
from mbcp.mp_math.equation import get_partial_derivative_func
partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 0))
def df_dydx(x, y):
"""原函数关于x和y的偏导"""
return 6 * x * y ** 2
logging.info(f"Expected: {df_dydx(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
assert Approx(partial_derivative_func(1, 2)) == df_dydx(1, 2)
def test_2v_3o_1v3(self):
"""高阶偏导d^3f/(dx^3)"""
from mbcp.mp_math.utils import Approx
from mbcp.mp_math.equation import get_partial_derivative_func
partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 0, 0))
def d3f_dx3(x, y):
"""原函数关于x的三阶偏导"""
return 6 * (y ** 2)
logging.info(f"Expected: {d3f_dx3(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
assert Approx(partial_derivative_func(1, 2)) == d3f_dx3(1, 2)
def test_possible_error(self):
from mbcp.mp_math.equation import get_partial_derivative_func
def two_vars_func(x: RealNumber, y: RealNumber) -> RealNumber:
return x ** 2 * y ** 2
partial_func = get_partial_derivative_func(two_vars_func, 0)
partial_func_2 = get_partial_derivative_func(two_vars_func, (0, 0))
assert Approx(partial_func_2(1, 2)) == 8
TestPartialDerivative().test_2v_1o_1v()
TestPartialDerivative().test_2v_1o_2v()
TestPartialDerivative().test_2v_2o_12v()
TestPartialDerivative().test_2v_2o_1v2()
TestPartialDerivative().test_2v_3o_1v3()
TestPartialDerivative().test_possible_error()

94
mbcp/mp_math/angle.py Normal file
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@ -0,0 +1,94 @@
# -*- coding: utf-8 -*-
"""
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/26 上午6:29
@Author : snowykami
@Email : snowykami@outlook.com
@File : angle.py
@Software: PyCharm
"""
from typing import overload
from .const import PI
class AnyAngle:
def __init__(self, value: float, is_radian: bool = False):
"""
任意角度。
Args:
value: 角度或弧度值
is_radian: 是否为弧度，默认为否
"""
if is_radian:
self.radian = value
else:
self.radian = value * PI / 180
@property
def complementary(self) -> "AnyAngle":
"""
余角：两角的和为90°。
Returns:
余角
"""
return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> "AnyAngle":
"""
补角：两角的和为180°。
Returns:
补角
"""
return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float:
"""
角度。
Returns:
弧度
"""
return self.radian * 180 / PI
@property
def minimum_positive(self) -> "AnyAngle":
"""
最小正角。
Returns:
最小正角度
"""
return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> "AnyAngle":
"""
最大负角。
Returns:
最大负角度
"""
return AnyAngle(-self.radian % (2 * PI), is_radian=True)
def __add__(self, other: "AnyAngle") -> "AnyAngle":
return AnyAngle(self.radian + other.radian, is_radian=True)
def __sub__(self, other: "AnyAngle") -> "AnyAngle":
return AnyAngle(self.radian - other.radian, is_radian=True)
def __mul__(self, other: float) -> "AnyAngle":
return AnyAngle(self.radian * other, is_radian=True)
@overload
def __truediv__(self, other: float) -> "AnyAngle":
...
@overload
def __truediv__(self, other: "AnyAngle") -> float:
...
def __truediv__(self, other):
if isinstance(other, AnyAngle):
return self.radian / other.radian
return AnyAngle(self.radian / other, is_radian=True)

4
mbcp/mp_math/equation.py
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@ -46,13 +46,15 @@ class CurveEquation:
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc:
"""
求N元函数一阶偏导函数。
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Args:
func: 函数
var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
epsilon: 偏移量
Returns:
偏导函数
Raises:
ValueError: 无效变量类型
"""
if isinstance(var, int):
def partial_derivative_func(*args: Var) -> Var:

140
mbcp/mp_math/line.py
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@ -5,49 +5,67 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/6 下午12:57
@Author : snowykami
@Email : snowykami@outlook.com
@File : line.py
@File : other.py
@Software: PyCharm
"""
from typing import TYPE_CHECKING
import math
from typing import TYPE_CHECKING, overload
from .vector import Vector3
if TYPE_CHECKING:
from .point import Point3 # type: ignore
from .angle import AnyAngle
from .plane import Plane3
from .point import Point3
class Line3:
def __init__(self, a: float, b: float, c: float, d: float):
"""
三维空间中的直线。
:param a:
:param b:
:param c:
:param d:
Args:
a: 直线方程的系数a
b: 直线方程的系数b
c: 直线方程的系数c
d: 直线方程的常数项d
"""
self.a = a
self.b = b
self.c = c
self.d = d
def __str__(self):
return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
def cal_angle(self, other: "Line3") -> "AnyAngle":
"""
计算直线和直线或面之间的夹角。
Args:
other: 另一条直线或面
Returns:
夹角弧度
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, Line3):
return self.direction.cal_angle(other.direction)
elif isinstance(other, Plane3):
return self.direction.cal_angle(other.normal).complementary # 方向向量和法向量的夹角的余角
else:
raise TypeError(f"Unsupported type: {type(other)}")
def get_perpendicular(self, point: "Point3") -> "Line3":
@property
def direction(self) -> "Vector3":
"""
获取直线经过指定点p的垂线。
:param point: 指定点p，直线外的点
:return: 垂直于self且过点p的直线
直线的方向向量。
Returns:
方向向量
"""
a = -self.b
b = self.a
c = 0
d = -(a * point.x + b * point.y + self.c * point.z)
return Line3(a, b, c, d)
return Vector3(self.a, self.b, self.c)
def get_intersection(self, line: "Line3") -> "Point3":
def cal_intersection(self, line: "Line3") -> "Point3":
"""
获取两条直线的交点。
:param line:
:return:
计算两条直线的交点。
Args:
line: 另一条直线
Returns:
交点
"""
if self.is_parallel(line):
@ -70,21 +88,39 @@ class Line3:
return Point3(x, y, z)
def cal_perpendicular(self, point: "Point3") -> "Line3":
"""
计算直线经过指定点p的垂线。
Args:
point: 指定点
Returns:
垂线
"""
a = -self.b
b = self.a
c = 0
d = -(a * point.x + b * point.y + self.c * point.z)
return Line3(a, b, c, d)
def is_parallel(self, line: "Line3") -> bool:
"""
判断两条直线是否平行。
直线平行的条件是它们的法向量成比例
:param line:
:return:
Args:
line: 另一条直线
Returns:
是否平行
"""
return self.a * line.b == self.b * line.a and self.c * line.b == self.d * line.a
return self.direction.is_parallel(line.direction)
def is_collinear(self, line: "Line3") -> bool:
"""
判断两条直线是否共线。
直线共线的条件是它们的法向量成比例且常数项也成比例
:param line:
:return:
Args:
line: 另一条直线
Returns:
是否共线
"""
return self.is_parallel(line) and (self.d * line.b - self.b * line.d) / (self.a * line.b - self.b * line.a) == 0
@ -92,10 +128,56 @@ class Line3:
"""
判断两条直线是否共面。
两条直线共面的条件是它们的方向向量和法向量的叉乘为零向量
:param line:
:return:
Args:
line: 另一条直线
Returns:
是否共面
"""
direction1 = (-self.c, 0, self.a)
direction2 = (line.c, -line.b, 0)
cross_product = direction1[0] * direction2[1] - direction1[1] * direction2[0]
return cross_product == 0
@classmethod
def from_point_and_direction(cls, point: "Point3", direction: "Vector3") -> "Line3":
"""
工厂函数 由点和方向向量构造直线(点向式构造)。
Args:
point: 点
direction: 方向向量
Returns:
直线
"""
a, b, c = direction.x, direction.y, direction.z
d = -(a * point.x + b * point.y + c * point.z)
return cls(a, b, c, d)
@classmethod
def from_two_points(cls, p1: "Point3", p2: "Point3") -> "Line3":
"""
工厂函数 由两点构造直线。
Args:
p1: 点1
p2: 点2
Returns:
直线
"""
direction = p2 - p1
return cls.from_point_and_direction(p1, direction)
def __eq__(self, other) -> bool:
"""
判断两条直线是否等价。
Args:
other:
Returns:
"""
return self.a / other.a == self.b / other.b == self.c / other.c == self.d / other.d
def __repr__(self):
return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"
def __str__(self):
return f"Line3({self.a}, {self.b}, {self.c}, {self.d})"

128
mbcp/mp_math/plane.py
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@ -1,10 +1,124 @@
# -*- coding: utf-8 -*-
"""
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/6 下午1:45
@Author : snowykami
@Email : snowykami@outlook.com
@File : plane.py
@Software: PyCharm
平面模块
"""
import math
from typing import TYPE_CHECKING
import numpy as np
from .vector import Vector3
from .line import Line3
from .point import Point3
if TYPE_CHECKING:
from .angle import AnyAngle
class Plane3:
def __init__(self, a: float, b: float, c: float, d: float):
"""
平面方程：ax + by + cz + d = 0
Args:
a:
b:
c:
d:
"""
self.a = a
self.b = b
self.c = c
self.d = d
def cal_angle(self, other: "Line3 | Plane3") -> "AnyAngle":
"""
计算平面与平面之间的夹角。
Args:
other: 另一个平面
Returns:
夹角弧度
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, Line3):
return self.normal.cal_angle(other.direction).complementary
elif isinstance(other, Plane3):
return AnyAngle(math.acos(self.normal * other.normal / (self.normal.length * other.normal.length)), is_radian=True)
else:
raise TypeError(f"Unsupported type: {type(other)}")
def cal_distance(self, other: "Plane3 | Point3") -> float:
"""
计算平面与平面或点之间的距离。
Args:
other: 另一个平面或点
Returns:
距离
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, Plane3):
return 0
elif isinstance(other, Point3):
return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
else:
raise TypeError(f"Unsupported type: {type(other)}")
def cal_intersection_line3(self, other: "Plane3") -> "Line3":
"""
计算两平面的交线。该方法有问题，待修复。
Args:
other: 另一个平面
Returns:
交线
"""
# 计算两法向量的叉积作为交线的方向向量
s = self.normal.cross(other.normal) # 交线的方向向量
# 联立两平面方程求交线的一点
# 两平面方程联立得到的方程组
# | a1x + b1y + c1z = -d1
# | a2x + b2y + c2z = -d2
# 用numpy解方程组
a = np.array([[self.a, self.b, self.c], [other.a, other.b, other.c]])
b = np.array([-self.d, -other.d])
p = np.linalg.lstsq(a, b, rcond=None)[0]
return Line3.from_point_and_direction(Point3(*p), s)
def cal_parallel_plane3(self, point: "Point3") -> "Plane3":
"""
计算平行于该平面且过指定点的平面。
Args:
point: 指定点
Returns:
平面
"""
return Plane3.from_point_and_normal(point, self.normal)
@property
def normal(self) -> "Vector3":
"""
平面的法向量。
Returns:
法向量
"""
return Vector3(self.a, self.b, self.c)
@classmethod
def from_point_and_normal(cls, point: "Point3", normal: "Vector3") -> "Plane3":
"""
工厂函数 由点和法向量构造平面(点法式构造)。
Args:
point: 平面上的一点
normal: 法向量
Returns:
平面
"""
a, b, c = normal.x, normal.y, normal.z
d = -a * point.x - b * point.y - c * point.z # d = -ax - by - cz
return cls(a, b, c, d)
def __repr__(self):
return f"Plane3({self.a}, {self.b}, {self.c}, {self.d})"
def __str__(self):
return f"{self.a}x + {self.b}y + {self.c}z + {self.d} = 0"

1
mbcp/mp_math/point.py
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@ -44,6 +44,7 @@ class Point3:
:param other:
:return:
"""
from .vector import Vector3
return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
def __truediv__(self, other: float) -> "Point3":

2
mbcp/mp_math/py.typed
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@ -1,2 +0,0 @@
# py.typed
partial

188
mbcp/mp_math/vector.py
View File

@ -1,9 +1,10 @@
import math
from typing import overload, TYPE_CHECKING
import numpy as np
from .point import Point3
if TYPE_CHECKING:
from .point import Point3 # type: ignore
from .angle import AnyAngle
class Vector3:
@ -14,75 +15,59 @@ class Vector3:
:param y:
:param z:
"""
self._x = x
self._y = y
self._z = z
self._length = (x ** 2 + y ** 2 + z ** 2) ** 0.5
self._normalized = self / self._length
self.x = x
self.y = y
self.z = z
def __str__(self):
return f"Vector3({self._x}, {self._y}, {self._z})"
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
"""
计算两个向量之间的夹角。
Args:
other: 另一个向量
Returns:
夹角
"""
return AnyAngle(math.acos(self * other / (self.length * other.length)), is_radian=True)
def _unset_properties(self):
self._length = None
self._normalized = None
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 @ other == Vector3(0, 0, 0)
@property
def x(self):
return self._x
@x.setter
def x(self, value):
self._x = value
self._unset_properties()
@property
def y(self):
return self._y
@y.setter
def y(self, value):
self._y = value
self._unset_properties()
@property
def z(self):
return self._z
@z.setter
def z(self, value):
self._z = value
self._unset_properties()
def cross(self, other: 'Vector3') -> 'Vector3':
"""
向量积 叉乘：V1 @ V2 -> V3
Args:
other:
Returns:
叉乘结果，为0向量则两向量平行，否则垂直于两向量
"""
return Vector3(self.y * other.z - self.z * other.y,
self.z * other.x - self.x * other.z,
self.x * other.y - self.y * other.x)
@property
def length(self) -> float:
"""
向量的模。
:return:
Returns:
模
"""
if self._length is None:
self._length = (self._x ** 2 + self._y ** 2 + self._z ** 2) ** 0.5
return self._length
return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def normalized(self) -> 'Vector3':
def unit(self) -> 'Vector3':
"""
返回该向量的单位向量。
:return:
获取该向量的单位向量。
Returns:
单位向量
"""
if self._normalized is None:
self._normalized = self / self.length
return self._normalized
def normalize(self):
"""
自体归一化。
"""
self._x /= self.length
self._y /= self.length
self._z /= self.length
self._length = 1
self._normalized = self
return self / self.length
@overload
def __add__(self, other: 'Vector3') -> 'Vector3':
@ -96,16 +81,28 @@ class Vector3:
"""
V + P -> P\n
V + V -> V
:param other:
:return:
Args:
other:
Returns:
"""
if isinstance(other, Vector3):
return Vector3(self._x + other.x, self._y + other.y, self._z + other.z)
return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
elif isinstance(other, Point3):
return Point3(self._x + other.x, self._y + other.y, self._z + other.z)
return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
else:
raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other):
"""
判断两个向量是否相等。
Args:
other:
Returns:
是否相等
"""
return self.x == other.x and self.y == other.y and self.z == other.z
def __radd__(self, other: 'Point3') -> 'Point3':
"""
P + V -> P\n
@ -113,7 +110,7 @@ class Vector3:
:param other:
:return:
"""
return Point3(self._x + other.x, self._y + other.y, self._z + other.z)
return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def __sub__(self, other: 'Vector3') -> 'Vector3':
@ -127,25 +124,28 @@ class Vector3:
"""
V - P -> P\n
V - V -> V
:param other:
:return:
Args:
other:
Returns:
"""
if isinstance(other, Vector3):
return Vector3(self._x - other.x, self._y - other.y, self._z - other.z)
return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
elif isinstance(other, Point3):
return Point3(self._x - other.x, self._y - other.y, self._z - other.z)
return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
else:
raise TypeError(f"unsupported operand type(s) for -: 'Vector3' and '{type(other)}'")
def __rsub__(self, other: Point3):
"""
P - V -> P
:param other:
:return:
Args:
other:
Returns:
"""
if isinstance(other, Point3):
return Point3(other.x - self._x, other.y - self._y, other.z - self._z)
return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
else:
raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@ -159,34 +159,52 @@ class Vector3:
def __mul__(self, other):
"""
乘法。包括点乘和数乘。
:param other:
:return:
点乘法。包括点乘和数乘。
V * V -> float\n
Args:
other:
Returns:
float
Raises:
TypeError: 不支持的类型
"""
if isinstance(other, (int, float)):
return Vector3(self._x * other, self._y * other, self._z * other)
return Vector3(self.x * other, self.y * other, self.z * other)
elif isinstance(other, Vector3):
return self._x * other.x + self._y * other.y + self._z * other.z
return self.x * other.x + self.y * other.y + self.z * other.z
else:
raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def __rmul__(self, other: float) -> 'Vector3':
"""
右乘。
:param other:
:return:
Args:
other:
Returns:
乘积
"""
return Vector3(self._x * other, self._y * other, self._z * other)
return Vector3(self.x * other, self.y * other, self.z * other)
def __matmul__(self, other: 'Vector3') -> 'Vector3':
"""
叉乘。
:param other: 另一个向量
:return: 叉乘结果向量
向量积 叉乘：V1 @ V2 -> V3
Args:
other:
Returns:
叉乘结果，为0向量则两向量平行，否则垂直于两向量
"""
return Vector3(self._y * other.z - self._z * other.y,
self._z * other.x - self._x * other.z,
self._x * other.y - self._y * other.x)
return Vector3(self.y * other.z - self.z * other.y,
self.z * other.x - self.x * other.z,
self.x * other.y - self.y * other.x)
def __truediv__(self, other: float) -> 'Vector3':
return Vector3(self._x / other, self._y / other, self._z / other)
return Vector3(self.x / other, self.y / other, self.z / other)
def __neg__(self):
return Vector3(-self.x, -self.y, -self.z)
def __repr__(self):
return f"Vector3({self.x}, {self.y}, {self.z})"
def __str__(self):
return f"Vector3({self.x}, {self.y}, {self.z})"

2
mbcp/py.typed
View File

@ -1,2 +0,0 @@
# py.typed
partial

33
tests/test_line3.py Normal file
View File

@ -0,0 +1,33 @@
# -*- coding: utf-8 -*-
"""
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/26 上午7:54
@Author : snowykami
@Email : snowykami@outlook.com
@File : test_line3.py
@Software: PyCharm
"""
import logging
from mbcp.mp_math.point import Point3
from mbcp.mp_math.vector import Vector3
from mbcp.mp_math.line import Line3
class TestLine3:
def test_point_and_normal_factory(self):
"""
测试通过点和法向量构造直线
"""
correct_ans = Line3(1, -2, 3, -8)
p = Point3(2, -3, 0)
n = Vector3(1, -2, 3)
actual_ans = Line3.from_point_and_direction(p, n)
logging.info(f"正确答案：{correct_ans} 实际答案：{actual_ans}")
assert actual_ans == correct_ans

29
tests/test_plane3.py Normal file
View File

@ -0,0 +1,29 @@
# -*- coding: utf-8 -*-
"""
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/26 上午9:07
@Author : snowykami
@Email : snowykami@outlook.com
@File : test_plane3.py
@Software: PyCharm
"""
import logging
from mbcp.mp_math.line import Line3
from mbcp.mp_math.plane import Plane3
class TestPlane3:
def test_intersection_line3(self):
"""
测试平面的交线
"""
correct_ans = Line3(4, 3, 1, 1)
pl1 = Plane3(1, 0, -4, 23)
pl2 = Plane3(2, -1, -5, 33)
actual_ans = pl1.cal_intersection_line3(pl2)
logging.info(f"正确答案：{correct_ans} 实际答案：{actual_ans}")
assert actual_ans == correct_ans

22
tests/test_vector.py
View File

@ -1,22 +0,0 @@
# -*- coding: utf-8 -*-
"""
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/6 下午1:05
@Author : snowykami
@Email : snowykami@outlook.com
@File : test_vector.py
@Software: PyCharm
"""
from mbcp.mp_math.vector import Vector3
from mbcp.mp_math.point import Point3
def test_v():
v1 = Vector3(1, 2, 3)
v2 = Vector3(4, 5, 6)
v3 = v1 + v2
assert v3._x == 5
assert v3._y == 7
assert v3._z == 9
print("test_v 1111passed")

52
tests/test_vector3.py Normal file
View File

@ -0,0 +1,52 @@
# -*- coding: utf-8 -*-
"""
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/26 上午6:58
@Author : snowykami
@Email : snowykami@outlook.com
@File : test_question_1.py
@Software: PyCharm
"""
import logging
from mbcp.mp_math.vector import Vector3
class TestVector3:
"""测试问题集"""
def test_vector_cross_product(self):
"""
测试向量叉乘
Returns:
"""
v1 = Vector3(1, 2, 3)
v2 = Vector3(3, 4, 5)
actual_ans = v1 @ v2
correct_ans = Vector3(-2, 4, -2)
logging.info(f"正确答案{correct_ans} 实际答案{v1 @ v2}")
assert correct_ans == actual_ans
def test_determine_vector_parallel(self):
"""
测试判断向量是否平行
Returns:
"""
v1 = Vector3(1, 2, 3)
v2 = Vector3(3, 6, 9)
actual_ans = v1.is_parallel(v2)
correct_ans = True
logging.info("v1和v2是否平行：%s", v1.is_parallel(v2))
assert correct_ans == actual_ans
v1 = Vector3(1, 2, 3)
v2 = Vector3(3, 6, 8)
actual_ans = v1.is_parallel(v2)
correct_ans = False
logging.info("v1和v2是否平行：%s", v1.is_parallel(v2))
assert correct_ans == actual_ans

43
tests/test_word_problem.py Normal file
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@ -0,0 +1,43 @@
# -*- coding: utf-8 -*-
"""
应用题测试集
"""
import logging
from mbcp.mp_math.line import Line3
from mbcp.mp_math.plane import Plane3
from mbcp.mp_math.point import Point3
class TestWordProblem:
def test_c8s4e4(self):
"""
同济大学《高等数学》第八版 下册 第八章第四节例4
问题：求与两平面x-4z-3=0和2x-y-5z-1=0的交线平行且过点(-3, 2, 5)的直线方程。
"""
correct_ans = Line3(4, 3, 1, 1)
pl1 = Plane3(1, 0, -4, -3)
pl2 = Plane3(2, -1, -5, -1)
p = Point3(-3, 2, 5)
"""解法1"""
# 求直线方向向量s
s = pl1.normal @ pl2.normal
actual_ans = Line3.from_point_and_direction(p, s)
logging.info(f"正确答案：{correct_ans} 实际答案：{actual_ans}")
assert actual_ans == correct_ans
"""解法2"""
# 过点p且与pl1平行的平面pl3
pl3 = pl1.cal_parallel_plane3(p)
# 过点p且与pl2平行的平面pl4
pl4 = pl2.cal_parallel_plane3(p)
# 求pl3和pl4的交线
actual_ans = pl3.cal_intersection_line3(pl4)
print(pl3, pl4, actual_ans)
logging.info(f"正确答案：{correct_ans} 实际答案：{actual_ans}")
assert actual_ans == correct_ans