mirror of
https://github.com/snowykami/mbcp.git
synced 2024-11-24 15:25:03 +08:00
🐛 fix line.cal_intersection
This commit is contained in:
parent
04d7c82783
commit
5f4adbb75f
@ -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)
|
||||
|
||||
|
||||
@ -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"""
|
||||
|
||||
@ -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:
|
||||
"""
|
||||
|
||||
@ -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)
|
||||
|
||||
|
||||
|
||||
@ -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":
|
||||
"""
|
||||
|
||||
@ -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})"
|
||||
|
||||
@ -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:
|
||||
|
||||
@ -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:
|
||||
|
||||
@ -8,16 +8,19 @@ Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
|
||||
@File : .answer.py
|
||||
@Software: PyCharm
|
||||
"""
|
||||
from typing import Optional
|
||||
|
||||
from liteyuki.log import logger # type: ignore
|
||||
|
||||
|
||||
def output_answer(correct_ans, actual_ans, question: str = None):
|
||||
def output_ans(correct_ans, actual_ans, condition: Optional[bool] = None,question: Optional[str] = None):
|
||||
"""
|
||||
输出答案
|
||||
Args:
|
||||
correct_ans:
|
||||
actual_ans:
|
||||
question:
|
||||
condition: 判对条件
|
||||
question: 问题
|
||||
|
||||
Returns:
|
||||
|
||||
@ -25,8 +28,31 @@ def output_answer(correct_ans, actual_ans, question: str = None):
|
||||
print("")
|
||||
if question is not None:
|
||||
logger.info(f"问题：{question}")
|
||||
r = correct_ans == actual_ans
|
||||
r = (correct_ans == actual_ans) if condition is None else condition
|
||||
if r:
|
||||
logger.success(f"测试正确 正确答案：{correct_ans} 实际答案：{actual_ans}")
|
||||
else:
|
||||
logger.error(f"测试错误 正确答案：{correct_ans} 实际答案：{actual_ans}")
|
||||
assert r
|
||||
|
||||
|
||||
def output_step_ans(correct_ans, actual_ans, condition: Optional[bool] = None, question: Optional[str] = None):
|
||||
"""
|
||||
输出步骤答案
|
||||
Args:
|
||||
correct_ans: 正确答案
|
||||
actual_ans: 实际答案
|
||||
condition: 判对条件
|
||||
question: 问题
|
||||
|
||||
Returns:
|
||||
|
||||
"""
|
||||
print("")
|
||||
if question is not None:
|
||||
logger.info(f" 步骤：{question}")
|
||||
r = (correct_ans == actual_ans) if condition is None else condition
|
||||
if r:
|
||||
logger.success(f" 正确 正确：{correct_ans} 实际：{actual_ans}")
|
||||
else:
|
||||
logger.error(f" 错误 正确：{correct_ans} 实际：{actual_ans}")
|
||||
|
||||
@ -13,8 +13,50 @@ import logging
|
||||
from mbcp.mp_math.point import Point3
|
||||
from mbcp.mp_math.vector import Vector3
|
||||
from mbcp.mp_math.line import Line3
|
||||
from tests.answer import output_answer
|
||||
from tests.answer import output_ans
|
||||
|
||||
|
||||
class TestLine3:
|
||||
|
||||
def test_equal(self):
|
||||
line1 = Line3(Point3(1, 1, 1), Vector3(1, 1, 1))
|
||||
line2 = Line3(Point3(1, 1, 1), Vector3(2, 2, 2))
|
||||
output_ans(True, line1 == line2, question="判断两条直线是否相等")
|
||||
|
||||
# 反例
|
||||
line1 = Line3(Point3(1, 1, 1), Vector3(1, 1, 1))
|
||||
line2 = Line3(Point3(1, 1, 1), Vector3(2, 2, 2.000000001))
|
||||
output_ans(False, line1 == line2, question="判断两条直线是否不相等")
|
||||
|
||||
def test_approx(self):
|
||||
line1 = Line3(Point3(1, 1, 1), Vector3(1, 1, 1))
|
||||
line2 = Line3(Point3(1, 1, 1), Vector3(2, 2, 2.000000001))
|
||||
output_ans(True, line1.approx(line2), question="判断两条直线是否近似相等")
|
||||
|
||||
# 反例
|
||||
line1 = Line3(Point3(1, 1, 1), Vector3(1, 1, 1))
|
||||
line2 = Line3(Point3(1, 1, 1), Vector3(2, 2, 3.1))
|
||||
output_ans(False, line1.approx(line2), question="判断两条直线是否不近似相等")
|
||||
|
||||
def test_cal_intersection(self):
|
||||
line1 = Line3.from_two_points(Point3(0, 0, 0), Point3(2, 2, 2))
|
||||
line2 = Line3.from_two_points(Point3(0, 0, 2), Point3(2, 2, 0))
|
||||
output_ans(Point3(1, 1, 1), line1 & line2, question="计算两条直线的交点测1")
|
||||
|
||||
line1 = Line3.from_two_points(Point3(0, 0, 0), Point3(0, 2, 2))
|
||||
line2 = Line3.from_two_points(Point3(0, 0, 2), Point3(0, 2, 0))
|
||||
output_ans(Point3(0, 1, 1), line1 & line2, question="计算两条直线的交点测2")
|
||||
|
||||
line1 = Line3.from_two_points(Point3(0, 0, 0), Point3(0, 0, 2))
|
||||
line2 = Line3.from_two_points(Point3(0, 0, 2), Point3(0, 2, 0))
|
||||
output_ans(Point3(0, 0, 2), line1 & line2, question="计算两条直线的交点测3")
|
||||
|
||||
# 反例：平行线无交点
|
||||
line1 = Line3(Point3(1, 1, 1), Vector3(1, 1, 1))
|
||||
line2 = Line3(Point3(2, 3, 1), Vector3(1, 1, 1))
|
||||
output_ans(None, line1 & line2, question="平行线交集为空集")
|
||||
|
||||
# 反例：重合线交集为自身
|
||||
line1 = Line3(Point3(1, 1, 1), Vector3(1, 1, 1))
|
||||
line2 = Line3(Point3(0, 0, 0), Vector3(2, 2, 2))
|
||||
output_ans(line1, line1 & line2, question="重合线的交集为自身")
|
||||
|
||||
@ -12,7 +12,7 @@ import logging
|
||||
|
||||
from mbcp.mp_math.vector import Vector3
|
||||
|
||||
from tests.answer import output_answer
|
||||
from tests.answer import output_ans
|
||||
|
||||
|
||||
class TestVector3:
|
||||
@ -41,7 +41,7 @@ class TestVector3:
|
||||
v1 = Vector3(1, 2, 3)
|
||||
v2 = Vector3(3, 6, 9)
|
||||
actual_ans = v1.is_parallel(v2)
|
||||
output_answer(correct_ans, actual_ans)
|
||||
output_ans(correct_ans, actual_ans)
|
||||
assert correct_ans == actual_ans
|
||||
|
||||
"""小题2"""
|
||||
@ -49,7 +49,7 @@ class TestVector3:
|
||||
v1 = Vector3(1, 2, 3)
|
||||
v2 = Vector3(3, 6, 8)
|
||||
actual_ans = v1.is_parallel(v2)
|
||||
output_answer(correct_ans, actual_ans)
|
||||
output_ans(correct_ans, actual_ans)
|
||||
assert correct_ans == actual_ans
|
||||
|
||||
|
||||
|
||||
@ -7,7 +7,7 @@ from mbcp.mp_math.line import Line3
|
||||
from mbcp.mp_math.plane import Plane3
|
||||
from mbcp.mp_math.point import Point3
|
||||
from mbcp.mp_math.vector import Vector3
|
||||
from .answer import output_answer
|
||||
from .answer import output_ans, output_step_ans
|
||||
|
||||
|
||||
class TestWordProblem:
|
||||
@ -27,7 +27,7 @@ class TestWordProblem:
|
||||
s = pl1.normal.cross(pl2.normal)
|
||||
actual_ans = Line3(p, s)
|
||||
|
||||
output_answer(correct_ans, actual_ans, question)
|
||||
output_ans(correct_ans, actual_ans, question=question)
|
||||
assert actual_ans == correct_ans
|
||||
|
||||
"""解法2"""
|
||||
@ -38,7 +38,7 @@ class TestWordProblem:
|
||||
# 求pl3和pl4的交线
|
||||
actual_ans = pl3.cal_intersection_line3(pl4)
|
||||
|
||||
output_answer(correct_ans, actual_ans, question)
|
||||
output_ans(correct_ans, actual_ans, question=question)
|
||||
assert actual_ans == correct_ans
|
||||
|
||||
def test_c8s4e5(self):
|
||||
@ -56,21 +56,37 @@ class TestWordProblem:
|
||||
|
||||
"""解"""
|
||||
actual_ans = plane & line
|
||||
output_answer(correct_ans, actual_ans, question)
|
||||
output_ans(correct_ans, actual_ans, question=question)
|
||||
|
||||
def test_c8s4e6(self):
|
||||
question = "求过点(2, 3, 1)且与直线(x+1)/3 = (y-1)/2 = z/-1垂直相交的直线的方程。"
|
||||
"""正确答案"""
|
||||
correct_ans = Line3(Point3(2, 1, 3), Vector3(2, -1, 4))
|
||||
"""题目已知量"""
|
||||
point = Point3(2, 3, 1)
|
||||
point = Point3(2, 1, 3)
|
||||
line = Line3(Point3(-1, 1, 0), Vector3(3, 2, -1))
|
||||
|
||||
"""解"""
|
||||
# 先作平面过点且垂直与已知直线
|
||||
pl = line.cal_perpendicular(point)
|
||||
logger.debug(line.get_point(1))
|
||||
# 先作过点且垂直与已知直线的平面
|
||||
s1_correct_ans = Plane3(3, 2, -1, -5)
|
||||
pl = Plane3.from_point_and_normal(point, line.direction)
|
||||
|
||||
# output_answer(correct_ans, actual_ans, question)
|
||||
output_step_ans(s1_correct_ans, pl, question="作过点且垂直与已知直线的平面")
|
||||
|
||||
# 求该平面与已知直线的交点
|
||||
s2_correct_ans = Point3(2 / 7, 13 / 7, -3 / 7)
|
||||
s2_actual_ans = pl & line
|
||||
|
||||
output_step_ans(s2_correct_ans, s2_actual_ans, s1_correct_ans.approx(s1_correct_ans), question="求该平面与已知直线的交点")
|
||||
|
||||
# 求所求直线的方向向量
|
||||
s3_correct_ans = (-6 / 7) * Vector3(2, -1, 4)
|
||||
|
||||
dv = s2_correct_ans - point
|
||||
|
||||
output_step_ans(s3_correct_ans, dv, condition=s3_correct_ans.unit.approx(dv.unit), question="求所求直线的方向向量")
|
||||
|
||||
# 求所求直线的方程
|
||||
actual_ans = Line3(point, dv)
|
||||
|
||||
output_ans(correct_ans, actual_ans, correct_ans.approx(actual_ans), question=question)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user