import{_ as n,c as i,j as s,a as t,a4 as e,o as a}from"./chunks/framework.DpC1ZpOZ.js";const rs=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},h=e('模組 mbcp.mp_math.line 本模块定义了三维空间中的直线类
class Line3 method __init__(self, point: Point3, direction: Vector3) 説明 : 三维空间中的直线。由一个点和一个方向向量确定。
變數説明 :
源碼 或 於GitHub上查看 python def __init__ (self, point: 'Point3' , direction: 'Vector3' ): self .point = point self .direction = direction method approx(self, other: Line3, epsilon: float = APPROX) -> bool 説明 : 判断两条直线是否近似相等。
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def approx (self, other: 'Line3' , epsilon: float = APPROX ) -> bool : return self .is_approx_parallel(other, epsilon) and ( self .point - other.point).is_approx_parallel( self .direction, epsilon) method cal_angle(self, other: Line3) -> AnyAngle 説明 : 计算直线和直线之间的夹角。
變數説明 :
返回 : AnyAngle
源碼 或 於GitHub上查看 python def cal_angle (self, other: 'Line3' ) -> 'AnyAngle' : return self .direction.cal_angle(other.direction) method cal_distance(self, other: Line3 | Point3) -> float 説明 : 计算直线和直线或点之间的距离。
',22),o={class:"tip custom-block"},p=s("p",{class:"custom-block-title"},"TIP",-1),r=s("p",null,"直线和直线之间的距离计算公式:",-1),k=s("li",null,"平行/重合 = 0",-1),d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.391ex"},xmlns:"http://www.w3.org/2000/svg",width:"7.356ex",height:"4.296ex",role:"img",focusable:"false",viewBox:"0 -1284.3 3251.5 1899","aria-hidden":"true"},c=e('變數説明 :
返回 : float
抛出 :
源碼 或 於GitHub上查看 python def cal_distance (self, other: 'Line3 | Point3' ) -> float : if isinstance (other, Line3): if self == other: return 0 elif self .is_parallel(other): return (other.point - self .point).cross( self .direction).length / self .direction.length elif not self .is_coplanar(other): return abs ( self .direction.cross(other.direction) @ ( self .point - other.point) / self .direction.cross(other.direction).length) else : return 0 elif isinstance (other, Point3): return (other - self .point).cross( self .direction).length / self .direction.length else : raise TypeError ( 'Unsupported type.' ) method cal_intersection(self, other: Line3) -> Point3 説明 : 计算两条直线的交点。
變數説明 :
返回 : Point3
抛出 :
源碼 或 於GitHub上查看 python def cal_intersection (self, other: 'Line3' ) -> 'Point3' : 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) @ other.direction.cross( self .point - other.point) / self .direction.cross(other.direction).length ** 2 * self .direction method cal_perpendicular(self, point: Point3) -> Line3 説明 : 计算直线经过指定点p的垂线。
變數説明 :
返回 : Line3
源碼 或 於GitHub上查看 python def cal_perpendicular (self, point: 'Point3' ) -> 'Line3' : return Line3(point, self .direction.cross(point - self .point)) method get_point(self, t: RealNumber) -> Point3 説明 : 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明 :
返回 : Point3
源碼 或 於GitHub上查看 python def get_point (self, t: RealNumber) -> 'Point3' : return self .point + t * self .direction method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] 説明 : 获取直线的参数方程。
返回 : tupleOneSingleVarFuncOneSingleVarFunc, OneSingleVarFunc]: 参数方程
源碼 或 於GitHub上查看 python def get_parametric_equations (self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: return ( lambda t: self .point.x + self .direction.x * t, lambda t: self .point.y + self .direction.y * t, lambda t: self .point.z + self .direction.z * t) method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool 説明 : 判断两条直线是否近似平行。
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def is_approx_parallel (self, other: 'Line3' , epsilon: float = 1e-06 ) -> bool : return self .direction.is_approx_parallel(other.direction, epsilon) method is_parallel(self, other: Line3) -> bool 説明 : 判断两条直线是否平行。
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def is_parallel (self, other: 'Line3' ) -> bool : return self .direction.is_parallel(other.direction) method is_collinear(self, other: Line3) -> bool 説明 : 判断两条直线是否共线。
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def is_collinear (self, other: 'Line3' ) -> bool : return self .is_parallel(other) and ( self .point - other.point).is_parallel( self .direction) method is_point_on(self, point: Point3) -> bool 説明 : 判断点是否在直线上。
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def is_point_on (self, point: 'Point3' ) -> bool : return (point - self .point).is_parallel( self .direction) method is_coplanar(self, other: Line3) -> bool 説明 : 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。
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def is_coplanar (self, other: 'Line3' ) -> bool : return self .direction.cross(other.direction) @ ( self .point - other.point) == 0 method simplify(self) 説明 : 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼 或 於GitHub上查看 python def simplify (self): self .direction.normalize() if self .direction.x == 0 : self .point.x = 0 if self .direction.y == 0 : self .point.y = 0 if self .direction.z == 0 : self .point.z = 0 @classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 説明 : 工厂函数 由两点构造直线。
變數説明 :
返回 : Line3
源碼 或 於GitHub上查看 python @ classmethod def from_two_points (cls, p1: 'Point3' , p2: 'Point3' ) -> 'Line3' : direction = p2 - p1 return cls (p1, direction) method self & other: Line3 => Line3 | Point3 | None 説明 : 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。
變數説明 :
返回 : Line3Point3None
源碼 或 於GitHub上查看 python def __and__ (self, other: 'Line3' ) -> 'Line3 | Point3 | None' : 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) method self == other => bool 説明 : 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明 :
返回 : bool
源碼 或 於GitHub上查看 python def __eq__ (self, other) -> bool : return self .direction.is_parallel(other.direction) and ( self .point - other.point).is_parallel( self .direction)