import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t('Module mbcp.mp_math.vector 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 method __init__(self, x: float, y: float, z: float) Description : 3维向量
Arguments :
x (float y (float): y轴分量 z (float): z轴分量 Source code or View on GitHub python def __init__ (self, x: float , y: float , z: float ): self .x = x self .y = y self .z = z method approx(self, other: Vector3, epsilon: float = APPROX) -> bool Description : 判断两个向量是否近似相等。
Arguments :
Return : bool
Source code or View on GitHub python def approx (self, other: 'Vector3' , epsilon: float = APPROX ) -> bool : return all ([ abs ( self .x - other.x) < epsilon, abs ( self .y - other.y) < epsilon, abs ( self .z - other.z) < epsilon]) method cal_angle(self, other: Vector3) -> AnyAngle Description : 计算两个向量之间的夹角。
',16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),d={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t('Arguments :
Return : AnyAngle
Source code or View on GitHub python def cal_angle (self, other: 'Vector3' ) -> 'AnyAngle' : return AnyAngle(math.acos( self @ other / ( self .length * other.length)), is_radian = True ) method cross(self, other: Vector3) -> Vector3 Description : 向量积 叉乘：v1 x v2 -> v3
',6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t('Arguments :
Return : Vector3
Source code or View on GitHub python def cross (self, other: 'Vector3' ) -> 'Vector3' : 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) method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool Description : 判断两个向量是否近似平行。
Arguments :
Return : bool
Source code or View on GitHub python def is_approx_parallel (self, other: 'Vector3' , epsilon: float = APPROX ) -> bool : return self .cross(other).length < epsilon method is_parallel(self, other: Vector3) -> bool Description : 判断两个向量是否平行。
Arguments :
Return : bool
Source code or View on GitHub python def is_parallel (self, other: 'Vector3' ) -> bool : return self .cross(other).approx(zero_vector3) method normalize(self) Description : 将向量归一化。
自体归一化，不返回值。
Source code or View on GitHub python def normalize (self): length = self .length self .x /= length self .y /= length self .z /= length method project(self, other: Vector3) -> Vector3 Description : 计算自向量在另一个向量上的投影向量。
',22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t('Arguments :
Return : Vector3
Source code or View on GitHub python def project (self, other: 'Vector3' ) -> 'Vector3' : return self @ other / other.length * other.unit @property
method np_array(self) -> np.ndarray Return : np.ndarray
Source code or View on GitHub python @ property def np_array (self) -> 'np.ndarray' : return np.array([ self .x, self .y, self .z]) @property
method length(self) -> float Description : 向量的模。
Return : float
Source code or View on GitHub python @ property def length (self) -> float : return math.sqrt( self .x ** 2 + self .y ** 2 + self .z ** 2 ) @property
method unit(self) -> Vector3 Description : 获取该向量的单位向量。
Return : Vector3
Source code or View on GitHub python @ property def unit (self) -> 'Vector3' : return self / self .length method __abs__(self) Source code or View on GitHub python def __abs__ (self): return self .length @overload
method self + other: Vector3 => Vector3 Source code or View on GitHub python @overload def __add__ (self, other: 'Vector3' ) -> 'Vector3' : ... @overload
method self + other: Point3 => Point3 Source code or View on GitHub python @overload def __add__ (self, other: 'Point3' ) -> 'Point3' : ... method self + other Description : V + P -> P
V + V -> V
Arguments :
Return : Vector3Point3
Source code or View on GitHub python def __add__ (self, other): if isinstance (other, Vector3): 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) else : raise TypeError ( f "unsupported operand type(s) for +: 'Vector3' and ' {type (other) } '" ) method self == other Description : 判断两个向量是否相等。
Arguments :
Return : bool
Source code or View on GitHub python def __eq__ (self, other): return approx( self .x, other.x) and approx( self .y, other.y) and approx( self .z, other.z) method self + other: Point3 => Point3 Description : P + V -> P
别去点那边实现了。
Arguments :
Return : Point3
Source code or View on GitHub python def __radd__ (self, other: 'Point3' ) -> 'Point3' : return Point3( self .x + other.x, self .y + other.y, self .z + other.z) @overload
method self - other: Vector3 => Vector3 Source code or View on GitHub python @overload def __sub__ (self, other: 'Vector3' ) -> 'Vector3' : ... @overload
method self - other: Point3 => Point3 Source code or View on GitHub python @overload def __sub__ (self, other: 'Point3' ) -> 'Point3' : ... method self - other Description : V - P -> P
V - V -> V
Arguments :
Return : Vector3Point3
Source code or View on GitHub python def __sub__ (self, other): if isinstance (other, Vector3): 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) else : raise TypeError ( f 'unsupported operand type(s) for -: "Vector3" and " {type (other) } "' ) method self - other: Point3 Description : P - V -> P
Arguments :
Return : Point3
Source code or View on GitHub python def __rsub__ (self, other: 'Point3' ): if isinstance (other, Point3): 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'" ) @overload
method self * other: Vector3 => Vector3 Source code or View on GitHub python @overload def __mul__ (self, other: 'Vector3' ) -> 'Vector3' : ... @overload
method self * other: RealNumber => Vector3 Source code or View on GitHub python @overload def __mul__ (self, other: RealNumber) -> 'Vector3' : ... method self * other: int | float | Vector3 => Vector3 Description : 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments :
Return : Vector3
Source code or View on GitHub python def __mul__ (self, other: 'int | float | Vector3' ) -> 'Vector3' : if isinstance (other, Vector3): return Vector3( self .x * other.x, self .y * other.y, self .z * other.z) elif isinstance (other, ( float , int )): return Vector3( self .x * other, self .y * other, self .z * other) else : raise TypeError ( f "unsupported operand type(s) for *: 'Vector3' and ' {type (other) } '" ) method self * other: RealNumber => Vector3 Source code or View on GitHub python def __rmul__ (self, other: 'RealNumber' ) -> 'Vector3' : return self . __mul__ (other) method self @ other: Vector3 => RealNumber Description : 点乘。
Arguments :
Return : float
Source code or View on GitHub python def __matmul__ (self, other: 'Vector3' ) -> 'RealNumber' : return self .x * other.x + self .y * other.y + self .z * other.z method self / other: RealNumber => Vector3 Source code or View on GitHub python def __truediv__ (self, other: RealNumber) -> 'Vector3' : return Vector3( self .x / other, self .y / other, self .z / other) method - self => Vector3 Description : 取负。
Return : Vector3
Source code or View on GitHub python def __neg__ (self) -> 'Vector3' : return Vector3( - self .x, - self .y, - self .z) var zero_vector3 var x_axis var y_axis var z_axis ',99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",d,[(i(),a("svg",T,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",V,H)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",S,j)),G]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default};