U Pe"(@s$dZdZddlZGdddeZdS)aYVector ====== The :class:`Vector` represents a 2D vector (x, y). Our implementation is built on top of a Python list. An example of constructing a Vector:: >>> # Construct a point at 82,34 >>> v = Vector(82, 34) >>> v[0] 82 >>> v.x 82 >>> v[1] 34 >>> v.y 34 >>> # Construct by giving a list of 2 values >>> pos = (93, 45) >>> v = Vector(pos) >>> v[0] 93 >>> v.x 93 >>> v[1] 45 >>> v.y 45 Optimized usage --------------- Most of the time, you can use a list for arguments instead of using a Vector. For example, if you want to calculate the distance between 2 points:: a = (10, 10) b = (87, 34) # optimized method print('distance between a and b:', Vector(a).distance(b)) # non-optimized method va = Vector(a) vb = Vector(b) print('distance between a and b:', va.distance(vb)) Vector operators ---------------- The :class:`Vector` supports some numeric operators such as +, -, /:: >>> Vector(1, 1) + Vector(9, 5) [10, 6] >>> Vector(9, 5) - Vector(5, 5) [4, 0] >>> Vector(10, 10) / Vector(2., 4.) [5.0, 2.5] >>> Vector(10, 10) / 5. [2.0, 2.0] You can also use in-place operators:: >>> v = Vector(1, 1) >>> v += 2 >>> v [3, 3] >>> v *= 5 [15, 15] >>> v /= 2. [7.5, 7.5] VectorNcs,eZdZdZfddZddZddZeeeZdd Z d d Z ee e Z fd d Z ddZ ddZddZddZddZddZddZddZddZd d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/Zd0d1Zd2d3Zd4d5Z d6d7Z!e"d8d9Z#e"d:d;Z$e"drzAVector class. See module documentation for more information. csLt|dkr"tt||dn&t|dkr@tt||ntddS)NrzInvalid vector)lensuperr__init__ Exception)selflargs __class__//tmp/pip-unpacked-wheel-xzebddm3/kivy/vector.pyr\s   zVector.__init__cCs|dSNrrr rrr_get_xdsz Vector._get_xcCs ||d<dSrr)r xrrr_set_xgsz Vector._set_xcCs|dSNrrrrrr_get_ytsz Vector._get_ycCs ||d<dSrr)r yrrr_set_ywsz Vector._set_ycs:zttt|||WStk r4tdYnXdS)Nzvector::FAILURE in __getslice__)rr __getslice__r TypeError)r ijr rrrszVector.__getslice__cCstttdd||S)NcSs||SNrrrrrrz Vector.__add__..rlistmapr valrrr__add__szVector.__add__cCsRt|ttfkr.|j|7_|j|7_n |j|j7_|j|j7_|Srtypeintfloatrrr$rrr__iadd__s zVector.__iadd__cCstdd|DS)NcSsg|] }| qSrr.0rrrr sz"Vector.__neg__..rrrrr__neg__szVector.__neg__cCstttdd||S)NcSs||Srrrrrrrr z Vector.__sub__..r!r$rrr__sub__szVector.__sub__cCsRt|ttfkr.|j|8_|j|8_n |j|j8_|j|j8_|Srr'r$rrr__isub__s zVector.__isub__csJztttdd|WStk rDtfdd|DYSXdS)NcSs||Srrrrrrrr z Vector.__mul__..csg|] }|qSrrr,r%rrr.sz"Vector.__mul__..rr"r#r r$rr2r__mul__szVector.__mul__cCsRt|ttfkr.|j|9_|j|9_n |j|j9_|j|j9_|Srr'r$rrr__imul__s zVector.__imul__cCs||Srrr$rrr__rmul__szVector.__rmul__csJztttdd|WStk rDtfdd|DYSXdS)NcSs||Srrrrrrrr z$Vector.__truediv__..csg|] }|qSrrr,r2rrr.sz&Vector.__truediv__..r3r$rr2r __truediv__szVector.__truediv__csJztttdd|WStk rDtfdd|DYSXdS)NcSs||Srrrrrrrr z Vector.__div__..csg|] }|qSrrr,r2rrr.sz"Vector.__div__..r3r$rr2r__div__szVector.__div__cCs6zt||WStk r0t|||YSXdSrrr r$rrr __rtruediv__szVector.__rtruediv__cCs6zt||WStk r0t|||YSXdSrr9r$rrr__rdiv__szVector.__rdiv__cCsRt|ttfkr.|j|_|j|_n |j|j_|j|j_|Srr'r$rrr__idiv__s zVector.__idiv__cCst|dd|ddS)zReturns the length of a vector. >>> Vector(10, 10).length() 14.142135623730951 >>> pos = (10, 10) >>> Vector(pos).length() 14.142135623730951 rrrmathsqrtrrrrlengths z Vector.lengthcCs|dd|ddS)zReturns the length of a vector squared. >>> Vector(10, 10).length2() 200 >>> pos = (10, 10) >>> Vector(pos).length2() 200 rrrrrrrrlength2s zVector.length2cCs.t|d|dd|d|ddS)zReturns the distance between two points. >>> Vector(10, 10).distance((5, 10)) 5. >>> a = (90, 33) >>> b = (76, 34) >>> Vector(a).distance(b) 14.035668847618199 rrrr=r torrrdistances zVector.distancecCs(|d|dd|d|ddS)ztReturns the distance between two points squared. >>> Vector(10, 10).distance2((5, 10)) 25 rrrrrBrrr distance2szVector.distance2cCs.|ddkr"|ddkr"tddS||S)zReturns a new vector that has the same direction as vec, but has a length of one. >>> v = Vector(88, 33).normalize() >>> v [0.93632917756904444, 0.3511234415883917] >>> v.length() 1.0 rgr)rr@rrrr normalize s  zVector.normalizecCs |d|d|d|dS)z_Computes the dot product of a and b. >>> Vector(2, 4).dot((2, 2)) 12 rrr)r arrrdotsz Vector.dotcCsTdtj t|d|d|d|d|d|d|d|d}|S)zComputes the angle between a and b, and returns the angle in degrees. >>> Vector(100, 0).angle((0, 100)) -90.0 >>> Vector(87, 23).angle((-77, 10)) -157.7920283010705 rr)r>piatan2)r rGanglerrrrL!s z Vector.anglecCsTt|}t|dt||dt||dt||dt|S)zRotate the vector with an angle in degrees. >>> v = Vector(100, 0) >>> v.rotate(45) [70.71067811865476, 70.71067811865474] rr)r>radiansrcossin)r rLrrrrotate0s  ""z Vector.rotatecCst|dt|dt|dt|df\}}}}t|dt|dt|dt|df\}} } } || ||} || | |} ||| | || ||}|dkrdS| ||||| |}| | | || | |}t||S)a Finds the intersection point between the lines (1)v1->v2 and (2)v3->v4 and returns it as a vector object. >>> a = (98, 28) >>> b = (72, 33) >>> c = (10, -5) >>> d = (20, 88) >>> Vector.line_intersection(a, b, c, d) [15.25931928687196, 43.911669367909241] .. warning:: This is a line intersection method, not a segment intersection. For math see: http://en.wikipedia.org/wiki/Line-line_intersection rrNr*r)v1v2v3v4x1x2x3x4y1y2y3y4uvdenompxpyrrrline_intersection=s44 zVector.line_intersectioncCst|dt|dt|dt|df\}}}}t|dt|dt|dt|df\}} } } || ||} || | |} ||| | || ||}|dkrdS| ||||| |}| | | || | |}||ko|knp(||ko|knp(||k}||ko>| knph| |koZ|knph|| k}||ko~|knp||ko|knp||k}| |ko| knp| |ko| knp| | k}|r |r |r |r t||SdSdS)a Finds the intersection point between segments (1)v1->v2 and (2)v3->v4 and returns it as a vector object. >>> a = (98, 28) >>> b = (72, 33) >>> c = (10, -5) >>> d = (20, 88) >>> Vector.segment_intersection(a, b, c, d) None >>> a = (0, 0) >>> b = (10, 10) >>> c = (0, 10) >>> d = (10, 0) >>> Vector.segment_intersection(a, b, c, d) [5, 5] rrNrQ)rRrSrTrUrVrWrXrYrZr[r\r]r^r_r`rarbZc1c2c3Zc4rrrsegment_intersection_s 44 >@@@ zVector.segment_intersectioncCs|d|dkr |d|dks@|d|dko~|d|dko~|d|dkr`|d|dkp~|d|dko~|d|dkS)aReturn True if `point` is in the bounding box defined by `a` and `b`. >>> bmin = (0, 0) >>> bmax = (100, 100) >>> Vector.in_bbox((50, 50), bmin, bmax) True >>> Vector.in_bbox((647, -10), bmin, bmax) False rrr)ZpointrGbrrrin_bboxs  zVector.in_bbox)'__name__ __module__ __qualname____doc__rrrpropertyrrrrrr&r+r/r0r1r4r5r6r7r8r:r;r<r@rArDrErFrHrLrP staticmethodrcrfrh __classcell__rrr rrXsH              ! ,r)rl__all__r>r"rrrrrsR