ó ~9­\c@ sædZddlmZmZddlmZddlmZddlm Z ddl m Z m Z m Z ddlmZmZddlmZmZdd lmZmZmZmZmZdd lmZd efd „ƒYZd S(s4Parabolic geometrical entity. Contains * Parabola iÿÿÿÿ(tdivisiontprint_function(tS(tordered(t_symbol(tsymbolstsimplifytsolve(tGeometryEntityt GeometrySet(tPointtPoint2D(tLinetLine2DtRay2Dt Segment2DtLinearEntity3D(tEllipsetParabolacB s­eZdZddd„Zed„ƒZed„ƒZed„ƒZed„ƒZ ddd„Z ed „ƒZ ed „ƒZ d „Z ed „ƒZed „ƒZRS(s•A parabolic GeometryEntity. A parabola is declared with a point, that is called 'focus', and a line, that is called 'directrix'. Only vertical or horizontal parabolas are currently supported. Parameters ========== focus : Point Default value is Point(0, 0) directrix : Line Attributes ========== focus directrix axis of symmetry focal length p parameter vertex eccentricity Raises ====== ValueError When `focus` is not a two dimensional point. When `focus` is a point of directrix. NotImplementedError When `directrix` is neither horizontal nor vertical. Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7,8))) >>> p1.focus Point2D(0, 0) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) cK sš|rt|ddƒ}ntddƒ}t|ƒ}|jdkrf|jtjkrftdƒ‚n|j|ƒr„tdƒ‚ntj ||||S(Ntdimiis3The directrix must be a horizontal or vertical lines*The focus must not be a point of directrix( R R tslopeRtInfinitytNotImplementedErrortcontainst ValueErrorRt__new__(tclstfocust directrixtkwargs((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyR@s !cC s tdƒS(sXReturns the ambient dimension of parabola. Returns ======= ambient_dimension : integer Examples ======== >>> from sympy import Parabola, Point, Line >>> f1 = Point(0, 0) >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) >>> p1.ambient_dimension 2 i(R(tself((s6lib/python2.7/site-packages/sympy/geometry/parabola.pytambient_dimensionQscC s|jj|jƒS(s¢The axis of symmetry of the parabola. Returns ======= axis_of_symmetry : Line See Also ======== sympy.geometry.line.Line Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.axis_of_symmetry Line2D(Point2D(0, 0), Point2D(0, 1)) (Rtperpendicular_lineR(R((s6lib/python2.7/site-packages/sympy/geometry/parabola.pytaxis_of_symmetryfscC s |jdS(s¡The directrix of the parabola. Returns ======= directrix : Line See Also ======== sympy.geometry.line.Line Examples ======== >>> from sympy import Parabola, Point, Line >>> l1 = Line(Point(5, 8), Point(7, 8)) >>> p1 = Parabola(Point(0, 0), l1) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) i(targs(R((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyRscC s tdƒS(s×The eccentricity of the parabola. Returns ======= eccentricity : number A parabola may also be characterized as a conic section with an eccentricity of 1. As a consequence of this, all parabolas are similar, meaning that while they can be different sizes, they are all the same shape. See Also ======== https://en.wikipedia.org/wiki/Parabola Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.eccentricity 1 Notes ----- The eccentricity for every Parabola is 1 by definition. i(R(R((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyt eccentricity™s!txtycC sŸt|dtƒ}t|dtƒ}|jjdkrhd|j||jj}||jjd}n/d|j||jj}||jjd}||S(szThe equation of the parabola. Parameters ========== x : str, optional Label for the x-axis. Default value is 'x'. y : str, optional Label for the y-axis. Default value is 'y'. Returns ======= equation : sympy expression Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.equation() -x**2 - 16*y + 64 >>> p1.equation('f') -f**2 - 16*y + 64 >>> p1.equation(y='z') -x**2 - 16*z + 64 trealiii(RtTrueR!Rt p_parametertvertexR$R%(RR$R%tt1tt2((s6lib/python2.7/site-packages/sympy/geometry/parabola.pytequation¼scC s#|jj|jƒ}|d}|S(sYThe focal length of the parabola. Returns ======= focal_lenght : number or symbolic expression Notes ===== The distance between the vertex and the focus (or the vertex and directrix), measured along the axis of symmetry, is the "focal length". See Also ======== https://en.wikipedia.org/wiki/Parabola Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.focal_length 4 i(RtdistanceR(RR-t focal_length((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyR.ãs cC s |jdS(sThe focus of the parabola. Returns ======= focus : Point See Also ======== sympy.geometry.point.Point Examples ======== >>> from sympy import Parabola, Point, Line >>> f1 = Point(0, 0) >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) >>> p1.focus Point2D(0, 0) i(R"(R((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyRscC sîtddtƒ\}}|jƒ}t|tƒr||krF|gSttgt||jƒg||gƒD]}t|ƒ^qnƒƒSn]t|t ƒråt |j ||j df||j dfgƒƒdkrÞ|gSgSnt|t tfƒrgt|t|jd|jdƒjƒg||gƒ}ttg|D]}||kr?t |ƒ^q?ƒƒSt|ttfƒrÀttgt||jƒg||gƒD]}t |ƒ^q¤ƒƒSt|tƒrÞtdƒ‚n tdƒ‚dS(súThe intersection of the parabola and another geometrical entity `o`. Parameters ========== o : GeometryEntity, LinearEntity Returns ======= intersection : list of GeometryEntity objects Examples ======== >>> from sympy import Parabola, Point, Ellipse, Line, Segment >>> p1 = Point(0,0) >>> l1 = Line(Point(1, -2), Point(-1,-2)) >>> parabola1 = Parabola(p1, l1) >>> parabola1.intersection(Ellipse(Point(0, 0), 2, 5)) [Point2D(-2, 0), Point2D(2, 0)] >>> parabola1.intersection(Line(Point(-7, 3), Point(12, 3))) [Point2D(-4, 3), Point2D(4, 3)] >>> parabola1.intersection(Segment((-12, -65), (14, -68))) [] sx yR&iis5Entity must be two dimensional, not three dimensionalsWrong type of argument were putN(RR'R,t isinstanceRtlistRRR R Rtsubst_argsRRR tpointsRRt TypeError(RtoR$R%t parabola_eqtitresult((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyt intersection s$  G;85DcC s“|jjdkrR|jjd }||jjdkrE|j}q|j }n=|jjd }||jjdkr†|j }n |j}|S(s P is a parameter of parabola. Returns ======= p : number or symbolic expression Notes ===== The absolute value of p is the focal length. The sign on p tells which way the parabola faces. Vertical parabolas that open up and horizontal that open right, give a positive value for p. Vertical parabolas that open down and horizontal that open left, give a negative value for p. See Also ======== http://www.sparknotes.com/math/precalc/conicsections/section2.rhtml Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.p_parameter -4 iii(R!RRt coefficientsRR"R.(RR$tpR%((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyR(Rs!    cC sj|j}|jjdkrBt|jd|j|jdƒ}n$t|jd|jd|jƒ}|S(spThe vertex of the parabola. Returns ======= vertex : Point See Also ======== sympy.geometry.point.Point Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.vertex Point2D(0, 4) ii(RR!RR R"R((RRR)((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyR)‚s  '$N(t__name__t __module__t__doc__tNoneRtpropertyRR!RR#R,R.RR9R(R)(((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyRs+#'# 20N(R>t __future__RRt sympy.coreRtsympy.core.compatibilityRtsympy.core.symbolRtsympyRRRtsympy.geometry.entityRR tsympy.geometry.pointR R tsympy.geometry.lineR R RRRtsympy.geometry.ellipseRR(((s6lib/python2.7/site-packages/sympy/geometry/parabola.pyts(