*hPSrSSKJr SSKJr SSKJr SSKJrJ r SSK J r SSK J r SSKJr SS KJrJrJr SS KJr SS KJr SS KJr SS KJrJrJr SSKJr SSK J!r! SSK"J#r# SSK$J%r% SSK&J'r' /SQr(\)"S5Vs/sH n\ "S5PM snur*r+\ "SSS9r,"SS\\5r-"SS\-\5r.\"\.\5S5r!\"\.\5S5rSr/S"S jr0S!r1gs snf)#aThe definition of the base geometrical entity with attributes common to all derived geometrical entities. Contains ======== GeometryEntity GeometricSet Notes ===== A GeometryEntity is any object that has special geometric properties. A GeometrySet is a superclass of any GeometryEntity that can also be viewed as a sympy.sets.Set. In particular, points are the only GeometryEntity not considered a Set. Rn is a GeometrySet representing n-dimensional Euclidean space. R2 and R3 are currently the only ambient spaces implemented. ) annotations)Basic)Tuple) EvalfMixinN)oo)Dummy)sympify)cossinataneye)dispatch)sstr)SetUnion FiniteSet)intersection_sets) union_sets)solve) func_name) is_sequence)Point2DPoint3DPoint Segment2DRay2DLine2D Segment3DLine3DRay3DSegmentRayLinePlaneTriangleRegularPolygonPolygonCircleEllipseCurveParabola entity_dummyT)realc\rSrSr%SrSrS\S'SrSrSr S r S r S r S r S rSrSrSrSrSrS!SjrSr\S5r\S5rSrSrSrSrSrS"SjrS#SjrS$Sjr S r!Sr"g)%GeometryEntityGzThe base class for all geometrical entities. This class does not represent any particular geometric entity, it only provides the implementation of some methods common to all subclasses. ztuple[str, ...] __slots__cURRnURRnX#:X#:- nU(dgSnURRH#n[R UR5n O US:XaU$SnURRH#n[R UR5n O US:XaU$XW:XW:- $![ a SnMf=f![ a SnMZf=f)z#Comparison of two GeometryEntities.r) __class____name____mro__ordering_of_classesindex ValueError)selfothern1n2ci1clsi2s R/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/geometry/entity.py__cmp__GeometryEntity.__cmp__Qs ^^ $ $ __ % % W ! >>))C (..s||<* 8H ??**C (..s||<+ 8HBG$$    s$C!C( C%$C%( C87C8cL[U5[U5LaX:H$[5e)zPSubclasses should implement this method for anything more complex than equality.)typeNotImplementedErrorr>r?s rF __contains__GeometryEntity.__contains__os# :e $= !##c,[UR5$)z=Returns a tuple that will be passed to __new__ on unpickling.)tupleargsr>s rF__getnewargs__GeometryEntity.__getnewargs__usTYYrOc X:X+$)z,Test inequality of two geometrical entities.r4r>os rF__ne__GeometryEntity.__ne__ys }rOcSnUVs/sH"oC"U5(a[U6O [U5PM$ nn[R"U/UQ76$s snf)Nc^[US5(aUR(ag[U5$)Nis_PointF)hasattrr]r)as rFis_seq_and_not_point4GeometryEntity.__new__..is_seq_and_not_points"q*%%!**q> !rO)rr r__new__)rDrRkwargsr`r_s rFrbGeometryEntity.__new__}sQ " OSSd1!44q '!*DdS}}S(4((Ts)A c$URU5$)z%Implementation of reverse add method.)__add__r>r_s rF__radd__GeometryEntity.__radd__yyrOc$URU5$)z*Implementation of reverse division method.) __truediv__rgs rF __rtruediv__GeometryEntity.__rtruediv__s}}T""rOcX[U5R[UR5-$)zIString representation of a GeometryEntity that can be evaluated by sympy.)rJr9reprrRrSs rF__repr__GeometryEntity.__repr__s!Dz""T$))_44rOc$URU5$)z0Implementation of reverse multiplication method.)__mul__rgs rF__rmul__GeometryEntity.__rmul__rjrOc$URU5$)z-Implementation of reverse subtraction method.)__sub__rgs rF__rsub__GeometryEntity.__rsub__rjrOcX[U5R[UR5-$)z*String representation of a GeometryEntity.)rJr9rrRrSs rF__str__GeometryEntity.__str__sDz""T$))_44rOcSSKJnJn [U5(d[U5(aB[ X5(aU"U5nU"U5nOU"U5nU"U5nUR X5$g)Nr)rr)sympy.geometry.pointrrr isinstance_subs)r>oldnewrrs rF _eval_subsGeometryEntity._eval_subss]7 s  {3//$((clclCjCjJJs( ( 0rOcURn[SU55(dgSn[ [ U5up4pVX5:XaXF:XaUS- US- US-US-4up4pVO'Sn[ XS- Xd- /5nX-n X9-nXI-nXY- nXi- nXS- n Xd- n [[ SU /5S/5n [[ SU /5S/5n [ X5S:XaS O[ X5[ X5- nURU5nS RX4X5nS RXd-5nURUX5nUS RUU5-$![[4a gf=f![[4a gf=f) z;SVG representation of a GeometryEntity suitable for IPythonNc3^# UH#oR=(a URv M% g7fN) is_number is_finite).0xs rF ,GeometryEntity._repr_svg_..s?1;;.1;;.s+-a g������?g?g������Y@i,��r���������?z {} {} {} {}zmatrix(1,0,0,-1,0,{})z{}) boundsrK TypeErrorallmaprmaxmin_svgformat)r>rsvg_topxminyminxmaxymaxexpand widest_part expand_amountdxdywidthheight scale_factorsvgview_box transforms rF _repr_svg_GeometryEntity._repr_svg_s [[F ????("%QD r fill_colors rFrGeometryEntity._svgs "##rOcU$rr4rSs rF_sympy_GeometryEntity._sympy_s rOc[5e)zCWhat is the dimension of the space that the object is contained in?rrSs rFambient_dimension GeometryEntity.ambient_dimensions "##rOc[5e)zgReturn a tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the geometric figure. rrSs rFrGeometryEntity.boundss "##rOc^SSKJn SSKJnJnJn SSKJn SSKJ nJ n [X5(aTRU5$[X5(a[U4SjUR55$[XU45(ag[X5(aTRUR5=(aj TRU"URR UR"-URR$55=(a TR'U5(+$[X5(aP[X5(a!TRUR5(dg[U4SjUR(55$[+5e) a- Return True if o is inside (not on or outside) the boundaries of self. The object will be decomposed into Points and individual Entities need only define an encloses_point method for their class. See Also ======== sympy.geometry.ellipse.Ellipse.encloses_point sympy.geometry.polygon.Polygon.encloses_point Examples ======== >>> from sympy import RegularPolygon, Point, Polygon >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) >>> t2 = Polygon(*RegularPolygon(Point(0, 0), 2, 3).vertices) >>> t2.encloses(t) True >>> t.encloses(t2) False rr)r#r$r%)r+)r)r(c3F># UHnTRU5v M g7frencloses_point)rrr>s rFr*GeometryEntity.encloses..0s@x!t**1--x!Fc3F># UHnTRU5v M g7frr)rvr>s rFrr<sBz!t**1--zr)rrsympy.geometry.liner#r$r%sympy.geometry.ellipser+sympy.geometry.polygonr)r(rrrpointscenterrhradiusy intersectionverticesrK) r>rXrr#r$r%r+r)r(s ` rFenclosesGeometryEntity.enclosess 4 /::2B a  &&q) )  # #@qxx@@ @ ; ' '  # #&&qxx0)##ahhjj199,ahhjj9;)%%a(( ) # #!,,**18844 BqzzBB B!##rOc X:H$rr4rWs rFequalsGeometryEntity.equals?s yrOc[5e)a\ Returns a list of all of the intersections of self with o. Notes ===== An entity is not required to implement this method. If two different types of entities can intersect, the item with higher index in ordering_of_classes should implement intersections with anything having a lower index. See Also ======== sympy.geometry.util.intersection rrWs rFrGeometryEntity.intersectionBs &"##rOc[5e)aIs this geometrical entity similar to another geometrical entity? Two entities are similar if a uniform scaling (enlarging or shrinking) of one of the entities will allow one to obtain the other. Notes ===== This method is not intended to be used directly but rather through the `are_similar` function found in util.py. An entity is not required to implement this method. If two different types of entities can be similar, it is only required that one of them be able to determine this. See Also ======== scale rrLs rF is_similarGeometryEntity.is_similarWs *"##rOc ^ SSKJm UnUnT "SS5nURR(aoURSR nU(dUR SS9$URT 5Vs/sH"ofURSXVR - -S94PM$ nnGOUR[LaoURSRnU(dUR SS9$URT 5Vs/sH"ofURSXVR- -S94PM$ nnGO[US5(d2[U 4SjUR55(d[S U-5e[UR5nURn U S*U S - n T "[[ 5n U RU *S9R!U*U5R SS9R!X5RU S9n URT 5Vs/sH5ofU R#[UR[ UR 054PM7 nnUR#[%U55$s snfs snfs snf) a1 Reflects an object across a line. Parameters ========== line: Line Examples ======== >>> from sympy import pi, sqrt, Line, RegularPolygon >>> l = Line((0, pi), slope=sqrt(2)) >>> pent = RegularPolygon((1, 2), 1, 5) >>> rpent = pent.reflect(l) >>> rpent RegularPolygon(Point2D(-2*sqrt(2)*pi/3 - 1/3 + 4*sqrt(2)/3, 2/3 + 2*sqrt(2)/3 + 2*pi/3), -1, 5, -atan(2*sqrt(2)) + 3*pi/5) >>> from sympy import pi, Line, Circle, Point >>> l = Line((0, pi), slope=1) >>> circ = Circle(Point(0, 0), 5) >>> rcirc = circ.reflect(l) >>> rcirc Circle(Point2D(-pi, pi), -5) rrr7)rr.)rreflectc3<># UHn[UT5v M g7fr)r)rargrs rFr)GeometryEntity.reflect..s5>6lineglrXrprepsr_rBdxfrs @rFrGeometryEntity.reflectns6 /   !QK 77??q Awww}$=>WWU^L^ aSSk 23^DLD WW]q Awww}$=>WWU^L^ aSSk 23^DLD1i((5>67ff5>2>2>)?!CEEQWW AA2qt Aq!B#**A2q177"7&,yy1y~ ABO1 QQ$456DOzz$t*%%)M MPs2)I4)I?>> from sympy import Point, RegularPolygon, Polygon, pi >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) >>> t # vertex on x axis Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2)) >>> t.rotate(pi/2) # vertex on y axis now Triangle(Point2D(0, 1), Point2D(-sqrt(3)/2, -1/2), Point2D(sqrt(3)/2, -1/2)) )rRrr2appendrrJ)r>angleptnewargsr_s rFrGeometryEntity.rotatesV*A!^,,qxx23q!  Dz7##rOc "SSKJn U(aGU"USS9nUR"U*R6R X5R"UR6$[ U5"URVs/sHoUR X5PM sn6$s snf)aeScale the object by multiplying the x,y-coordinates by x and y. If pt is given, the scaling is done relative to that point; the object is shifted by -pt, scaled, and shifted by pt. See Also ======== rotate, translate Examples ======== >>> from sympy import RegularPolygon, Point, Polygon >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) >>> t Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2)) >>> t.scale(2) Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)/2), Point2D(-1, -sqrt(3)/2)) >>> t.scale(2, 2) Triangle(Point2D(2, 0), Point2D(-1, sqrt(3)), Point2D(-1, -sqrt(3))) rrr.dim)rrrrRrrJ)r>rrrrr_s rFrGeometryEntity.scalesp0 / rq!B>>RC::.44Q:DDbggN NDz499=9aGGAM9=>>=s.B c/nURHKn[U[5(a"URUR X55 M:URU5 MM UR "U6$)aShift the object by adding to the x,y-coordinates the values x and y. See Also ======== rotate, scale Examples ======== >>> from sympy import RegularPolygon, Point, Polygon >>> t = Polygon(*RegularPolygon(Point(0, 0), 1, 3).vertices) >>> t Triangle(Point2D(1, 0), Point2D(-1/2, sqrt(3)/2), Point2D(-1/2, -sqrt(3)/2)) >>> t.translate(2) Triangle(Point2D(3, 0), Point2D(3/2, sqrt(3)/2), Point2D(3/2, -sqrt(3)/2)) >>> t.translate(2, 2) Triangle(Point2D(3, 2), Point2D(3/2, sqrt(3)/2 + 2), Point2D(3/2, 2 - sqrt(3)/2)) )rRrr2rrfunc)r>rrrr_s rFrGeometryEntity.translatesV*A!^,,q{{101q!  yy'""rOc.SSKJn [U[5(dU"XRS9n[X5(d [ S5e[ UR[5U- [SS9nU(d[ S[U5-5eX$S[0$)a}Return the parameter corresponding to the given point. Evaluating an arbitrary point of the entity at this parameter value will return the given point. Examples ======== >>> from sympy import Line, Point >>> from sympy.abc import t >>> a = Point(0, 0) >>> b = Point(2, 2) >>> Line(a, b).parameter_value((1, 1), t) {t: 1/2} >>> Line(a, b).arbitrary_point(t).subs(_) Point2D(1, 1) rrrzother must be a pointT)rzGiven point is not on %s) rrrr2rr=rarbitrary_pointTr)r>r?trsols rFparameter_valueGeometryEntity.parameter_values" /%00%%;%;# UHnTRU5v M g7fr)rM)rir>s rFr(GeometrySet._contains..&s;Ut((++Ur)rr is_FiniteSetrrMrLs` rF _containsGeometrySet._contains"s< eS ! !e&8&8;U;; ;  ''rON)r9rrrrr5r rr4rOrFrrsI(rOrcUR(aTUVs/sHo RU5(aMUPM nn[U5[U5:Xag[U[ U65$URU5(aU$gs snf)zJReturns the union of self and o for use with sympy.sets.Set, if possible. N)r r lenrr)r>rXr other_pointss rFrr*sj ~~#$>1aNN1,=1 > | A &T9l344 ~~a  ?s A?A?c f^SSKJn UR(a[U4SjU56nOTR U5n[UVs/sHn[ XB5(dMUPM sn6nUVs/sHn[ XB5(aMUPM nn[Xe/-6$![ a gf=fs snfs snf)z?Returns a sympy.sets.Set of intersection objects, if possible. rrc3X># UHnTRU5(dMUv M! g7fr)contains)rrr>s rFr$intersection_sets..GsA1a a0@1s* *N)rrr rrrKrr)r>rXrinterrr non_pointss` rFrr<s +  >>A1ABE%%a(EEBEqZ-AEB CF"?U*Q*>!UJ? :( **  C?s.#BBB) B).B.B. B&%B&c,[S5nXS'XS'U$)z6Return the matrix to translate a 2-D point by x and y.)r.r)r.rr)rrrvs rFrrUs QBtHtH IrONc[S5nXS'XS'U(a9SSKJn U"USS9n[U*R6n[UR6nXS-U-$U$)zReturn the matrix to multiply a 2-D point's coordinates by x and y. If pt is given, the scaling is done relative to that point.rr)rrrrr.r)rrrrrR)rrrrrtr1tr2s rFrr]s\ QBtHtH . 21 2#$!vcz IrOch[U5n[S5[U5-nXS'U*US'SUS'U$)aReturn the matrix to rotate a 2-D point about the origin by ``angle``. The angle is measured in radians. To Point a point about a point other then the origin, translate the Point, do the rotation, and translate it back: >>> from sympy.geometry.entity import rotate, translate >>> from sympy import Point, pi >>> rot_about_11 = translate(-1, -1)*rotate(pi/2)*translate(1, 1) >>> Point(1, 1).transform(rot_about_11) Point2D(1, 1) >>> Point(0, 0).transform(rot_about_11) Point2D(2, 0) r)rr)rrr)r.r.)r rr )thsrs rFrrms> BA QBBtHrBtHBtH IrOr)2r __future__rsympy.core.basicrsympy.core.containersrsympy.core.evalfrrsympy.core.numbersrsympy.core.symbolr sympy.core.sympifyr (sympy.functions.elementary.trigonometricr r r sympy.matricesrsympy.multipledispatchrsympy.printingr sympy.setsrrr sympy.sets.handlers.intersectionrsympy.sets.handlers.unionrsympy.solvers.solversrsympy.utilities.miscrsympy.utilities.iterablesrr;rangerrrr2rrrr)r s0rFr2s*#"'*!#&CC+,,>0'*10(-Qx0x!nx01 .t$RUJRj (.# ( +s" +s++0  U1sC"