l jBj6dZddlmZgdZddlmZddlmZmZm Z ddl Z ddl Tddl mZdd lmZdd lmZmZdd lmZmZmZdd lmZmZdd lmZddlmZmZm Z erddlm!Z!ddl"mZ#ddl$m%Z%m&Z&m'Z'm(Z(ddlmZGddeeZ)Gdde)Z*Gdde)Z+Gdde+Z,Gdde*Z-Gdde,Z.Gdd e*Z/Gd!d"e/Z0Gd#d$e/Z1Gd%d&eeZ2Gd'd(e)Z3dS))z*Mobjects that are simple geometric shapes.) annotations) PolygramPolygonRegularPolygramRegularPolygonStarTriangle RectangleSquareRoundedRectangleCutout ConvexHull)ceil) TYPE_CHECKINGAnyLiteralN)*)ArcBetweenPoints)ConvertToOpenGL)VGroupVMobject)BLUEWHITEParsableManimColor)adjacent_n_tuplesadjacent_pairs) QuickHull)angle_between_vectors normalizeregular_vertices)Self)Point3D Point3D_Array Point3DLikePoint3DLike_Array)rcJeZdZdZeddfd Zdd ZddZ dddZxZ S)raA generalized :class:`Polygon`, allowing for disconnected sets of edges. Parameters ---------- vertex_groups The groups of vertices making up the :class:`Polygram`. The first vertex in each group is repeated to close the shape. Each point must be 3-dimensional: ``[x,y,z]`` color The color of the :class:`Polygram`. kwargs Forwarded to the parent constructor. Examples -------- .. manim:: PolygramExample import numpy as np class PolygramExample(Scene): def construct(self): hexagram = Polygram( [[0, 2, 0], [-np.sqrt(3), -1, 0], [np.sqrt(3), -1, 0]], [[-np.sqrt(3), 1, 0], [0, -2, 0], [np.sqrt(3), 1, 0]], ) self.add(hexagram) dot = Dot() self.play(MoveAlongPath(dot, hexagram), run_time=5, rate_func=linear) self.remove(dot) self.wait() color vertex_groupsr%r(rkwargsrctjdd|i||D]R}|^}}tj|}|||gd|D|SdS)Nr(c3>K|]}tj|VdSN)nparray).0vertexs Z/home/agentuser/manim-venv/lib/python3.11/site-packages/manim/mobject/geometry/polygram.py z$Polygram.__init__..cs,;;28F##;;;;;;)super__init__r.r/start_new_pathadd_points_as_corners)selfr(r)r*vertices first_vertex __class__s r2r7zPolygram.__init__Ss //u////%  H'/ #L88L11L    - - -  & &J;;(;;;J\J      r4returnr#c*|S)aGets the vertices of the :class:`Polygram`. Returns ------- :class:`numpy.ndarray` The vertices of the :class:`Polygram`. Examples -------- :: >>> sq = Square() >>> sq.get_vertices() array([[ 1., 1., 0.], [-1., 1., 0.], [-1., -1., 0.], [ 1., -1., 0.]]) )get_start_anchorsr:s r2 get_verticeszPolygram.get_verticesfs&%%'''r4list[Point3D_Array]c:g}g}t||dD]_\}}|||||dr)|t j|g}`|S)aGets the vertex groups of the :class:`Polygram`. Returns ------- list[Point3D_Array] The list of vertex groups of the :class:`Polygram`. Examples -------- :: >>> poly = Polygram([ORIGIN, RIGHT, UP, LEFT + UP], [LEFT, LEFT + UP, 2 * LEFT]) >>> groups = poly.get_vertex_groups() >>> len(groups) 2 >>> groups[0] array([[ 0., 0., 0.], [ 1., 0., 0.], [ 0., 1., 0.], [-1., 1., 0.]]) >>> groups[1] array([[-1., 0., 0.], [-1., 1., 0.], [-2., 0., 0.]]) Tstrictr)zipr@get_end_anchorsappendconsider_points_equalsr.r/)r:r)groupstartends r2get_vertex_groupszPolygram.get_vertex_groups{s4   " " $ $d&:&:&<&z*Polygram.round_corners..s+&R&R&Rsc#*ooPQ>Q>Qs>Q>Q>Qr4c6g|]}|Sr5)get_arc_lengthr`s r2rbz*Polygram.round_corners..s$MMM#++--MMMr4c6g|]}t|jSr5r]r`s r2rbz*Polygram.round_corners..s LLLS__LLLr4r\g?NLine)rN isinstancerVfloatr^rrGrrrr.signtancrossrrIsummanim.mobject.geometry.linerhrextendr_get_end get_startinsert_n_curves get_length set_pointsr/)r:rQrSrU new_points vertex_grouparcs radius_listcurrent_radiusv1v2v3vect1vect2 unit_vect1 unit_vect2rYcut_off_lengthrkranonzero_length_arcstotal_arc_length num_curvesaverage_arc_lengthrharc1arc2lines r2 round_cornerszPolygram.round_cornerss,| Q;;K$&  2244? /? /LD&3,// M%h\):):: $tC ,=,=F ,K'L'LL 03.|Q??111 ! !, RRR&u-- &u-- -eU;;000"0"&2C2C!Cwrxu55a899&n44n44,#@   C    ( -&R&Rd&R&R&R#*++a//'*MM9LMMM(($LL8KLLLMMPQQ*:J)F&&),&H)tCRCy)D 8 8 8 8 8 8,T22 / / d!!$+...tDLLNNDNN,<,<==-W((doo.?.?BT.T)U)UVVV!!$+.... / ,,--- r4)r)r%r(rr*r)r>r#)r>rC)rOFrP)rQrRrSrTrUrVr>r!) __name__ __module__ __qualname____doc__rr7rBrNr __classcell__r=s@r2rr0s  J%)&((((*((((X'**/-. FFFFFFFFFr4r) metaclassc$eZdZdZd fd ZxZS) raA shape consisting of one closed loop of vertices. Parameters ---------- vertices The vertices of the :class:`Polygon`. kwargs Forwarded to the parent constructor. Examples -------- .. manim:: PolygonExample :save_last_frame: class PolygonExample(Scene): def construct(self): isosceles = Polygon([-5, 1.5, 0], [-2, 1.5, 0], [-3.5, -2, 0]) position_list = [ [4, 1, 0], # middle right [4, -2.5, 0], # bottom right [0, -2.5, 0], # bottom left [0, 3, 0], # top left [2, 1, 0], # middle [4, 3, 0], # top right ] square_and_triangles = Polygon(*position_list, color=PURPLE_B) self.add(isosceles, square_and_triangles) r;r$r*rr>Nonec<tj|fi|dSr-r6r7)r:r;r*r=s r2r7zPolygon.__init__Ls(,,V,,,,,r4)r;r$r*rr>rrrrrr7rrs@r2rr.sG:----------r4rc.eZdZdZdddddfdZxZS)raRA :class:`Polygram` with regularly spaced vertices. Parameters ---------- num_vertices The number of vertices. density The density of the :class:`RegularPolygram`. Can be thought of as how many vertices to hop to draw a line between them. Every ``density``-th vertex is connected. radius The radius of the circle that the vertices are placed on. start_angle The angle the vertices start at; the rotation of the :class:`RegularPolygram`. kwargs Forwarded to the parent constructor. Examples -------- .. manim:: RegularPolygramExample :save_last_frame: class RegularPolygramExample(Scene): def construct(self): pentagram = RegularPolygram(5, radius=2) self.add(pentagram) rPN)densityrQ start_angle num_verticesrVrrQrjr float | Noner*rr>rc Vtj}|z|zdfd }||\}|_|g} td|D]=} |j| |z tzz z}||\} } | | >t j| i|dS)Nrrr>tuple[list[Any], float]ct|\}}g}d} ||||z }|z}|dkrn-||fS)NrQrr)r rI)r reg_verticesr;irrrQs r2gen_polygon_verticesz6RegularPolygram.__init__..gen_polygon_verticess}(8'))) %L+ HA  Q000W \!66  [( (r4r)rrr>r)r.gcdrrangeTAUrIr6r7)r:rrrQrr*num_gonsr first_groupr)rrK_r=s ``` r2r7zRegularPolygram.__init__ps,6,00! H ) ) ) ) ) ) ) )&)=(<[(I(I% T%$ q(## ( (A*a(lc-AL-PPK++K88HE1   ' ' ' '-2622222r4) rrVrrVrQrjrrr*rr>rrrs@r2rrPs]F$( 838383838383838383838383r4rc&eZdZdZd d fd ZxZS) raAn n-sided regular :class:`Polygon`. Parameters ---------- n The number of sides of the :class:`RegularPolygon`. kwargs Forwarded to the parent constructor. Examples -------- .. manim:: RegularPolygonExample :save_last_frame: class RegularPolygonExample(Scene): def construct(self): poly_1 = RegularPolygon(n=6) poly_2 = RegularPolygon(n=6, start_angle=30*DEGREES, color=GREEN) poly_3 = RegularPolygon(n=10, color=RED) poly_group = Group(poly_1, poly_2, poly_3).scale(1.5).arrange(buff=1) self.add(poly_group) nrVr*rr>rc @tj|fddi|dS)Nrrr)r:rr*r=s r2r7zRegularPolygon.__init__s-00A000000r4)r)rrVr*rr>rrrs@r2rrsL011111111111r4rc:eZdZdZ ddddedz ddfdZxZS)raA regular polygram without the intersecting lines. Parameters ---------- n How many points on the :class:`Star`. outer_radius The radius of the circle that the outer vertices are placed on. inner_radius The radius of the circle that the inner vertices are placed on. If unspecified, the inner radius will be calculated such that the edges of the :class:`Star` perfectly follow the edges of its :class:`RegularPolygram` counterpart. density The density of the :class:`Star`. Only used if ``inner_radius`` is unspecified. See :class:`RegularPolygram` for more information. start_angle The angle the vertices start at; the rotation of the :class:`Star`. kwargs Forwardeds to the parent constructor. Raises ------ :exc:`ValueError` If ``inner_radius`` is unspecified and ``density`` is not in the range ``[1, n/2)``. Examples -------- .. manim:: StarExample class StarExample(Scene): def construct(self): pentagram = RegularPolygram(5, radius=2) star = Star(outer_radius=2, color=RED) self.add(pentagram) self.play(Create(star), run_time=3) self.play(FadeOut(star), run_time=2) .. manim:: DifferentDensitiesExample :save_last_frame: class DifferentDensitiesExample(Scene): def construct(self): density_2 = Star(7, outer_radius=2, density=2, color=RED) density_3 = Star(7, outer_radius=2, density=3, color=PURPLE) self.add(VGroup(density_2, density_3).arrange(RIGHT)) rNrPr\) outer_radius inner_radiusrrrrVrrjrrrrr*rr>rc <td|zz }||dks ||dz krtd|d|t|z|z }dtj|tj|dz tj|z zz } |tj|| zz }t |||\} |_t |||j|z\} } g} t| | dD]}| |tj | i|dS) NrPrzIncompatible density z for number of points rrTrE) r ValueErrorr.rlcossinr rrGrpr6r7)r:rrrrrr* inner_angle outer_angle inverse_xouter_verticesinner_verticesrr;pairr=s r2r7z Star.__init__sjQUm   !||w!a%// NGNN1NN-!+KBF;// $$q(BF;,?,??I(26++>+>+JKL+; #, , , (( - (;6    ')tDDD " "D OOD ! ! ! !(-f-----r4)r)rrVrrjrrrrVrrr*rr>r)rrrrrr7rrs@r2rrsn77v,. %)$'!G,.,.,.,.,.,.,.,.,.,.,.,.r4rc$eZdZdZdfd ZxZS)r aAn equilateral triangle. Parameters ---------- kwargs Additional arguments to be passed to :class:`RegularPolygon` Examples -------- .. manim:: TriangleExample :save_last_frame: class TriangleExample(Scene): def construct(self): triangle_1 = Triangle() triangle_2 = Triangle().scale(2).rotate(60*DEGREES) tri_group = Group(triangle_1, triangle_2).arrange(buff=1) self.add(tri_group) r*rr>rc >tjdddi|dS)NrrXr5r)r:r*r=s r2r7zTriangle.__init__Fs+''1''''''r4)r*rr>rrrs@r2r r 1sG(((((((((((r4r c4eZdZdZeddddddfdfd ZxZS)r a*A quadrilateral with two sets of parallel sides. Parameters ---------- color The color of the rectangle. height The vertical height of the rectangle. width The horizontal width of the rectangle. grid_xstep Space between vertical grid lines. grid_ystep Space between horizontal grid lines. mark_paths_closed No purpose. close_new_points No purpose. kwargs Additional arguments to be passed to :class:`Polygon` Examples ---------- .. manim:: RectangleExample :save_last_frame: class RectangleExample(Scene): def construct(self): rect1 = Rectangle(width=4.0, height=2.0, grid_xstep=1.0, grid_ystep=0.5) rect2 = Rectangle(width=1.0, height=4.0) rect3 = Rectangle(width=2.0, height=2.0, grid_xstep=1.0, grid_ystep=1.0) rect3.grid_lines.set_stroke(width=1) rects = Group(rect1, rect2, rect3).arrange(buff=1) self.add(rects) @g@NTr(rheightrjwidth grid_xstepr grid_ystepmark_paths_closedrTclose_new_pointsr*rc 0 tjtttt fdi|||| t|_ srddl m | rbttz } t  fdtd| D} |j | rbttz } t  fdtd| D} |j | |j r||j dSdS)Nr(rrgc3K|]E}d|ztzzd|ztzztzzVFdSrr'N)RIGHTDOWN)r0rrhr(rrvs r2r3z%Rectangle.__init__..s  D!q:~55!q:~55 E#r4rc3K|]E}d|ztzzd|ztzztzzVFdSr)rr)r0rrhr(rrrs r2r3z%Rectangle.__init__..s  D!q:~44!q:~44uu}D#r4)r6r7URULDLDRstretch_to_fit_widthstretch_to_fit_heightrBr grid_linesrorhabsrVradd)r:r(rrrrrrr*countgridrhrr=s ````` @@r2r7zRectangle.__init__ps RR??u???? !!%((( ""6***      ((  $ $ 8 8 8 8 8 8!!##A  &ZJ *++E #1e__  D O   % % %  &ZJ+,,E #1e__  D O   % % % ? & HHT_ % % % % % & &r4)r(rrrjrrjrrrrrrTrrTr*r)rrrrrr7rrs@r2r r Jsd##N%*#'#'"&!%6&6&6&6&6&6&6&6&6&6&6&r4r c`eZdZdZd dfd Zedd Zejdd ZxZS)r aA rectangle with equal side lengths. Parameters ---------- side_length The length of the sides of the square. kwargs Additional arguments to be passed to :class:`Rectangle`. Examples -------- .. manim:: SquareExample :save_last_frame: class SquareExample(Scene): def construct(self): square_1 = Square(side_length=2.0).shift(DOWN) square_2 = Square(side_length=1.0).next_to(square_1, direction=UP) square_3 = Square(side_length=0.5).next_to(square_2, direction=UP) self.add(square_1, square_2, square_3) r side_lengthrjr*rr>rc @tjd||d|dS)N)rrr5r)r:rr*r=s r2r7zSquare.__init__s-I ;II&IIIIIr4cttj|d|dz S)Nrr)rjr.linalgnormrBrAs r2rzSquare.side_lengthsFRY^^D$5$5$7$7$:T=N=N=P=PQR=S$STTUUUr4valuec@|||jz dSr-)scaler)r:rs r2rzSquare.side_lengths" 54++,,,,,r4)r)rrjr*rr>r)r>rj)rrjr>r) rrrrr7propertyrsetterrrs@r2r r s,JJJJJJJVVVXV--------r4r c&eZdZdZdd fd ZxZS) r aA rectangle with rounded corners. Parameters ---------- corner_radius The curvature of the corners of the rectangle. kwargs Additional arguments to be passed to :class:`Rectangle` Examples -------- .. manim:: RoundedRectangleExample :save_last_frame: class RoundedRectangleExample(Scene): def construct(self): rect_1 = RoundedRectangle(corner_radius=0.5) rect_2 = RoundedRectangle(corner_radius=1.5, height=4.0, width=4.0) rect_group = Group(rect_1, rect_2).arrange(buff=1) self.add(rect_group) rO corner_radiusrRr*rc |tjdi|||_||jdS)Nr5)r6r7rr)r:rr*r=s r2r7zRoundedRectangle.__init__sE""6"""* 4-.....r4)rO)rrRr*rrrs@r2r r sL.///////////r4r c$eZdZdZd fd ZxZS) r aA shape with smaller cutouts. Parameters ---------- main_shape The primary shape from which cutouts are made. mobjects The smaller shapes which are to be cut out of the ``main_shape``. kwargs Further keyword arguments that are passed to the constructor of :class:`~.VMobject`. .. warning:: Technically, this class behaves similar to a symmetric difference: if parts of the ``mobjects`` are not located within the ``main_shape``, these parts will be added to the resulting :class:`~.VMobject`. Examples -------- .. manim:: CutoutExample class CutoutExample(Scene): def construct(self): s1 = Square().scale(2.5) s2 = Triangle().shift(DOWN + RIGHT).scale(0.5) s3 = Square().shift(UP + RIGHT).scale(0.5) s4 = RegularPolygon(5).shift(DOWN + LEFT).scale(0.5) s5 = RegularPolygon(6).shift(UP + LEFT).scale(0.5) c = Cutout(s1, s2, s3, s4, s5, fill_opacity=1, color=BLUE, stroke_color=RED) self.play(Write(c), run_time=4) self.wait() main_shapermobjectsr*rr>rc tjdi|||j|dkrdnd}|D]/}|||j0dS)NCWCCWr5)r6r7 append_pointsr_ get_directionforce_direction)r:rrr* sub_directionmobjectr=s r2r7zCutout.__init__ s ""6""" :,-----//477EET   N NG   w66}EEL M M M M N Nr4)rrrrr*rr>rrrs@r2r r sR  D N N N N N N N N N Nr4r c*eZdZdZddd fd ZxZS)raConstructs a convex hull for a set of points in no particular order. Parameters ---------- points The points to consider. tolerance The tolerance used by quickhull. kwargs Forwarded to the parent constructor. Examples -------- .. manim:: ConvexHullExample :save_last_frame: :quality: high class ConvexHullExample(Scene): def construct(self): points = [ [-2.35, -2.25, 0], [1.65, -2.25, 0], [2.65, -0.25, 0], [1.65, 1.75, 0], [-0.35, 2.75, 0], [-2.35, 0.75, 0], [-0.35, -1.25, 0], [0.65, -0.25, 0], [-1.35, 0.25, 0], [0.15, 0.75, 0] ] hull = ConvexHull(*points, color=BLUE) dots = VGroup(*[Dot(point) for point in points]) self.add(hull) self.add(dots) gh㈵>) tolerancer_r$rrjr*rr>rctj|ddddf}t|}||t |j|jz }|}t|j }t|t|kr]|d} |j | |hz \}|j | hz \} | | t|t|k]tj d|D} tj| tjt| dff} t!j| fi|dS)NrPrfcg|] }|j Sr5) coordinates)r0sfs r2rbz'ConvexHull.__init__..Rs D D DB D D Dr4r)r.r/rbuildsetfacetsremovedpoplist subfacetsr^ neighborsrIvstackhstackzerosr6r7) r:rr_r*r/hullrfacetrrrr;r=s r2r7zConvexHull.__init__?s\  BQB'## 5T[!!DL0 )) )nnF ++2B~b)UG3HUOrd*ER   R )nnF ++i D D) D D DEE 9k28S5E5Eq4I+J+JKLL ,,V,,,,,r4)r_r$rrjr*rr>rrrs@r2rrsW##L8<------------r4r)4r __future__r__all__mathrtypingrrrnumpyr.manim.constantsmanim.mobject.geometry.arcr)manim.mobject.opengl.opengl_compatibilityr&manim.mobject.types.vectorized_mobjectrrmanim.utils.colorrrrmanim.utils.iterablesrrmanim.utils.qhullrmanim.utils.space_opsrrr r! numpy.typingnpt manim.typingr"r#r$r%rrrrrr r r r r rr5r4r2rs11""""""   ..........777777EEEEEECCCCCCCC==========CCCCCCCC''''''TTTTTTTTTT 5 544444{{{{{x?{{{{|-----h---DX3X3X3X3X3hX3X3X3v11111_111:f.f.f.f.f.7f.f.f.R(((((~(((2\&\&\&\&\&\&\&\&~ - - - - -Y - - -F/////y///<,N,N,N,N,NX,N,N,N,N^=-=-=-=-=-=-=-=-=-=-r4