l j>=FdZddlmZddlmZddlmZmZddlZ ddl m Z ddl m Z ddlmZdd lmZdd lmZerdd lmZdd lmZmZgd ZGddeZGddeZGddeZGddeZGddeZGddeZdS)z-General polyhedral class and platonic solids.) annotations)Hashable) TYPE_CHECKINGAnyN)Polygon)Graph)Dot3D)VGroup) QuickHull)Mobject)Point3DPoint3DLike_Array) Polyhedron Tetrahedron Octahedron Icosahedron Dodecahedron ConvexHull3DcJeZdZdZiifdfd Zdd ZddZddZddZxZ S)ra: An abstract polyhedra class. In this implementation, polyhedra are defined with a list of vertex coordinates in space, and a list of faces. This implementation mirrors that of a standard polyhedral data format (OFF, object file format). Parameters ---------- vertex_coords A list of coordinates of the corresponding vertices in the polyhedron. Each coordinate will correspond to a vertex. The vertices are indexed with the usual indexing of Python. faces_list A list of faces. Each face is a sublist containing the indices of the vertices that form the corners of that face. faces_config Configuration for the polygons representing the faces of the polyhedron. graph_config Configuration for the graph containing the vertices and edges of the polyhedron. Examples -------- To understand how to create a custom polyhedra, let's use the example of a rather simple one - a square pyramid. .. manim:: SquarePyramidScene :save_last_frame: class SquarePyramidScene(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) vertex_coords = [ [1, 1, 0], [1, -1, 0], [-1, -1, 0], [-1, 1, 0], [0, 0, 2] ] faces_list = [ [0, 1, 4], [1, 2, 4], [2, 3, 4], [3, 0, 4], [0, 1, 2, 3] ] pyramid = Polyhedron(vertex_coords, faces_list) self.add(pyramid) In defining the polyhedron above, we first defined the coordinates of the vertices. These are the corners of the square base, given as the first four coordinates in the vertex list, and the apex, the last coordinate in the list. Next, we define the faces of the polyhedron. The triangular surfaces of the pyramid are polygons with two adjacent vertices in the base and the vertex at the apex as corners. We thus define these surfaces in the first four elements of our face list. The last element defines the base of the pyramid. The graph and faces of polyhedra can also be accessed and modified directly, after instantiation. They are stored in the `graph` and `faces` attributes respectively. .. manim:: PolyhedronSubMobjects :save_last_frame: class PolyhedronSubMobjects(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) octahedron = Octahedron(edge_length = 3) octahedron.graph[0].set_color(RED) octahedron.faces[2].set_color(YELLOW) self.add(octahedron) vertex_coordsr faces_listlist[list[int]] faces_config#dict[str, str | int | float | bool] graph_configdict[str, Any]cttdddfi|_ttddidfi|_|_tttj_ ttj_ |_ fd|D_j _j_t'j jfdj ij_jjjdS) N?T) fill_opacity shade_in_3dstroke_opacityr) vertex_type edge_configc,g|]}fd|DS)c*g|]}j|S)layout).0jselfs Z/home/agentuser/manim-venv/lib/python3.11/site-packages/manim/mobject/three_d/polyhedra.py z2Polyhedron.__init__...zs777T[^777r&)r(ir*s r+r,z'Polyhedron.__init__..zs.LLLA7777Q777LLLr-r')super__init__dictrr rrlistrangelenvertex_indices enumerater'r face_coords get_edgesedges create_facesfacesrgraphadd add_updater update_faces)r*rrrr __class__s` r+r0zPolyhedron.__init__bs    6 6  :F  !$$a       +"5T-?)@)@#A#ABB+/ $:L0M0M+N+N $LLLLLLL^^DO44 &&t'788     48K CGCT    TZ((( *+++++r-returnlist[tuple[int, int]]c dg}|D]*}|t||dd|ddzdz }+|S)z'Creates list of cyclic pairwise tuples.NT)strict)zip)r*rr9faces r+r8zPolyhedron.get_edgessM') A AD StABBx$rr(24@@@ @EE r-r7r ctt}|D]&}|t|i|j'|S)z8Creates VGroup of faces from a list of face coordinates.)r r=rr)r*r7 face_grouprGs r+r:zPolyhedron.create_facessI XX  @ @D NN7D>D,=>> ? ? ? ?r-mr Nonec|}||}|j|dS)N)extract_face_coordsr:r; match_points)r*rJr7 new_facess r+r?zPolyhedron.update_facessB..00 %%k22   *****r-cfdjjD}tt|fdjDS)z`Extracts the coordinates of the vertices in the graph. Used for updating faces. cNg|]!}j|"Sr&)r< get_center)r(vr*s r+r,z2Polyhedron.extract_face_coords..s+UUUATZ]5577UUUr-c,g|]}fd|DS)c g|] }| Sr&r&)r(r)r's r+r,z=Polyhedron.extract_face_coords...s&&&q&&&r-r&)r(r.r's r+r,z2Polyhedron.extract_face_coords..s.@@@1&&&&A&&&@@@r-)r<verticesr1r6r)r*new_vertex_coordsr's` @r+rMzPolyhedron.extract_face_coordssXVUUUATUUUi 12233@@@@@@@@r-)rrrrrrrr)rrrArB)r7rrAr )rJr rArK)rAr) __name__ __module__ __qualname____doc__r0r8r:r?rM __classcell__r@s@r+rrsAAN=?') ,,,,,,,B++++ AAAAAAAAr-rc&eZdZdZdd fd ZxZS) raA tetrahedron, one of the five platonic solids. It has 4 faces, 6 edges, and 4 vertices. Parameters ---------- edge_length The length of an edge between any two vertices. Examples -------- .. manim:: TetrahedronScene :save_last_frame: class TetrahedronScene(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) obj = Tetrahedron() self.add(obj) rD edge_lengthfloatkwargsrc H|tjdzdz }tjdtj|||gtj|| | gtj| || gtj| | |gggdgdgdgdgd|dS) N)rrDrc)rrc)rrDre)rerDrcrrr&npsqrtr/r0arrayr*r_raunitr@s r+r0zTetrahedron.__init__sRWQZZ'!+ $d+,,$u-..4%u-..4%$-..  " 999iiiC  r-rDr_r`rarrXrYrZr[r0r\r]s@r+rrsL(            r-rc&eZdZdZdd fd ZxZS) raAn octahedron, one of the five platonic solids. It has 8 faces, 12 edges and 6 vertices. Parameters ---------- edge_length The length of an edge between any two vertices. Examples -------- .. manim:: OctahedronScene :save_last_frame: class OctahedronScene(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) obj = Octahedron() self.add(obj) rDr_r`rarc |tjdzdz }tjd tj|ddgtj| ddgtjd|dgtjd| dgtjdd|gtjdd| gggdgdgdgdgdgdgd gd gd |dS) Nrcr)rcrdrD)rrdrc)rdrer)rDrerd)rer)rDrrre)rcrrrD)rrrrcrfr&rgrks r+r0zOctahedron.__init__sRWQZZ'!+ $1&&4%A''!T1&&!dUA''!Q&&!Q''            &'     r-rmrnror]s@r+rrsL(           r-rc&eZdZdZdd fd ZxZS) raAn icosahedron, one of the five platonic solids. It has 20 faces, 30 edges and 12 vertices. Parameters ---------- edge_length The length of an edge between any two vertices. Examples -------- .. manim:: IcosahedronScene :save_last_frame: class IcosahedronScene(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) obj = Icosahedron() self.add(obj) rDr_r`rarc $|dtjdzdz z}|dz}tjdtjd||gtjd| |gtjd|| gtjd| | gtj||dgtj|| dgtj| |dgtj| | dgtj|d|gtj|d| gtj| d|gtj| d| gg gdgdgdgd gd gd gd gd gdgdgdgdgdgdgdgdgdgdgdgdgd|dS)NrDrrrdrr)rDr)rDrr)rurrrD)rvrerr)rr re)rurwrr)rercrw)rwrdrc)rurdrw)rrdru)rdr)rxrcrd) rcrx)reryrc)rrx )rzrDr)rzrvrD)ryrvre)rzryrv)rzryrxrfr&rg)r*r_raunit_aunit_br@s r+r0zIcosahedron.__init__sRWQZZ1 45&& !VV,--!fWf-..!VfW-..!fWvg.//&&!,--&6'1-..6'61-..6'F7A.//&!V,--&!fW-..6'1f-..6'1vg.//                     )& & JK& & & & & r-rmrnror]s@r+rrsL() ) ) ) ) ) ) ) ) ) ) r-rc&eZdZdZdd fd ZxZS) raA dodecahedron, one of the five platonic solids. It has 12 faces, 30 edges and 20 vertices. Parameters ---------- edge_length The length of an edge between any two vertices. Examples -------- .. manim:: DodecahedronScene :save_last_frame: class DodecahedronScene(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) obj = Dodecahedron() self.add(obj) rDr_r`rarc |dtjdzdz z}|dtjdzdz z}|dz}tjdtj|||gtj||| gtj|| |gtj|| | gtj| ||gtj| || gtj| | |gtj| | | gtjd||gtjd|| gtjd| | gtjd| |gtj||dgtj| |dgtj|| dgtj| | dgtj|d|gtj| d|gtj|d| gtj| d| gggdgdgd gd gd gd gd gdgdgdgdgdg d|dS)NrDrrrdrerr)r rD)rerrrc)rerzrwrDr)rDrwrr r)rrurdrr)rcrrrury)rdrxryru)rrrrrd)rrvrxr)rxrrrcry)rrrrwrzrv)rvrzrerrrfr&rg)r*r_rar{r|unit_cr@s r+r0zDodecahedron.__init__IsRWQZZ1 45RWQZZ1 45&& &&&122&&6'233&6'6233&6'F73446'662336'6F73446'F7F3446'F7VG455!VV,--!VfW-..!fWvg.//!fWf-..&&!,--6'61-..&6'1-..6'F7A.//&!V,--6'1f-..&!fW-..6'1vg.//).#"""""!!!!!!!!!!!!!!!"""""""""!!!""" /& & JK& & & & & r-rmrnror]s@r+rr4sL(* * * * * * * * * * * r-rc*eZdZdZddd fd ZxZS) raA convex hull for a set of points Parameters ---------- points The points to consider. tolerance The tolerance used for quickhull. kwargs Forwarded to the parent constructor. Examples -------- .. manim:: ConvexHull3DExample :save_last_frame: :quality: high class ConvexHull3DExample(ThreeDScene): def construct(self): self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES) points = [ [ 1.93192757, 0.44134585, -1.52407061], [-0.93302521, 1.23206983, 0.64117067], [-0.44350918, -0.61043677, 0.21723705], [-0.42640268, -1.05260843, 1.61266094], [-1.84449637, 0.91238739, -1.85172623], [ 1.72068132, -0.11880457, 0.51881751], [ 0.41904805, 0.44938012, -1.86440686], [ 0.83864666, 1.66653337, 1.88960123], [ 0.22240514, -0.80986286, 1.34249326], [-1.29585759, 1.01516189, 0.46187522], [ 1.7776499, -1.59550796, -1.70240747], [ 0.80065226, -0.12530398, 1.70063977], [ 1.28960948, -1.44158255, 1.39938582], [-0.93538943, 1.33617705, -0.24852643], [-1.54868271, 1.7444399, -0.46170734] ] hull = ConvexHull3D( *points, faces_config = {"stroke_opacity": 0}, graph_config = { "vertex_type": Dot3D, "edge_config": { "stroke_color": BLUE, "stroke_width": 2, "stroke_opacity": 0.05, } } ) dots = VGroup(*[Dot3D(point) for point in points]) self.add(hull) self.add(dots) gh㈵>) tolerancepointsr rr`rarctj|}t|}||g}g}d}it |j|jz } | D]} t } | jD]I} | jD]?} | vr$| | j || <|dz }| | @J| fd| Dtj d||d|dS)NrrDc g|] }| Sr&r&)r(pointds r+r,z)ConvexHull3D.__init__..s444u!E(444r-rfr&)rhrjr buildsetfacetsremoved subfacetsrappend coordinatesr=r/r0)r*rrrarjhullrVr;crfacettmpsubfacetrrr@s @r+r0zConvexHull3D.__init__sM  ## 5  T[!!DL0 6 6E%%C!O # #%_##EA~~ (9:::#$%QGGENNNN # LL4444444 5 5 5 5  "       r-)rr rr`rarror]s@r+rrvsX44l=A            r-r) r[ __future__rcollections.abcrtypingrrnumpyrhmanim.mobject.geometry.polygramrmanim.mobject.graphr&manim.mobject.three_d.three_dimensionsr &manim.mobject.types.vectorized_mobjectr manim.utils.qhullr manim.mobject.mobjectr manim.typingr r__all__rrrrrrr&r-r+rs33""""""$$$$$$%%%%%%%%333333%%%%%%888888999999''''''8------77777777   AAAAAAAAAAAAAAAAH      *    F+ + + + + + + + \> > > > > *> > > B? ? ? ? ? :? ? ? 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