� ��g�P����dZddlmZddlmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZdd lmZmZmZdd lmZdd lmZdd lmZdd lmZmZmZddlmZddl m!Z!ddl"m#Z#ddl$m%Z%ddl&m'Z'gd�Z(d�e)d��D��\Z*Z+e dd���Z,Gd�dee��Z-Gd�de-e��Z.ee.e��d���Z!ee.e��d���Zd�Z/d#d!�Z0d"�Z1d S)$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. 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Parameters ========== scale_factor : float Multiplication factor for the SVG stroke-width. Default is 1. fill_color : str, optional Hex string for fill color. Default is "#66cc99". �rO)rDr�� fill_colors r3r�zGeometryEntity._svg�s��"�#�#�#r5c��|Sr�r:rUs r3�_sympy_zGeometryEntity._sympy_�s��� r5c��t���)zCWhat is the dimension of the space that the object is contained in?r�rUs r3�ambient_dimensionz GeometryEntity.ambient_dimensions��"�#�#�#r5c��t���)zwReturn a tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the geometric figure. r�rUs r3r�zGeometryEntity.boundss��"�#�#�#r5c����ddlm}ddlm}m}m}ddlm}ddlm }m }t||��r�� |��St||��r t�fd�|jD����St|||f��rdSt||��rk�� |j��oP�� ||jj|jz|jj����o��|�� St||��rLt||��r�� |j��sdSt�fd�|jD����St+���) 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 r�r)r$r%r&)r,)r*r)c3�B�K�|]}��|��V��dSr���encloses_point)r1r�rDs �r3r�z*GeometryEntity.encloses.<locals>.<genexpr>0s1�����@�@�!�t�*�*�1�-�-�@�@�@�@�@�@r5Fc3�B�K�|]}��|��V��dSr�r�)r1�vrDs �r3r�z*GeometryEntity.encloses.<locals>.<genexpr><s1�����B�B�!�t�*�*�1�-�-�B�B�B�B�B�Br5)rxr�sympy.geometry.liner$r%r&�sympy.geometry.ellipser,�sympy.geometry.polygonr*r)ryr�r��points�centerr��hradius�y� intersection�verticesrO) rDrYrr$r%r&r,r*r)s ` r3�encloseszGeometryEntity.enclosess����4 /�.�.�.�.�.�:�:�:�:�:�:�:�:�:�:�2�2�2�2�2�2�B�B�B�B�B�B�B�B� �a�� � � C��&�&�q�)�)� )� ��7� #� #� C��@�@�@�@�q�x�@�@�@�@�@� @� ��C��;� '� '� C��5� ��7� #� #� C��&�&�q�x�0�0�)��#�#���a�h�j�1�9�,�a�h�j�9�9�;�;�)��%�%�a�(�(�(� )���7� #� #� C��!�^�,�,� !��*�*�1�8�4�4�!� �5��B�B�B�B�q�z�B�B�B�B�B� B�!�#�#�#r5c��||kSr�r:rXs r3�equalszGeometryEntity.equals?s ���q�y�r5c��t���)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 r�rXs r3r�zGeometryEntity.intersectionBs��&"�#�#�#r5c��t���)amIs 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 r�rPs r3� is_similarzGeometryEntity.is_similarWs��*"�#�#�#r5c��� � � �ddlm� |}|}� dd��}|jjrM|jdj� � s|�d���S� fd�|�� ��D��}�ni|jturM|jdj � � s|�d���S� fd�|�� ��D��}�nt|d��s2t� fd �|jD����std |z���t|j��}|j}|d |d z }� tt ��� � �| ����| |���d����||���|���� � fd �|�� ��D��}|�t%|����S) a� 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) rr�r=�r�c�V��g|]%}||�d�|jz z���f��&S)r6r�)� translater��r1�pr�s �r3r4z*GeometryEntity.reflect.<locals>.<listcomp>��6���L�L�L��Q�� � �a��Q�S��k� �2�2�3�L�L�Lr5�r�c�V��g|]%}||�d�|jz z���f��&S)r6r�)r�r�r�s �r3r4z*GeometryEntity.reflect.<locals>.<listcomp>�r�r5�reflectc3�8�K�|]}t|���V��dSr��ry)r1�argrs �r3r�z)GeometryEntity.reflect.<locals>.<genexpr>�s>�����5>�5>�/2�J�s�E�*�*�5>�5>�5>�5>�5>�5>r5z)reflect undefined or non-Point args in %s�c �n��g|]1}|��t|jt|ji��f��2Sr:)�xreplacer�r�)r1r��xfs �r3r4z*GeometryEntity.reflect.<locals>.<listcomp>�s7���O�O�O�1�Q�� � �Q���Q���$4�5�5�6�O�O�Or5)rxr�slope�is_zerorTr��scale�atomsrr�r^r�rOr� coefficientsr��rotater��dict) rD�line�g�lrY�repsr_rH�drr�r�s @@@r3r�zGeometryEntity.reflectns�����6 /�.�.�.�.�.� �� �� �E�!�Q�K�K�� �7�?� P���q� � �A�� %��w�w��w�}�}�$�L�L�L�L�Q�W�W�U�^�^�L�L�L�D�D� �W��]�]���q� � �A�� %��w�w��w�}�}�$�L�L�L�L�Q�W�W�U�^�^�L�L�L�D�D��1�i�(�(� E��5>�5>�5>�5>�67�f�5>�5>�5>�2>�2>� E�)�?�!�C�E�E�E��Q�W� � �A���A��2���q��t� �A���q�!���B�������#�#�*�*�A�2�q�1�1�7�7�"�7����&��A�,�,�y�y�1�y�~�~� �P�O�O�O�������O�O�O�D��z�z�$�t�*�*�%�%�%r5Nc���g}|jD]V}t|t��r*|�|�||�����A|�|���Wt |��|�S)a^Rotate ``angle`` radians counterclockwise about Point ``pt``. The default pt is the origin, Point(0, 0) See Also ======== scale, translate Examples ======== >>> 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)) )rTryr9�appendr�rN)rD�angle�pt�newargsr_s r3r�zGeometryEntity.rotate�sw��*���� "� "�A��!�^�,�,� "����q�x�x��r�2�2�3�3�3�3����q�!�!�!�!��t�D�z�z�7�#�#r5r�c�����ddlm}|r>||d���}|j| j������j|j�St |����fd�|jD���S)a�Scale 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))) rr�r6��dimc�<��g|]}|�������Sr:)r�)r1r_r�r�s ��r3r4z(GeometryEntity.scale.<locals>.<listcomp>�s%���=�=�=�a�A�G�G�A�q�M�M�=�=�=r5)rxrr�rTr�rN)rDr�r�r�rs `` r3r�zGeometryEntity.scale�s�����0 /�.�.�.�.�.� � O���r�q�!�!�!�B�D�>�4�>�R�C�:�.�4�4�Q��:�:�D�b�g�N� N��t�D�z�z�=�=�=�=�=�4�9�=�=�=�>�>r5rc���g}|jD]V}t|t��r*|�|�||�����A|�|���W|j|�S)axShift 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)) )rTryr9r�r��func)rDr�r�r�r_s r3r�zGeometryEntity.translate�ss��*���� "� "�A��!�^�,�,� "����q�{�{�1�a�0�0�1�1�1�1����q�!�!�!�!��t�y�'�"�"r5c�j�ddlm}t|t��s|||j���}t||��st d���t |�t��|z td���}|st dt|��z���||dtiS)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) rr�r�zother must be a pointT)r�zGiven point is not on %s) rxrryr9r�rCr�arbitrary_point�Tr)rDrE�tr�sols r3�parameter_valuezGeometryEntity.parameter_values���" /�.�.�.�.�.��%��0�0� =��E�%�T�%;�<�<�<�E��%��'�'� 6��4�5�5� 5��D�(�(��+�+�e�3�Q�T�B�B�B��� K��7�)�D�/�/�I�J�J� J��3�q�6�!�9�~�r5)r�r�r�)r�r�N�rr)!r?� __module__� __qualname__�__doc__r;�__annotations__rLrQrVrZrbrgrkrnrqrtrvr}r�r�r��propertyr�r�r�r�r�r�r�r�r�r�r�r:r5r3r9r9Gs����������"$�I�#�#�#�#�%�%�%�<$�$�$�  � � ���� )� )� )����#�#�#�5�5�5� ������5�5�5� )� )� )�A%�A%�A%�F $� $� $� $�����$�$��X�$��$�$��X�$�/$�/$�/$�b���$�$�$�*$�$�$�.8&�8&�8&�t$�$�$�$�:?�?�?�?�<#�#�#�#�:����r5r9c��eZdZdZdZd�ZdS)� GeometrySetz[Parent class of all GeometryEntity that are also Sets (compatible with sympy.sets) r:c���t|t��r"|jrt�fd�|D����S��|��S)zFsympy.sets uses the _contains method, so include it for compatibility.c3�B�K�|]}��|��V��dSr�)rQ)r1r2rDs �r3r�z(GeometrySet._contains.<locals>.<genexpr>&s1�����;�;��t�(�(��+�+�;�;�;�;�;�;r5)ryr� is_FiniteSetr�rQrPs` r3� _containszGeometrySet._contains"sX��� �e�S� !� !� <�e�&8� <��;�;�;�;�U�;�;�;�;�;� ;�� � ��'�'�'r5N)r?r�r�r�r;r�r:r5r3r�r�s4���������I�(�(�(�(�(r5r�c����|jrG�fd�|D��}t|��t|��krdSt�t|���S��|��r�SdS)zO Returns the union of self and o for use with sympy.sets.Set, if possible. c�>��g|]}��|���|��Sr:)r��r1r�rDs �r3r4zunion_sets.<locals>.<listcomp>3s*���>�>�>�a�D�N�N�1�,=�,=�>��>�>�>r5N)r��lenrrr�)rDrY� other_pointss` r3rr*sy��� �~�5�>�>�>�>�1�>�>�>� � �|� � ��A��� &� &��4��T�9�l�3�4�4�4� �~�~�a����� � �4r5c�����ddlm� |jrt�fd�|D���}n��|��}n#t $rYdSwxYwt�fd�|D���}�fd�|D��}t ||gz�S)zD Returns a sympy.sets.Set of intersection objects, if possible. rr�c3�F�K�|]}��|���|V��dSr�)�containsr�s �r3r�z$intersection_sets.<locals>.<genexpr>Gs4�����A�A�a�� � �a�0@�0@�A��A�A�A�A�A�Ar5Nc�4��g|]}t|����|��Sr:r��r1r�rs �r3r4z%intersection_sets.<locals>.<listcomp>Ps(���B�B�B�q�Z��5�-A�-A�B��B�B�Br5c�4��g|]}t|����|��Sr:r�rs �r3r4z%intersection_sets.<locals>.<listcomp>Qs(���?�?�?��*�Q��*>�*>�?�!�?�?�?r5)rxrr�rr�rOr)rDrY�interr�� non_pointsrs` @r3rr<s����� +�*�*�*�*�*� � �>� )��A�A�A�A�1�A�A�A�B�E�E��%�%�a�(�(�E��� �����t�t����� �B�B�B�B�E�B�B�B� C�F�?�?�?�?�U�?�?�?�J� �:���(� *�*s�2=� A � A c�8�td��}||d<||d<|S)z6Return the matrix to translate a 2-D point by x and y.�)r6r)r6r�r)r�r��rvs r3r�r�Us$�� �Q���B��B�t�H��B�t�H� �Ir5Nc��td��}||d<||d<|r8ddlm}||d���}t| j�}t|j�}||z|zS|S)z�Return the matrix to multiply a 2-D point's coordinates by x and y. If pt is given, the scaling is done relative to that point.rr�)r�r�rr�r6r�)rrxrr�rT)r�r�r�rr�tr1�tr2s r3r�r�]s|�� �Q���B��B�t�H��B�t�H� ��.�.�.�.�.�.� �U�2�1� � � ���2�#��$�����!���2�v�c�z�� �Ir5c��t|��}td��t|��z}||d<| |d<d|d<|S)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�)r�rr�)r6r6)r rr )�th�srs r3r�r�msF�� �B���A� �Q����B����B��B�t�H��r�B�t�H��B�t�H� �Ir5r�)2r�� __future__r�sympy.core.basicr�sympy.core.containersr�sympy.core.evalfrr�sympy.core.numbersr�sympy.core.symbolr �sympy.core.sympifyr �(sympy.functions.elementary.trigonometricr r r�sympy.matricesr�sympy.multipledispatchr�sympy.printingr� sympy.setsrrr� sympy.sets.handlers.intersectionr�sympy.sets.handlers.unionr�sympy.solvers.solversr�sympy.utilities.miscr�sympy.utilities.iterablesrrA�ranger�r�r�r9r�r�r�r�r:r5r3�<module>r s�����*#�"�"�"�"�"�"�"�"�"�"�"�'�'�'�'�'�'�*�*�*�*�*�*�*�*�!�!�!�!�!�!�#�#�#�#�#�#�&�&�&�&�&�&�C�C�C�C�C�C�C�C�C�C�������+�+�+�+�+�+�������,�,�,�,�,�,�,�,�,�,�>�>�>�>�>�>�0�0�0�0�0�0�'�'�'�'�'�'�*�*�*�*�*�*�1�1�1�1�1�1�����01�0�u�u�Q�x�x�0�0�0���1� �E�.�t�$�$�$��R�R�R�R�R�U�J�R�R�R�j (� (� (� (� (�.�#� (� (� (� ��+�s��������" ��+�s���+�+���+�0��� � � � � ����r5
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