Og8ddlmZddlmZddlZddlmZmZgdZddZ ddZ ddZ dd Z dd Z dd Z dd Zdd ZddZddZy)) annotations)AnyN)Vec2UVec) bulge_to_arcbulge_3_points bulge_center bulge_radius arc_to_bulgebulge_from_radius_and_chordbulge_from_arc_anglecFt|tj||zS)zReturns the point at a specified `angle` and `distance` from point `p`. Args: p: point as :class:`Vec2` compatible object angle: angle in radians distance: distance )r from_angle)pangledistances U/var/www/html/public_html/myphp/venv/lib/python3.12/site-packages/ezdxf/math/bulge.pypolarrs 7T__UH5 55cDt|t|z jS)zReturns angle a line defined by two endpoints and x-axis in radians. Args: p1: start point as :class:`Vec2` compatible object p2: end point as :class:`Vec2` compatible object )rr)p1p2s rrr"s HtBx  & &&rct|||}t|||}tjdz}tj|||z z|dz }tj|tj |z }|||fS)a4Returns bulge parameters from arc parameters. Args: center: circle center point as :class:`Vec2` compatible object start_angle: start angle in radians end_angle: end angle in radians radius: circle radius Returns: tuple: (start_point, end_point, bulge) @)rmathpifmodsincos) center start_angle end_angleradius start_point end_pointpi2abulges rr r -ss V4Kfi0I ''A+C 3)k12S9C?A HHQK$((1+ %E  5 ((rctjt||z t||zdz }tj|tj|z S)a2Returns bulge value defined by three points. Based on 3-Points to Bulge by `Lee Mac`_. Args: start_point: start point as :class:`Vec2` compatible object end_point: end point as :class:`Vec2` compatible object point: arbitrary point as :class:`Vec2` compatible object r)rrrrr )r%r&pointr(s rrrDsE 5 , ,uUI/F F!KA 88A;! $$rc>t|||}t||tjdz tj|dzz z}t |||}|dkr#|t||t||t |fS|t||t||t |fS)a4Returns arc parameters from bulge parameters. The arcs defined by bulge values of :class:`~ezdxf.entities.LWPolyline` and 2D :class:`~ezdxf.entities.Polyline` entities start at the vertex which includes the bulge value and ends at the following vertex. .. important:: The return values always describe a counter-clockwise oriented arc, so for clockwise arcs (negative bulge values) the start and end angles are swapped and the arc starts at the `end_point` and ends at the `start_point`. Based on Bulge to Arc by `Lee Mac`_. Args: start_point: start vertex as :class:`Vec2` compatible object end_point: end vertex as :class:`Vec2` compatible object bulge: bulge value Returns: Tuple: (center, start_angle, end_angle, radius) rr)signed_bulge_radiusrrratanrabs)r%r&r)rr(cs rrrSs4 KE:A k9%1tyy7G!7K)KLA k1a A qy%9%uQ 'rGs # !  6') )$)16)@E)). % E E"& E/4 E% EF&"&/4  C*!r