BPc<dZddlZddlZddlZddlmZddlmZdZ d$dZ d%d Z d Z d Z d$d Zd&dZd'dZdZdZdZdZdZdZdZdZd'dZdZdZd(dZd&dZdZd Zd)d!Z d"Z!d#Z"dS)*z Bezier calculations N)DirectedLineSegment) inkex_gettextcxtj|d|dz dz|d|dz dzzS)z-The straight line distance between two pointsrrmathsqrt)point_apoint_bs ./usr/share/inkscape/extensions/inkex/bezier.py pointdistancer%sB 9 !*wqz !a 'WQZ'!*-D,JK  ?cv|d||d|dz zz|d||d|dz zzfS)z-Returns the point between point a and point brr)r r times r between_pointr,sM 1: WQZ 78 8'!*t WQZH; rI@c*t|||dz S)z:Returns between_point but takes percent instead of 0.0-1.0gY@)r)r r percents r percent_pointr3s '7U? ; ;;rc|r||z ||z ||z }}}d|dzzd|z|zz d|zz}|dzd|zz }|dzd|dzzz } dd tjd zz} dd tjd zz } | d krktt|tj| zdz d } tt|tj| z dz d } n|t j| zd kr+t|t j| z dz d  } n(t|t j| zdz d } |t j| z d kr+t|t j| z dz d  } n(t|t j| z dz d } d || z| zzd || | zz| | zzzd || | zz| | zzzfS|rV|dzd|z|zz }|r<| tj|zd|zz | tj|z d|zz fS| d|zz fS|r d| |z zfSdS)z;Get the Cubic function, moic formular of roots, simple root@g"@g;@rg@@grgrgUUUUUU?gUUUUUUտ?r)cmathr powcomplexr )root_aroot_broot_croot_dmono_amono_bmono_cmknw1w2m1n1dets r root_wrapperr08s  #)6/6F?FVO &!)OcFlV3 3dVm C AIf $ qD3A:  C%*T*** * C%*T*** * q55Wa%*Q--/1455w??BWa%*Q--/1455w??BB49Q<<!##A ! ,-17;;;!dill*a/9949Q<<!##A ! ,-17;;;!dill*a/99  b( ) b(272 3 b(272 3  +ckC&L611  5:c??*sV|<5:c??*sV|< 3<(** +w'(** 2rct|d|dt|d|dzt|d|dzS)z0Return the aproximate length between two beziersrrr)r)sp1sp2s r bezlenapprxr4asR c!fc!f%% AA ' ' ( AA ' ' (rct|d|d|}t|d|d|}t|d|d|}t|||}t|||}t|||}|ddd|ddd|g|||g||ddd|dddggS)z'Split a cubic bezier at the time periodrrrNtpoint) r2r3rr-m2m3m4m5r(s r cspbezsplitr<js AA % %B AA % %B AA % %B B  B B  Br2tA VAAAYAqqq 2 &Q b#a&)SVAAAY5O PPrMbP?c|ddd|ddd|ddd|dddf}t|||}t|||S)zSplit a cubic bezier at lengthrNrr)beziertatlengthr<)r2r3length tolerancebezrs r cspbezsplitatlengthrCusc q6!!!9c!fQQQiQCF111I 6C 3 2 2D sC & &&rc|ddd|ddd|ddd|dddf}t||S)zGet cubic bezier segment lengthrNrr) bezierlength)r2r3rArBs r cspseglengthrF|sP q6!!!9c!fQQQiQCF111I 6C Y ' ''rcd}g}|D]v}|gtdt|D]A}t||dz ||}|d|||z }Bw||fS)zGet cubic bezier lengthrr)appendrangelenrF)csptotallengthsspils r csplengthrRs EGrq#b''""  ARAY1..A BK  q ! ! ! QJEE  E>rc|\\}}\}}\}}\}}|} |} d|| z z} d||z z| z } || z | z | z } d|| z z}d||z z|z }|| z |z |z }| || || || | fS)usReturn the bezier parameter size Converts the bezier parametrisation from the default form P(t) = (1-t)³ P_1 + 3(1-t)²t P_2 + 3(1-t)t² P_3 + t³ x_4 to the a form which can be differentiated more easily P(t) = a t³ + b t² + c t + P0 Args: bez (List[Tuple[float, float]]): the Bezier curve. The elements of the list the coordinates of the points (in this order): Start point, Start control point, End control point, End point. Returns: Tuple[float, float, float, float, float, float, float, float]: the values ax, ay, bx, by, cx, cy, x0, y0 rr)rBbx0by0bx1by1bx2by2bx3by3x0y0cxbxaxcybyays r bezierparameterizerds 8;4Zc3#sZc3#s B B cBhB cCi2 B rB B cBhB cCi2 B rB B r2r2r2r ))rc|\\}}\}}|}||z }|}||z } | r|| z } d} nd} | |z } t|\} } }}}}}}| | z| | zz }| |z| |zz }| |z| |zz }| ||z z| ||z zz }t||||}g}|D]q}t|tr|jdkr|j}t|ts3d|cxkrdkr&nN|t||r|S)z!Where a line and bezier intersectrr)rdr0 isinstancer imagrealrIbezierpointatt)arg_arBlx1ly1lx2ly2ddccbbaacoef1coef2r`rcr_rbr^rar\r]abcdrootsretvalrPs r linebezierintersectr{s\$Zc3#s B sB B sB RR%7%<%<"BBBB  URZA  URZA  URZA bER"W--A Aq! $ $E F 22 a ! ! afkkA!W%% 2!q++++A+++++ MM.a00 1 1 1 Mrct|\}}}}}}}} ||dzz||dzzz||zz|z} ||dzz||dzzz||zz| z} | | fS)z7Get coords at the given time point along a bezier curverrrd) rBtr`rcr_rbr^rar\r]xys r ririsy%7%<%<"BBBB ad bAqDk!BF*R/A ad bAqDk!BF*R/A a4Krct|\}}}}}}}}d|z|dzzd|z|zz|z} d|z|dzzd|z|zz|z} | | fS)aVGet slope at the given time point along a bezier curve The slope is computed as (dx, dy) where dx = df_x(t)/dt and dy = df_y(t)/dt. Note that for lines P1=P2 and P3=P4, so the slope at the end points is dx=dy=0 (slope not defined). Args: bez (List[Tuple[float, float]]): the Bezier curve. The elements of the list the coordinates of the points (in this order): Start point, Start control point, End control point, End point. t (float): time in the interval [0, 1] Returns: Tuple[float, float]: x and y increment rrr}) rBr~r`rcr_rbr^ra_dxdys r bezierslopeattrsq$6c#:#: BBBAq R1a41r6A: % *B R1a41r6A: % *B r6Mrct|\}}}}}}}}|\} } | r-d| | z z} d|zd|z| zz } d|zd|z| zz } ||| zz }n1| r-d| | z z} d|zd|z| zz } d|zd|z| zz } ||| zz }ngStd| | |}g}|D]c}t|tr|jdkr|j}t|ts%d|cxkrdkrnN||d|S)z1Reverse; get time from slope along a bezier curverrrrr)rdr0rfr rgrhrI)rBrxr`rcr_rbr^rarrrsloperurvrwryrzrPs r beziertatslopersZ#5c#:#: BBBAqHR rBw FQVe^ # FQVe^ # eO rBw FQVe^ # FQVe^ # eO Aq! $ $E F  a ! ! afkkA!W%% !q++++A+++++ MM!    MrcB|\}}|\}}||||z zz||||z zzfS)a4Linearly interpolate between p1 and p2. t = 0.0 returns p1, t = 1.0 returns p2. :return: Interpolated point :rtype: tuple :param p1: First point as sequence of two floats :param p2: Second point as sequence of two floats :param t: Number between 0.0 and 1.0 :type t: float r)p1p2r~x1y1x2y2s r r7r7s;FB FB R"W rAbM1 11rc,|\\}}\}}\}}\}} t||f||f|} t||f||f|} t||f|| f|} t| | |} t| | |}t| ||}||f| | |f||| || fffS)zSplit bezier at given timer6)rBr~rTrUrVrWrXrYrZr[r-r8r9r:r;r(s r beziersplitattrs7:4Zc3#sZc3#s c S#J * *B c S#J * *B c S#J * *B B  B B  Br2qA #JB "QBc $; ;;rc^d}tddD]$}|t||dz ||z }%t|d|d}||z |kr7t|d\}}t|||t|||dS|dxx|dz |dz zz cc<dS)zAGravesen, Add if the line is closed, in-place addition to array lrrrrrN)rJrr addifclose)rBrQerrorboxrPchordfirstseconds r rr&s C 1a[[11 }SQZQ000 #a&#a& ) )E e u&sC00 v5!U###61e$$$$$ !sus{++rc|\}}}}}}||dzz||zz|zdz||dzz||zz|zdzz}tj|S)zBezier Arc Length Functionrr) r~argsr`r_r^rcrbrarzs r balfr7sd!BBBAqDkBF"R'A -q!trAv1E1Jq0P PF 9V  rcd}||z dz }t||t||z}||z dz }d} t||z|} ||d| zzd| zzz} d| z} ||krt| | z |krr|dz}|dz}|dz}| | z } d} | } td|dD],} | t|| |zz|z } ||d| zzd| zzz} -||krt| | z |kr| S)aQCalculate the length of a bezier curve using Simpson's algorithm: http://steve.hollasch.net/cgindex/curves/cbezarclen.html Args: start (int): Start time (between 0 and 1) end (int): End time (between start time and 1) maxiter (int): Maximum number of iterations. If not a power of 2, the algorithm will behave like the value is set to the next power of 2. tolerance (float): maximum error ratio bezier_args (list): arguments as computed by bezierparametrize() Returns: float: the appoximate length of the bezier curve rg@rrr)rabsrJ)startendmaxiterrA bezier_argsr* multiplierendsumintervalasumbsumest1est0rPs r simpsonr>sM A+$J % % %S+(>(> >Fe s"H D  + . .D 3:.#*= >D :D g++#dTk**Y66 Qc C  q!Q G GA D!h,/== =D3:!6#*!EFDD g++#dTk**Y66 Krrc |t|\}}}}}}} } td|d|d|zd|z|d|zd|z|gS)zGet length of bezier curverirr)rdr) rBrArr`rcr_rbr^rars r rErEesU#5c#:#: BBBAq 3dIBBAFAPRFTV/W X XXrct||d}d}|}||z}||z }t||kr?|dz}|dkr||z }n||z}t|||}||z }t||k?|S)z-Get bezier curve time at the length specifiedrrr)rEr)rBrQrAcurlenrtdiv targetlendiffs r r?r?ks #y# . .F D DF I I D d))i     !88 DLDD DLDc9d33 ! d))i   Krct|d|d}t|j|d|j|dS)z(Get maximum distance within bezier curverrrr)rmaxdistance_to_point)rBsegs r maxdistr}sG c!fc!f - -C $s$c!f-/Ds/Dc!f/M N NNrc0|D]}t||dS)zSub-divide cubic sub-pathsN)subdiv)rLflatrOs r cspsubdivrs.r4rc|t|kr||dz d}||dz d}||d}||d}||||f}t|}||kr|dz }nWt|d\} } | d||dz d<| d||d<| d| d| dg} | g||d<|t|kdSdS)zsub divide bezier curverrrrrN)rKrr) rOrrPp0rrp3rBmdistonetwops r rrs c"gg++ AYq\ AYq\ U1X U1X2r2  D== FAA%c3//HCq6Bq1uIaL1vBqE!HQQQ(AcBqsG c"gg++++++rc ztjgdgdgdgdg}d}|D]}t|dkrt|D]I\}}|d||dz dd z|dd||dz ddz zz }Jt dt|D]}tj||dz dd ||dz dd ||d d ||dd g}tj||dz dd||dz dd||d d||ddg}tj||} |d tj| |jzz }| S) zGet area in cubic sub-path)rrr)rrr)rHrHrr)rrHrrrrrrrg333333?)numpyarrayrK enumeraterJmatmulT) rLMAT_AREAarearOrcoordrPvec_xvec_yvexs r csparears{  ~~~~~~FH D 6 6 r77Q;; !"  L LHAu C"QU)A,q/)U1Xa[2a!e9Q<?-JK KDDq#b''"" 6 6AKAE1a"QU)A,q/2a58A;1a LEKAE1a"QU)A,q/2a58A;1a LE,uh//C D5<UW555 5DD 6 5Lrc tjgdgdgdgdg}tjgdgdgdgdg}tjgd gd gd gd g}tjgd gdgdgdg}t|}d}d}t|dkrt t d|D]}t |D] \} } ||| dz dd|| dz dd| ddz z|| dz dd|| dz ddz| ddzzdz z }||| dz dd| dd|| dz ddz z|| dz dd|| dz ddz| ddzzdz z }tdt|D]Q} tj|| dz dd|| dz dd|| dd|| ddg} tj|| dz dd|| dz dd|| dd|| ddg} | | fd}tj||||||||g}|tj | |j dz z }|tj | |j dz z }S| |z | |z fS)zGet cubic sub-path coefficient)r# )r )r)-r)rr)r )rrr)rr)rrrr)rrrr)rrrr)rrrr)rrrr)rrrr)rrrr)rrrrrg:0yE>z-Area is zero, cannot calculate Center of Massrrrrc\tjtj|||jS)N)rrr)MATrrs r _mulzcspcofm.._muls"|EL$<$->->@Q@Q@QRJ ...///;K;K;KLJ ...///;K;K;KLJ   +++->->->@Q@Q@QRJ 3<rs, ++++++,,,,,, <<<< &&&RQQQQ''''((((   ***<B*8222$ < < < , , , ,"$$$NYYYY $OOO  (.4"4"4"4"4"r