U U¹fã@s¤ddlmZddlZddlZddddœZdd„Zd"d d „Zd d „Zd d„Z dd„Z dd„Z dd„Z dd„Z dd„Zdd„Zdd„Zdd„Zdd „Zed!kr eƒdS)#é©Ú euclideanNéé)ÚxÚyÚzcCsFt ||¡}t t ||¡¡}t t ||¡¡}||}t ||¡S©N)ÚnpÚdotÚsqrtÚarccos)Úv1Úv2Ú numeratorÚm1Úm2Ú denominator©rún/home/dh_an3skk/arjun-chandrasekhar-teaching.com/tomato/backend/backend_plant_architecture/optimal_midpoint.pyÚangle_between_vectorss  rrcCsdSr r)ÚvÚdimrrrÚrotation_anglesrc Csžt|ƒt|ƒkr t|ƒks&nt‚t|dd…ƒ}t|dd…ƒ}t|dd…ƒ}t|ƒD](\}}|||fD]}|||8<qpq^t|ƒt|ƒt|ƒfS)z¶ Takes three points (of any dimension) as input; translates the first point to be at the origin, and translates the other two points by the same amount in each dimension N)ÚlenÚAssertionErrorÚlistÚ enumerateÚtuple) Úp0Úp1ÚqÚp0_shiftÚp1_shiftÚq_shiftÚiÚcoordÚpointrrrÚtranslate_to_origins&r(cCsDt|ƒt|ƒkst‚g}tt|ƒƒD]}| ||||¡q$|Sr )rrÚrangeÚappend)rr Úmr%rrrÚ slope_vector$s r,cCsLt|ƒt|ƒkst‚g}tt|ƒƒD]}| |||||¡q$t|ƒSr )rrr)r*r)rr+ÚtÚmidpointr%rrrr.+s r.cCs:t||ƒ}t||ƒt||ƒ|}||d||}|S)Nrr)rr!r.ÚalphaÚdrootÚwiringÚdelayÚcostrrrÚ midpoint_cost4s r4c Cs°g}|d||d}d|||d||}|d|||}|dd||}|dkr¬| |dd|} | | ¡|dkr¬| |dd|} | | ¡|S)Nrérgà?)r*) rrrÚgammaÚcritical_valuesÚaÚbÚcZ determinantÚt1Út2rrrr7:s  r7cCs<t ||¡}t ||¡}t ||¡}d|d}||||fS)Nrr)r r )r+r!r/rrrr6rrrÚintermediate_variablesMs     r=cCs°t|||ƒ\}}}ddg}t||ƒ} t| ||ƒ\} } } } t| | | | ƒ}tdd„|ƒ}||7}tdƒ}d}d}|D]4}t|| |ƒ}t|||||ƒ}||krp|}|}|}qp|||fS)NrrcSsd|kodkSS©Nrrr)rrrrÚ_óz(optimal_midpoint_exact..Úinf)r(r,r=r7ÚfilterÚfloatr.r4)rr r!r/r0r"r#r$Zcandidate_timesr+rrrr6Z crit_valuesÚ best_costÚ best_midpointÚ best_deltaÚdeltaÚmpr3rrrÚoptimal_midpoint_exactUs$  rIcCsÎt|ƒt|ƒkr t|ƒks&nt‚t||ƒ}d}tdƒ}d}d} t dd||¡D]d} d} | dkrt|} t| ƒ} n"| dkrŠ|} t| ƒ} n | ||| ƒ} t||| ||ƒ} | |krV| }| }| } qVt|ƒ}||| fS)aŽ approximates the optimal point to insert a point onto a line segment. This method uses brute force to try all possible midpoints, within a certain granularity. p0, p1 - the points comprising a line segment q - the point that should be connected to the line segment alpha - the degree to which we prioritize conduction delay or wiring cost. The wiring cost is the distance from q to our chosen midpoint. the conduction delay is the sum of the distance from q to our chosen midpoint and the distance from our chosen midpoint to p0. We want to (mimimize alpha * wiring cost) + ((1 - alpha) * conduction delay) g{®Gáz„?rANrr) rrr,rCr ÚarangeÚintr4r)rr r!r/r0r+rGrDrErFr-r.rHr3rrrÚoptimal_midpoint_approxps,&    rLcCst|||||ƒSr )rI)rr r!r/r0rrrÚoptimal_midpoint¨srMc Cslt|||ƒ\}}}t||ƒ}t ||¡t ||¡}|dkr@d}|dkrLd}t|||ƒ}t||ƒ} | ||fSr>)r(r,r r r.r) rr r!r"r#r$r+r-rHr3rrrÚoptimal_midpoint_alpha1«s   rNcCs d}d}d}tt|||ƒƒdS)N)rr)rr)gffffffæ?g®Gázæ?)ÚprintrN)rr r!rrrÚmain»s rPÚ__main__)r)Úscipy.spatial.distancerÚnumpyr ÚrandomZDIMENSION_COORDrrr(r,r.r4r7r=rIrLrMrNrPÚ__name__rrrrÚs$    8