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in this function ,to caculate pfree,there are double freeDelta=map.getDelta()*m_freeCellRatio;and pfree.x+=(*r-map.getDelta()*freeDelta)*cos(lp.theta+*angle); pfree.y+=(*r-map.getDelta()*freeDelta)*sin(lp.theta+*angle);;
obviously r - delta^2sqrt(2) (freeDelta = sqrt(2))
i think r - deltasqart(2) can show the range of pfree ,but the equation above i don't know its mean.