function [X,Cost]=compute_transitions(s,ax,ay);global Map_Data Pos_Vector_Indexes Speed_Vector_Indexes Finish_Data VMAX% compute_transitions: given a state vector s and an action ax,ay, this function computes%                      the successor vector of s with respect to ax,ay and the cost vector %                      associated to the transition.% Arguments --------------------------------------------------------------%     s : the starting state vector whose successor vector we want to compute;%     [ax ay] : acceleration with respect to X and Y axis, i.e. the action taken.%               ay is optional, if not present, then ax is the action taken in 1..9 % Evaluation -------------------------------------------------------------%     successor : the successor vector of s;%     cost : the cost vector associated to the transition.%--------------------------------------------------------------------------% In verbose mode, there is no difference to silent mode.%--------------------------------------------------------------------------% MDP Toolbox, INRA, BIA Toulouse, France%--------------------------------------------------------------------------% If the argument was an action, we convert to (ax,ay) format.if nargin == 2    [ax,ay]=action_to_acceleration(ax);end% Some initialisationsm=size(Map_Data,1);n=size(Map_Data,2);state_length=(size(Pos_Vector_Indexes,1)*size(Speed_Vector_Indexes,1));X=zeros(size(s));Cost=ones(size(s));done=zeros(size(s));% We transform s into coordinates[x,y,vx,vy]=get_values_from_state(s);% We compute the 'raw' successorsxx=x;yy=y;vx=vx+ax;vy=vy+ay;x=x+vx;y=y+vy;% We check authorized speed vectorstest_speed=((vx.*vx+vy.*vy)<=VMAX.*VMAX);X=X+(~test_speed*(state_length+1));done=done+~test_speed;% We check whether the successors are inside the boundariesinside=(x>=1 & x<=n & y>=1 & y<=m);X=X+(~inside & ~done)*(state_length+1);done=done+(~inside & ~done);% We check whether the car transits via off-limits x_o=zeros(size(done));y_o=zeros(size(done));x_o=x.*(~done)+done;y_o=y.*(~done)+done;safe=safe_transition(xx,yy,x_o',y_o');X=X+((~safe & ~done)*(state_length+1));done=done+(~safe & ~done);% We check whether the car crosses the finish linex_o=zeros(size(done));y_o=zeros(size(done));x_o=x.*(~done)+done;y_o=y.*(~done)+done;test_end=race_end(xx,yy,x,y);% We test whether the crossing is made in the right senseFinish_Vector=zeros(1,2);x1=Finish_Data(1,2);y1=Finish_Data(1,1);x2=Finish_Data(2,2);y2=Finish_Data(3,1);if (y1~=y2 & x1~=x2)    Finish_Vector(1)=1/sqrt(1-(x1-x2)*(x1-x2)/((y1-y2)*(y1-y2)));    Finish_Vector(2)=Finish_Vector(1)*(x1-x2)/(y2-y1);elseif (x1==x2)    Finish_Vector(1)=1;    Finish_Vector(2)=0;elseif (y1==y2)    Finish_Vector(1)=0;    Finish_Vector(2)=-1;endsense=Finish_Vector*[vx; vy];X=X+(safe & test_end & (sense<=0) & ~done)*(state_length+1);done=done+(safe & test_end & (sense<=0) & ~done);% We compute the winning movestest_short=find(safe & test_end & (sense>0) & ~done);for t=1:size(test_short,2),    if Map_Data(yy(test_short(t)),xx(test_short(t)))~=2        X(test_short(t))=state_length+2;        done(test_short(t))=1;    endend% We check racetrack exitsx_o=zeros(size(done));y_o=zeros(size(done));x_o=x.*(~done)+done;y_o=y.*(~done)+done;out_of_track=(Map_Data((x_o-1)*m+y_o)~=1 & Map_Data((x_o-1)*m+y_o)~=2);out_of_track=out_of_track.*(~done);X=X+(out_of_track & (~done))*(state_length+1);done=done+(out_of_track & ~done);% We compute normal, on-track successors.x_o=zeros(size(done));y_o=zeros(size(done));vx_o=zeros(size(done));vy_o=zeros(size(done));x_o=x.*(~done)+x1*done;y_o=y.*(~done)+y1*done;vx_o=vx.*(~done);vy_o=vy.*(~done);X=X+(~done).*(convert_values_to_state(x_o,y_o,vx_o,vy_o));