q=c(18, 15, 24, 23, 18, 22, 19, 29,22,25,20,19,18,20,26,32,26,26,34,29,23,34,22,19
,21,19,34,23,23,23,30,21,15,29,32,19,21,28,22,32,29,25,28,28,23,12,26,24
,27,14,38,27,28,25,38,34,25,37,15,28,15,23,23,28,15,15,19,25,28,16,19,17
,23,19,16,18,18,17,20,18,21,13,11,12,13,16,13,16,10,13,14,6,19,18,19,15
,17,6,14,28,15,20,16,12)
 
m=length(q);t=1:m
B=c(q[1]);i=1;j=length(q)
er=rep(0,length(q))
dis=function(tt){a=(q[j]-q[i])/(j-i);b=(q[i]*j-q[j]*i)/(j-i);abs(a*tt-q[tt]+b)/sqrt(a^2+1)}
for(k in 1:length(q)){er[k]=dis(k)};ser=sd(er)
 
time=c(1)
while(l<j)
{
 j=length(q);error=ser
  dis=function(tt)
   {
     a=(q[j]-q[i])/(j-i)
     b=(q[i]*j-q[j]*i)/(j-i)
     abs(a*tt-q[tt]+b)/sqrt(a^2+1)
   }
stop=dis(l)
if(stop<=error){l=l+1}else
 {
  i2=l2=time[length(time)];j2=l
  dis2=function(tt2){a2=(q[j2]-q[i2])/(j2-i2);b2=(q[i2]*j2-q[j2]*i2)/(j2-i2); abs(a2*tt2-q[tt2]+b2)/sqrt(a2^2+1)}
  while(l2<j2){stop2=dis2(l2);if(stop2<=ser){l2=l2+1}else{B=c(B,q[l2]);time=c(time,l2);i2=l2;l2=l2+1}}
  B=c(B,q[l]);time=c(time,l);i=l;l=l+1
 }
}
 
B=c(B,q[j]);time=c(time,j)
 
plot(y=q,x=t,xlim=c(1,(m-1)),ylim=c(min(q),max(q)),type="o")
par(new=T)
plot(y=B,x=time,xlim=c(1,(m-1)),ylim=c(min(q),max(q)),type="l",col=2)
 

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