library(plyr)
#I am using cut function with 50 breaks for both v1 and v2 and ddply from plyr package for computing the mean
newdata<-ddply(df,.(cut(v1,50),cut(v2,50)),summarise,mean.v3=mean(v3))
> head(newdata)
cut(v1, 50) cut(v2, 50) mean.v3
1 (-49.4,-47.5] (-34.7,-32.7] 18.123
2 (-49.4,-47.5] (-0.576,1.43] 20.887
3 (-49.4,-47.5] (15.5,17.5] 20.887
4 (-47.5,-45.5] (-52.7,-50.7] 9.918
5 (-47.5,-45.5] (-44.7,-42.7] 14.477
6 (-47.5,-45.5] (-34.7,-32.7] 16.314
Updated as per the comments: If you want the lower, middle and mid-points, you can use the following function or use with details as follow(you need to use the sub function to deal with ( and ]):
df$newv1<-with(df,cut(v1,50))
df$newv2<-with(df,cut(v2,50))
df$lowerv1<-with(df,as.numeric( sub("\((.+),.*", "\1", newv1))) #lower value
df$upperv1<-with(df,as.numeric( sub("[^,]*,([^]]*)\]", "\1", newv1))) # upper value
df$midv1<-with(df,(lowerv1+upperv1)/2) #mid value
df$lowerv2<-with(df,as.numeric( sub("\((.+),.*", "\1",newv2))) #lower value
df$upperv2<-with(df,as.numeric( sub("[^,]*,([^]]*)\]", "\1", newv2))) # upper value
df$midv2<-with(df,(lowerv2+upperv2)/2)#mid value
newdata<-ddply(df,.(newv1,newv2),transform,mean.v3=mean(v3))
> head(newdata)
v1 v2 v3 newv1 newv2 lowerv1 upperv1 midv1 lowerv2 upperv2 midv2 mean.v3
1 -47.456 -32.714 18.123 (-49.4,-47.5] (-34.7,-32.7] -49.4 -47.5 -48.45 -34.700 -32.70 -33.700 18.123
2 -49.329 -0.465 20.887 (-49.4,-47.5] (-0.576,1.43] -49.4 -47.5 -48.45 -0.576 1.43 0.427 20.887
3 -48.652 16.558 20.800 (-49.4,-47.5] (15.5,17.5] -49.4 -47.5 -48.45 15.500 17.50 16.500 20.887
4 -48.323 17.153 20.974 (-49.4,-47.5] (15.5,17.5] -49.4 -47.5 -48.45 15.500 17.50 16.500 20.887
5 -45.713 -52.599 9.918 (-47.5,-45.5] (-52.7,-50.7] -47.5 -45.5 -46.50 -52.700 -50.70 -51.700 9.918
6 -45.805 -43.071 14.477 (-47.5,-45.5] (-44.7,-42.7] -47.5 -45.5 -46.50 -44.700 -42.70 -43.700 14.477
