How to set maximum length of triangle side in Delaunay triangulation?

Question

How to remove distances from Delaunay triangulation which are larger than I need? Example data: ``` x<-rep(1:12, c(2,2,7,9,10,5,4,6,10,10,9,4)) y<-c(1,2,1,2,1:3,5:8,1:9,1:10,2,7:10,8:11,7:12,3:12,3:12,4:12,5,8:10) x_plus<-seq(0.2:0.8, by=0.1) x<-x+sample(x_plus, 78, replace=TRUE) y<-y+sample(x_plus, 78, replace=TRUE) ``` Plotting the map: ``` plot(x,y) ``` Delaunay triangulation with tri.mesh() - package(tripack) ``` my.triangles<-tri.mesh(x,y) plot(my.triangles, do.points=FALSE, lwd=0.2) points(x,y, col = "blue", pch=20) ``` How can I extract only shorter distances? I do not need those large ones you surely know which distances I mean. Is there some argument to do this in tri.mesh() function? Or it could be done after it? Are distances even stored in this object? ``` my.triangles triangulation nodes with neigbours: node: (x,y): neighbours 1: (1.4,1.7) [5]: 2 3 4 11 12 2: (2,3) [6]: 1 4 7 8 9 11 3: (3,1.8) [4]: 1 4 5 12 . . . 76: (12.4,8.8) [5]: 68 69 70 75 77 77: (12.9,9.9) [6]: 70 7…

Accepted Answer

The documentation (`?tri`) suggests that the segments are of the form `r$tlist[k] -- r$tlist[r$tlptr[k]]`: you can remove those beyond some threshold.

```
r <- tri.mesh(x,y)
k <- seq_len( r$tlnew - 1 )
i <- r$tlist[k]          
j <- r$tlist[r$tlptr[k]]
keep <- i > 0
i <- abs( i[ keep ] )
j <- abs( j[ keep ] )
plot( x, y )
segments( r$x[i], r$y[i], r$x[j], r$y[j], col="grey" )
distances <- sqrt( ( r$x[i] - r$x[j] ) ^ 2 + ( r$y[i] - r$y[j] ) ^ 2 )
threshold <- 2.5  # Choose the threshold manually
i <- i[ distances < threshold ]
j <- j[ distances < threshold ]
segments( r$x[i], r$y[i], r$x[j], r$y[j], lwd = 2 )
```

How to set maximum length of triangle side in Delaunay triangulation?

Solution

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