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    <p>The way I understand it (and by that I mean if i understood correctly your question), because <code>plot.deldir</code> allows an argument <code>add=TRUE</code> to be passed, it can be done directly.</p> <pre><code>d&lt;-structure(list(V1 = c(-0.5561835, -2.3985544, -3.8833659, 3.1025836, 0.7438354, 7.0787294, -1.6633598, -0.675193, 1.4633841, -3.2118758), V2 = c(1.49947588, 3.07130217, -4.29331711, 5.4535916, -2.80116065, -2.78121213, -1.17898157, 0.03466162, 0.50173157, 0.49390863)), .Names = c("V1","V2"), class = "data.frame", row.names = c(NA, -10L)) library(MASS) library(deldir) dd &lt;- deldir(d[,1], d[,2]) plot(dd, wlines="tess") </code></pre> <p><img src="https://i.stack.imgur.com/119dJ.png" alt="enter image description here"></p> <p>First let's extract the data for the polygon: as you noticed in the comments it need more processing that i previously thought since the polygons in <code>plot.deldir</code> are plotted line by line and not polygon after polygon so the order of the lines is scrambled in <code>dd$dirsgs</code>.</p> <pre><code>ddd &lt;- as.matrix(dd$dirsgs[dd$dirsgs$ind2==1,1:4]) d1poly &lt;- rbind(ddd[1,1:2],ddd[1,3:4]) for( i in 2:nrow(ddd)){ x &lt;- ddd[ddd[,1]==d1poly[i,1], 3:4] d1poly &lt;- rbind(d1poly, x) } d1poly x2 y2 -2.096990 1.559118 0.303986 4.373353 x 1.550185 3.220238 x 0.301414 0.692558 x -1.834581 0.866098 x -2.096990 1.559118 </code></pre> <p>Let's create some random data in the polygon of interest using package <code>splancs</code>:</p> <pre><code>library(splancs) rd &lt;- csr(as.matrix(d1poly),10) # For 10 random points in the polygon containing point 1 rd xc yc [1,] -1.6904093 1.9281052 [2,] -1.1321334 1.7363064 [3,] 0.2264649 1.3986126 [4,] -1.1883844 2.5996515 [5,] -0.6929208 0.8745020 [6,] -0.8348241 2.3318222 [7,] 0.9101748 1.9439797 [8,] 0.1665160 1.8754703 [9,] -1.1100710 1.3517257 [10,] -1.5691826 0.8782223 rdd &lt;- deldir(c(rd[,1],d[1,1]),c(rd[,2],d[1,2])) # don't forget to add the coordinates of your point 1 so it s part of the sub-tessellation plot(dd, wlines="tess") plot(rdd, add=TRUE, wlines="tess") </code></pre> <p><img src="https://i.stack.imgur.com/WQ70B.png" alt="enter image description here"></p> <p><strong>Edit</strong><br> Concerning restricting the lines within the boundary, the only solution I can think of is a very ugly workaround: drawing first the subtesselation, then hiding the outside of the polygon of interest and then plotting the global tesselation. </p> <pre><code>plot(dd, wlines="tess", col="white", wpoints="none") plot(rdd, wlines="tess", add=TRUE) plotlim &lt;- cbind(par()$usr[c(1,2,2,1)],par()$usr[c(3,3,4,4)]) extpoly &lt;- rbind(plotlim, d1poly) #Here the first point of d1poly is oriented toward the upper left corner: if it is oriented otherwise the order of plotlim has to be changed accordingly polygon(extpoly, border=NA, col="white") plot(dd, wlines="tess", add=TRUE) </code></pre> <p><img src="https://i.stack.imgur.com/uzXZp.png" alt="enter image description here"></p>
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    1. POsubplot within a region of a plot in r
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    1. COThanks plannapus :) There are some more constraints in my problem...But using the information you have given I think i should find the solution...I will do some more work on this and if I have any problem I will let you know.
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    2. COIs there a way to restrict the lines of the tessellation within the boundary. I dont want them to go out of the boundary
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    3. CO@Chetan I'm trying to find a way but there is nothing obvious that comes to mind. I'll go back to you if I do find something
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