R_Calculating Thiessen weights for an area with irregular boundary

Question

I want to calculate Thiessen weights to compute areal rainfall from number of point measurements. I am using R and thanks to some previous question in the same topic, I got to know that I can use deldir. But the problem is my boundary polygon is not a rectangle; it's an irregular polygon (it's a catchment boundary derived using ArcGIS). But in deldir the boundary can only be a rectangle. Are there any other packages where I can calculate Thiessen weights of an area covered by an irregular boundary?

Given below are my measurement points (meas_points) and coordinates of a (simplified) boundary polygon(boundary)

> meas_points
          X      Y
[1,] 415720 432795
[2,] 415513 432834
[3,] 415325 432740
[4,] 415356 432847
[5,] 415374 432858
[6,] 415426 432774
[7,] 415395 432811
[8,] 415626 432762

> boundary
          x      y
[1,] 415491 432947
[2,] 415269 432919
[3,] 415211 432776
[4,] 415247 432657
[5,] 415533 432657
[6,] 415781 432677
[7,] 415795 432836
[8,] 415746 432937

Any help is really appreciated. Thanks.

Coonhound

Answer 1

You can try the dual of voronoi and find the convex hull. Then remove all interior triangles and edges exceeding alpha. Reinsert the interior triangles and find the dual of Delaunay triangulation.

Quiz

Would you mind helping me with an example, preferably using the given data? – Coonhound

First of all your answer simply describes 'what should be done' whereas I would also like to know 'how should it be done' (using R). Also, I am not an expert in spatial interpolation; hence find it difficult to understand some of the terms. Thanks – Coonhound

R is left as an exercise for you. You can try my PHP class concave hull for example. – Quiz