# Understanding difference between TIN interpolation methods Linear and Clough-Tocher of QGIS

I started to study TIN in QGIS and created my first TIN from a point layer with elevation. There are two interpolation methods called Linear and Clough-Tocher that give very different results. Linear looks like a regular Raster and with Clough-Tocher the result cannot be interpreted at first glance. Further the values of both methods vary a lot, as can be seen in the picture. I cannot find information in the QGIS Docs what the difference is between the two methods.

What is the difference and why are the results so different?

I am using QGIS 3.4.13.

• Really a good question. I can't answer it propperly. Just to comment that extreme values are inside the triangles of the triangulation and the surface satisfaces a continuous slope at each point. The algorithm creates "valleys and mountains" within triangles in order to satisfy that condition. Jan 31, 2020 at 22:06
• For Clough-Tocher see: xmswiki.com/wiki/GMS:Clough-Tocher Aug 31, 2021 at 16:22
• I tried out both interpolation methods on a small test dataset, and the results are comparable... Aug 31, 2021 at 16:23

It seems that `Linear` and `Clough-Tocher` are quite coherent in respect to each other. Out of curiosity, I tried interpolating a small, random dataset with both algorithms, also opting for the creation of the underlying triangulation networks: As expected, there is only a very limited difference: EDIT

With a larger dataset of 10.000 random points, differences surface (pun intended). In particular:

• the underpinning TIN is identical, while
• the single faces are interpolated differently

Clough-Tocher interpolation: Linear interpolation: Zoom in: Also, I find the histograms interesting:

Clough-Tocher interpolation histogram: Linear interpolation histogram: However, if we create a difference layer between the two interpolated rasters, and sample it with the original 10k vector points, we see that on average the two interpolation methods do not differ at vertexes/original points, which shows both behave "well":

``````{'COUNT': 9984,
'CV': 183.1713180828161,
'EMPTY': 16,
'FILLED': 9984,
'FIRSTQUARTILE': -0.14226750284433365,
'IQR': 0.28140850365161896,
'MAJORITY': -0.20819500088691711,
'MAX': 39.16905975341797,
'MEAN': 0.003276590218837291,
'MEDIAN': -0.001677999971434474,
'MIN': -15.795705795288086,
'MINORITY': -15.795705795288086,
'RANGE': 54.964765548706055,
'STD_DEV': 0.6001773492016894,
'SUM': 32.713476744871514,
'THIRDQUARTILE': 0.1391410008072853,
'UNIQUE': 9924}
``````