Triangulation with linear interpolation

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Triangulation with linear interpolation

The standard form of interpolation using triangulation of the data points is a widely available exact method. The Delaunay triangulation of the point set is first computed with the z-values of the vertices determining the tilt of the triangles. Interpolation is then simply a matter of identifying the value at each grid node by linearly interpolating within the relevant triangle.

Linear interpolation may be achieved, for example, using matrix determinants in a similar manner to those used in Section 4.2.3, Surface area. A plane surface through three points {xi,yi,zi}, i=1,2,3 has a formula in determinant form of:

For example, consider a TIN element defined by the three coordinates: (0,10,10), (10,0,20), (0,0,5). Points in the planar triangle defined by the three (x,y) coordinates (including the vertices) may be interpolated from the above plane surface. In this case evaluating the determinant gives z=5+3x/2+y/2, from which all values may be computed.