From Ohm

Barycentric Interpolation in a Tetrahedron

An interpolated scalar value at the point $\vec{v}$ within the domain of a tetrahedron is determined by the barycentric interpolation of corner scalar values $s_{1/2/3/4}$ at the corner points $\vec{v}_{1/2/3/4}$. The barzcentric interpolation is a linear combination of the scalar values with linear weights $w_{1/2/3/4}$:

$ f(\vec{v}) = f(w_1,w_2,w_3,w_4) = w_1s_1 + w_2s_2 + w_3s_3 + w_4s_4 $ with
$ w_1 = det(\vec{v_2}-\vec{v},\vec{v_3}-\vec{v},\vec{v_4}-\vec{v}) D^{-1} $
$ w_2 = det(\vec{v_1}-\vec{v},\vec{v_3}-\vec{v},\vec{v_4}-\vec{v}) D^{-1} $
$ w_3 = det(\vec{v_1}-\vec{v},\vec{v_2}-\vec{v},\vec{v_4}-\vec{v}) D^{-1} $
$ w_4 = det(\vec{v_1}-\vec{v},\vec{v_2}-\vec{v},\vec{v_3}-\vec{v}) D^{-1} $
$ D = det(\vec{v_4}-\vec{v_1},\vec{v_3}-\vec{v_1},\vec{v_2}-\vec{v1}) $

In a triangle:

In a tetrahedron:

Retrieved from http://schorsch.efi.fh-nuernberg.de/roettger/index.php/MedicalVisualization/BarycentricTetrahedraInterpolation

Page last modified on November 15, 2013, at 12:12 PM