MedicalVisualization
Barycentric Interpolation in a Tetrahedron
← Tetrahedra Decomposition | ● | Marching Tetrahedra →
An interpolated scalar value at the point →v within the domain of a tetrahedron is determined by the barycentric interpolation of corner scalar values s1/2/3/4 at the corner points →v1/2/3/4. The barzcentric interpolation is a linear combination of the scalar values with linear weights w1/2/3/4:
f(→v)=f(w1,w2,w3,w4)=w1s1+w2s2+w3s3+w4s4 with
w1=det(→v2−→v,→v3−→v,→v4−→v)D−1
w2=det(→v1−→v,→v3−→v,→v4−→v)D−1
w3=det(→v1−→v,→v2−→v,→v4−→v)D−1
w4=det(→v1−→v,→v2−→v,→v3−→v)D−1
D=det(→v4−→v1,→v3−→v1,→v2−→v1)
In a triangle:
In a tetrahedron: