Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

Figure 5

Helmholtz decomposition results for synthetic second-order tensor fields.

(a) Helix

(b) Saddle

(c) Source

(d) Spiral

(e) Vortex

(f) Helix solenoidal part

(g) Saddle solenoidal part

(h) Source solenoidal part

(i) Spiral solenoidal part

(j) Vortex solenoidal part

(k) Helix irrotational part

(l) Saddle irrotational part

(m) Source irrotational part

(n) Spiral irrotational part

(o) Vortex irrotational part

(p) Helix harmonic part

(q) Saddle harmonic part

(r) Source harmonic part

(s) Spiral harmonic part

(t) Vortex harmonic part