Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

Table 5

Detecting saddles and helices in third-order tensor fields.

	Div(Reduce(𝐿(𝐷)))	Tr(Helicity(𝐷))
Source	12175(𝑥^4+75𝑥^2𝑦^2+𝑦^4)	0
Vortex	24175(14𝑥^4−3𝑥^2𝑦^2+14𝑦^4)	0
Saddle	−6175(19𝑥^4+12𝑥^2𝑦^2+19𝑦^4)	0
Helix	8175(3+42𝑥^4+5𝑦^2+42𝑦^4+𝑥^2(5−9𝑦^2))	2(1+𝑥^4+𝑦^4)
Spiral	𝑐1𝑥^4−𝑐2𝑥^3𝑦+𝑐3𝑥^2𝑦^2+𝑐2𝑥𝑦^3+𝑐1𝑦^4	0