Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

Table 4

Detecting saddles and helices in second-order tensor fields.

	Div(Reduce(𝐿(𝐷)))	Tr(Helicity(𝐷))
Source	8(𝑥^2+𝑦^2)	0
Vortex	24(𝑥^2+𝑦^2)	0
Saddle	0	0
Helix	12(1+2𝑥^2+2𝑦^2)	2(1+𝑥^2+𝑦^2)
Spiral	𝑐1𝑥^2+𝑐2𝑥𝑦+𝑐1𝑦^2	0