Update Step on a triangulation

16

Vi,j,k

= min

0 t 1

tUj

+ (1 t)Uk

Distance function in (i, j, k):

(U)

i

= min

f=(i,j,k)

Vi,j,k

X = (xj xi, xk xi

) Rd 2

u = (Uj, Uk

) R2

S = (X X) 1 R2 2

I = (1, 1) R2

xi

xj

xk

+||txj

+ (1 t)xk xi

||Hijk

g

Notations:

Unknowns:

Discrete Eikonal equation:

= Vi,j,k

U(x) = x xi, g + d

gradient

Hi,j,k

= w2Id

3

(for simpliﬁty)