chrisyu-cs / repulsive-curves

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Replace vector D with scalar D #1

Open keenancrane opened 5 years ago

keenancrane commented 5 years ago

Currently we express the derivative operator D as

Du := du ° dγ†,

which when discretized (using the edge formulation) gets represented on each edge (i,j) as a 3x2 matrix

(ui - uj)T_ij^T/Lij.

For the systems we need to solve in the curve case, we could instead just let the smooth operator D be defined as just

Du := du,

i.e., the differential of the function u. The corresponding discrete operator would then be a trivial scalar operator

uj - ui

which both yields a matrix of smaller dimensions, and also does not involve the edge lengths (hence never has to be re-built).