euler operator造句

The Euler operator is a secondary differential operator of first order, even if, according to its expression in local coordinates, it looks like one of infinite order.
The Euler operator, which associates to each variational problem the corresponding Euler Lagrange equation, is the analog of the classical differential associating to a function on a variety its differential.
Euler operators modify the mesh's graph creating or removing faces, edges and vertices according to simple rules while preserving the overall topology thus maintaining a valid boundary ( i . e . not introducing holes ).
Its effectiveness has been demonstrated, e . g ., in the field of procedural mesh generation, with Euler operators as complete and closed set of invertible shape generating functions for meshes, operating on the half-edge level.
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