# dec_h1

## `dec_h1(V, F, E_to_he=None)`

Builds the DEC 1-Hodge-star operator as described, for example, in Crane et al. 2013. "Digital Geometry Processing with Discrete Exterior Calculus".

The edge labeling in E_to_he follows the convention from Gpytoolbox's `halfedge_edge_map`.

The input mesh must be a manifold mesh.

Parameters:

Name Type Description Default
`V` `(n,d) numpy array`

vertex list of a triangle mesh

required
`F` `(m,3) numpy int array`

face index list of a triangle mesh

required
`E_to_he` `(e,2,2) numpy int array, optional (default None)`

index map from e to corresponding row and col in the list of all halfedges `he` as computed by `halfedge_edge_map` for two halfedges (or -1 if only one halfedge exists) If absent, will be computed using `halfedge_edge_map`

`None`

Returns:

Name Type Description
`h1` `(e,e) scipy csr_matrix`

DEC operator h1

Examples:

``````# Mesh in V,F
h1 = gpy.dec_h1(V,F)
``````
Source code in `src/gpytoolbox/dec_h1.py`
 ``` 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42``` ``````def dec_h1(V,F,E_to_he=None): """Builds the DEC 1-Hodge-star operator as described, for example, in Crane et al. 2013. "Digital Geometry Processing with Discrete Exterior Calculus". The edge labeling in E_to_he follows the convention from Gpytoolbox's `halfedge_edge_map`. The input mesh _must_ be a manifold mesh. Parameters ---------- V : (n,d) numpy array vertex list of a triangle mesh F : (m,3) numpy int array face index list of a triangle mesh E_to_he : (e,2,2) numpy int array, optional (default None) index map from e to corresponding row and col in the list of all halfedges `he` as computed by `halfedge_edge_map` for two halfedges (or -1 if only one halfedge exists) If absent, will be computed using `halfedge_edge_map` Returns ------- h1 : (e,e) scipy csr_matrix DEC operator h1 Examples -------- ```python # Mesh in V,F h1 = gpy.dec_h1(V,F) ``` """ l_sq = halfedge_lengths_squared(V,F) return dec_h1_intrinsic(l_sq,F,E_to_he=E_to_he) ``````