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cotangent_weights_intrinsic

cotangent_weights_intrinsic(l_sq, F)

Builds the cotangent weights (cotangent/2) for each halfedge using only intrinsic information (squared halfedge edge lengths).

The ordering convention for halfedges is the following: [halfedge opposite vertex 0, halfedge opposite vertex 1, halfedge opposite vertex 2]

Parameters:

Name Type Description Default
l_sq (m,3) numpy array

squared halfedge lengths as computed by halfedge_lengths_squared

 required
F (m,3) numpy int array

face index list of a triangle mesh

 required

Returns:

Name Type Description
C (m,3) numpy array

cotangent weights for each halfedge

Examples:

```python

Mesh in V,F

from gpytoolbox import halfedge_lengths_squared, cotangent_weights_intrinsic l = halfedge_lengths_squared(V,F) L = cotangent_weights_intrinsic(l_sq,F) ```

Source code in src/gpytoolbox/cotangent_weights_intrinsic.py 
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def cotangent_weights_intrinsic(l_sq,F):
    """Builds the cotangent weights (cotangent/2) for each halfedge using only
    intrinsic information (squared halfedge edge lengths).

    The ordering convention for halfedges is the following:
    [halfedge opposite vertex 0,
     halfedge opposite vertex 1,
     halfedge opposite vertex 2]

    Parameters
    ----------
    l_sq : (m,3) numpy array
        squared halfedge lengths as computed by halfedge_lengths_squared
    F : (m,3) numpy int array
        face index list of a triangle mesh

    Returns
    -------
    C : (m,3) numpy array
        cotangent weights for each halfedge

    Examples
    --------
     ```python
    # Mesh in V,F
    from gpytoolbox import halfedge_lengths_squared, cotangent_weights_intrinsic
    l = halfedge_lengths_squared(V,F)
    L = cotangent_weights_intrinsic(l_sq,F)
    ```

    """

    assert F.shape[1] == 3
    assert l_sq.shape == F.shape
    assert np.all(l_sq>=0)

    a,b,c = l_sq[:,0], l_sq[:,1], l_sq[:,2]
    A = doublearea_intrinsic(l_sq, F)

    # See https://github.com/libigl/libigl/blob/main/include/igl/cotmatrix_entries.cpp
    C = 0.25 * np.stack((b+c-a, c+a-b, a+b-c), axis=1) / A[:,None]

    return C