Defining boundary condition on slant side

[notviral]

I am investigating soil slope stability and have represented the slope with deepxde.geometry.geometry_2d.Polygon(vertices). My current doubt concerns applying boundary conditions on slanted edges of the polygon: axis-aligned checks such as x[0] == c or x[1] == c are not valid for sloped sides. What is the recommended DeepXDE workflow to impose BCs on a non-vertical/non-horizontal boundary?

[lululxvi]

The code logic for non-vertical/non-horizontal boundary is the same as vertical/-horizontal boundary.

[echen5503]

I think an answer with more specificity is that DeepXDE already handles arbitrary geometry, but if you only want one slanted side, you can filter it using a line equation:

def on_slanted_edge(x, on_boundary):
    # Example: edge connecting (1,0) and (0.5,1)
    # Line equation: y = -2x + 2
    return on_boundary and np.isclose(x[1], -2 * x[0] + 2)

And this extends to circles, hypercubes, etc.

[echen5503]

Note that from then on, BCs are handled automatically. For example, for NeumannBC, the normal will be automatically calculated, no need to find perpendicular line equation.