API: Diagnostics

Mesh checks

`check_mesh`

check_mesh(mesh::SurfaceMesh) → NamedTuple

Returns a named tuple with:

Field	Type	Description
`n_vertices`	`Int`	Number of vertices
`n_edges`	`Int`	Number of (canonical) edges
`n_faces`	`Int`	Number of triangles
`closed`	`Bool`	All edges have 2 adjacent faces
`manifold`	`Bool`	All edges have ≤ 2 adjacent faces
`consistent_orientation`	`Bool`	Interior edges traversed oppositely
`euler_characteristic`	`Int`	$\chi = V - E + F$
`warnings`	`Vector{String}`	List of detected problems

`euler_characteristic`

euler_characteristic(mesh) → Int    # V - E + F

`is_closed` / `is_manifold` / `has_consistent_orientation`

is_closed(mesh) → Bool
is_manifold(mesh) → Bool
has_consistent_orientation(mesh) → Bool

DEC checks

`check_dec`

check_dec(mesh, geom, dec; tol=1e-10) → NamedTuple

Returns:

Field	Description
`d1_d0_zero`	`Bool`: $\|d_1 d_0\|_\infty < \text{tol}$
`d1_d0_max_residual`	`T`: \max
`lap_constant_nullspace`	`Bool`: $\|L \mathbf{1}\|_\infty < \text{tol}$
`star0_positive`	`Bool`: all dual areas $> 0$
`star1_positive`	`Bool`: all cotan weights $> 0$ (may be false for obtuse meshes)
`warnings`	`Vector{String}`

Gauss–Bonnet diagnostic

`gauss_bonnet_residual`

gauss_bonnet_residual(mesh, geom) → T

Returns $\left|\int_\Gamma K \, dA - 2\pi\chi\right|$. Should be near machine precision for any mesh produced by the built-in generators.

`integrated_gaussian_curvature`

integrated_gaussian_curvature(mesh, geom) → T    # Σ K_i A_i*

Hodge star quality

`star1_sign_report`

star1_sign_report(dec) → NamedTuple

Field	Description
`n_entries`	Total number of ⋆₁ diagonal entries
`n_nonpositive`	Count of entries $\leq 0$
`frac_nonpositive`	Fraction of non-positive entries
`min_entry`	Minimum value (negative if obtuse triangles present)
`all_positive`	`Bool`

Laplacian comparison

`compare_laplace_methods`

compare_laplace_methods(mesh, geom) → NamedTuple

Assembles both $L_{\text{dec}}$ and $L_{\text{cotan}}$ and returns:

Field	Description
`norm_inf`	$\|L_{\text{dec}} - L_{\text{cotan}}\|_\infty$
`norm_frob`	$\|L_{\text{dec}} - L_{\text{cotan}}\|_F$
`dec_nullspace`	$\|L_{\text{dec}} \mathbf{1}\|_\infty$
`cotan_nullspace`	$\|L_{\text{cotan}} \mathbf{1}\|_\infty$
`max_dec_res`	Maximum residual of DEC eigenvalue test
`max_cotan_res`	Maximum residual of cotan eigenvalue test

On well-shaped meshes norm_inf < 1e-12.

IO

Loading meshes

load_surface_stl(path::String) → SurfaceMesh{Float32}
# Returns Float32 (native STL precision)

load_curve_csv(path::String) → CurveMesh{Float64}
# CSV format: one "x,y" or "x,y,z" coordinate per line

load_curve_points(pts; closed=true) → CurveMesh{T}
# pts: Vector{SVector{2,T}} or Vector{Tuple{T,T}}