meshing.dual_contouring.qef_vertices

meshing.dual_contouring.qef_vertices(
    hermite,
    incidence,
    grid,
    *,
    regularization=0.001,
)

Place one vertex per active cell from its Hermite tangent planes.

Minimizes Σ (nᵢ · (v - pᵢ))² plus a Tikhonov pull toward the cell’s Hermite mass point, scaled so regularization is relative to the normal count. Planar cells (rank-1 systems) land on the face near the mass point, crease cells slide onto the crease line, and corner cells reproduce the corner; the bias a corner inherits from the regularization is of order regularization × cell size.

Fully JAX-traceable: call under jax.grad/jax.jit with a hermite built from traced parameters to differentiate vertex positions. Vertices are clamped to their cell as a final safety net; the clamp binds only on degenerate cells.

Parameters

Name	Type	Description	Default
hermite	HermiteData	Stage-1 Hermite data for the frozen edge set.	required
incidence	CellIncidence	Cell-to-edge mapping for the same edge set.	required
grid	GridSpec	The sampling grid (cell bounds for clamping).	required
regularization	float	Relative Tikhonov weight; must be positive.	0.001

Returns

Name	Type	Description
	tuple[Array, Array]	(vertices, normals), both shaped (cell_count, 3). Normals are the safely averaged incident unit normals; a cell whose normals cancel (opposed thin-sheet subgradients) falls back to its first sample’s normal so downstream orientation and shading stay finite.