raygeo.mesh.gradient

Functions

compute_gradient_field(
    mesh: types.TriangleMesh,
    u_field: Sequence[float],
) -> Sequence[tuple[float, float]]

Compute the gradient of the scalar field on each triangle.

Given the solution u to the Laplace equation, computes ∇u = (∂u/∂x, ∂u/∂y) in the interior of each triangle of the mesh (piecewise constant).

Parameter	Type	Description
`mesh`	`types.TriangleMesh`	TriangleMesh with the same vertex count as u_field.
`u_field`	`Sequence[float]`	Scalar field values, one per vertex.
Returns	`Sequence[tuple[float, float]]`	List of (gx, gy) pairs, one per triangle in mesh order.
Complexity		O(n) where n = number of triangles

Gradient field ∇u (red) and perpendicular flow ∇u⊥ (blue) on the Laplace solution

Gradient field ∇u (red) and perpendicular flow ∇u⊥ (blue) on the Laplace solution

Gradient field ∇u (red) and perpendicular flow ∇u⊥ (blue) on a multi-island domain

Gradient field ∇u (red) and perpendicular flow ∇u⊥ (blue) on a multi-island domain