sofia.geometry package

Submodules

Module contents

class sofia.geometry.Geometry(name: str, support_winding_number: bool = False)

Bases: Basic

is_commutative = True
sdf(domain: Domain, max_dist=1000.0, query_method: Literal['mesh_query_point', 'mesh_query_point_sign_normal', 'mesh_query_point_sign_parity', 'mesh_query_point_sign_winding_number', 'mesh_query_point_no_sign'] = 'mesh_query_point', epsilon: float = 0.001, n_sample: int = 1, perturbation_scale: float = 0.1, accuracy: float = 2.0, threshold: float = 0.5)

Return symbolic signed-distance field.

The generated warp kernel uses warp.mesh_query_point which is the most general and robust method, but requires watertight meshes.

Examples

The resulting symbolic SDF function can be used either on its own: >> sdf = Field(‘sdf’, G) >> geo = Geometry(‘geo’) >> sdf << geo.sdf(G, max_dist=1e2)

Or inside a larger expression: >> u = Field(‘u’, G) >> u << u + 2 * geo.sdf(G)

Parameters:

  • domain – Domain that contains the physical_coordinates on which the SDF should be computed.

  • max_dist – Maximal distance for the SDF kernel. Beyond this distance the SDF is not computed anymore to improve performance.

  • query_method –

    Warp query method to use. Each comes with its own tradeoffs between robustness, accuracy, versatility and efficiency:

    • mesh_query_point:

      • relatively robust

      • medium expensive

      • requires watertight mesh

      • sign check runs over entire mesh, closest point is limited

        by max_dist

    • mesh_query_point_sign_normal:

      • fast

      • robust for well-conditioned mesh

      • requires watertight and non-self intersecting mesh

      • extra arguments: epsilon

    • mesh_query_point_sign_parity:
      • sign (inside/outside) is determined by casting n_sample rays from

        point and counting how many mesh faces each ray crosses (deterministic)

      • sign check runs over entire mesh, closest point is limited by

        max_dist

      • extra arguments: n_sample, perturbation_scale

    • mesh_query_point_sign_winding_number:

      • most robust but also most expensive

      • robust for poorly conditioned mesh

      • does not require watertight mesh

      • extra arguments: accuracy, threshold

      • NOTE: requires support_winding_number=True in the

        Geometry construction, otherwise the kernel falls back to mesh_query_point

    • mesh_query_point_no_sign:

      • fastest, but does not compute the sign

  • epsilon – (only for mesh_query_point_sign_normal) Epsilon treating distance values as equal, when locating the minimum distance vertex/face/edge, as a fraction of the average edge length, also for treating closest point as being on edge/vertex

  • n_sample – (only for mesh_query_point_sign_parity) Number of rays used to classify the sign. Prefer a positive, odd value; larger values are more robust. A non-positive value casts no rays and classifies the point as inside.

  • perturbation_scale – (only for mesh_query_point_sign_parity) Scale of the perturbation. Each ray perturbs the base direction (1, 1, 1) by an offset drawn per axis from a uniform distribution over [-perturbation_scale, perturbation_scale).

  • accuracy – (only for mesh_query_point_sign_winding_number) Accuracy for computing the winding number with fast winding number method utilizing second-order dipole approximation

  • threshold – (only for mesh_query_point_sign_winding_number) The threshold of the winding number to be considered inside

Returns:

Symbolic SDF function that will be converted to an SDF kernel by codegen.

Return type:

sdf_function

default_assumptions = {'commutative': True}