Function FieldLines

python/webgui.py:565–650

(
    function: ngs.CoefficientFunction,
    start_region: Optional[ngs.Region] = None,
    mesh: Optional[ngs.Mesh] = None,
    start_points: Optional[list] = None,
    num_lines: int = 100,
    length: float = 0.5,
    name: str = "fieldlines",
    max_points_per_line: float = 500,
    thickness: float = 0.0015,
    tolerance: float = 0.0005,
    direction: int = 0,
)

    return data

def FieldLines(
    function: ngs.CoefficientFunction,
    start_region: Optional[ngs.Region] = None,
    mesh: Optional[ngs.Mesh] = None,
    start_points: Optional[list] = None,
    num_lines: int = 100,
    length: float = 0.5,
    name: str = "fieldlines",
    max_points_per_line: float = 500,
    thickness: float = 0.0015,
    tolerance: float = 0.0005,
    direction: int = 0,
):
    assert start_region or (mesh and start_points), "Either start_region or mesh and start_points must be provided"
    rules = {}
    # use 5th order integration rule for all element types as potential starting points
    for et in [
        ngs.ET.TRIG,
        ngs.ET.QUAD,
        ngs.ET.TET,
        ngs.ET.HEX,
        ngs.ET.PRISM,
        ngs.ET.PYRAMID,
        ngs.ET.SEGM
    ]:
        rules[et] = ngs.IntegrationRule(et, 5)

    if function.is_complex:
        num_lines = num_lines // 10

    if start_points is not None:
        all_mapped_points = mesh(start_points[:,0], start_points[:,1], start_points[:,2])
    else:
        mesh = start_region.mesh
        all_mapped_points = mesh.MapToAllElements(rules, start_region)

    num_angles = 100 if function.is_complex else 1
    for a in range(num_angles):
        phi = 2 * np.pi * a / num_angles

        if function.is_complex:
            cf = ngs.cos(phi) * function.real - ngs.sin(phi) * function.imag
        else:
            cf = function

        # randomize starting points to choose approx num_lines, higher function values increase selection probability
        values = ngs.Norm(cf)(all_mapped_points).flatten()
        sum_values = sum(values)

        rand_values = np.random.rand(len(values))
        selection = np.where(values > sum_values/num_lines * rand_values)
        mapped_points = all_mapped_points[selection]

        # generate raw staring point coordinates and call low_level interface routing
        points = ngs.CF((ngs.x, ngs.y, ngs.z))(mapped_points)

        data = cf._BuildFieldLines(
            mesh,