Vector Fields

Vector-valued CoefficientFunctions can be visualized as arrow glyphs on surfaces, clipping planes, or as field lines.

Surface Vectors

Arrows on the boundary surface of a 3D mesh:

from ngsolve import *
from ngsolve_webgpu import *
from webgpu.jupyter import Draw

mesh = Mesh(unit_cube.GenerateMesh(maxh=0.2))
cf = CF((x, y, 1))
md = MeshData(mesh)
fd = FunctionData(md, cf, order=1)
vecs = SurfaceVectors(fd)
Draw(vecs)

SurfaceVectors samples the vector field on surface elements and renders 3D arrows. grid_size controls the density of arrows (default 20).

Clipping Vectors

Arrows on a clipping plane through the volume:

from ngsolve import *
from ngsolve_webgpu import *
from webgpu.clipping import Clipping
from webgpu.jupyter import Draw

mesh = Mesh(unit_cube.GenerateMesh(maxh=0.2))
cf = CF((x, y, 1))
md = MeshData(mesh)
fd = FunctionData(md, cf, order=1)
clipping = Clipping()
clipping.center = [0.5, 0.5, 0.5]
vecs = ClippingVectors(fd, clipping=clipping)
Draw(vecs)

ClippingVectors works like SurfaceVectors but on the clipping cross-section. The clipping plane is controlled by the Clipping object.

Field Lines

Streamlines traced through a 3D vector field:

from ngsolve import *
from ngsolve_webgpu.cf import FieldLines
from webgpu.jupyter import Draw

mesh = Mesh(unit_cube.GenerateMesh(maxh=0.3))
cf = CF((-y, x, 0.1))
fieldlines = FieldLines(cf, mesh, num_lines=100, length=0.5, thickness=0.0015)
Draw(fieldlines)

FieldLines integrates streamlines from random start points. Key parameters:

• num_lines — number of streamlines (default 100)

• length — integration length (default 0.5)

• thickness — line thickness relative to bounding box (default 0.0015)

• direction — 0=both, 1=forward, -1=backward