Cross-Field Streamlines

This example traces both orthogonal arms of a smooth four-fold rotationally symmetric (4-RoSy) field across a triangulated shark surface. The field is stored per facet, transported across mesh edges, and rendered as one-pixel screen-space curves over the surface.

Interactive demo

Data

The cartoon shark model is designed by Calrais and published on Thingiverse.

It contains the triangular surface and the precomputed facet attribute smooth_direction_field_facets computed via the paper "Globally Optimal Direction Fields".

Input contract

• mesh: surface from data/shark.msh; smooth_direction_field_facets (facet 3-channel vector).

Reproduce and inspect

python ../render_gallery.py --check CrossField
python ../render_gallery.py --artifacts CrossField

Python · Manifest · Inspection · Canonical JSON · Validation

Code

#!/usr/bin/env python

import hakowan as hkw
import numpy as np

hkw.set_default_backend("mitsuba")

base = hkw.layer("data/shark.msh").rotate((0, 0, 1), np.radians(90))
surface = base.name("Surface")
stream_lines = (
    base.transform(
        hkw.transform.Streamline(
            vec_field="smooth_direction_field_facets",
            cross_field=True,
            n=500,
            max_steps=100,
        )
    )
    .name("Wireframe")
    .mark("Curve")
    .channel(size=hkw.channel.Size(data=1, space="screen"))
    .material("Diffuse", "#202020")
)


figure = (
    hkw.figure(surface + stream_lines)
    .camera("perspective", eye=(0, -3, 0), up=(0, 0, 1))
    .environment(up=(0, 0, 1))
)
RECIPE_FIGURE = figure
RECIPE_INSPECTIONS = {"mesh": "data/shark.msh"}

if __name__ == "__main__":
    hkw.render(figure, filename="results/shark_stream_lines.webp")
    hkw.render(figure, backend="webgl", filename="results/shark_stream_lines.html")