GoKawiilHand-hatched surfaces after the mid-century manner of Francis, Apéry, Hilbert–Cohn-Vossen. Drag to turn the model freely (shift-drag to roll it); scroll to approach.
The zero set is triangulated by marching tetrahedra; normals are taken from ∇f.
Stroke spacing re-traces the hatching when you release the slider.
Labels are hand-lettered, pinned to the surface, drag to move them, double-click to remove; they dim when their point is hidden.
Sources & method
The drawing is made of strokes, not pixels. Silhouettes are the zero set of n·v on the mesh (found with interpolated normals, so they chain into smooth curves), boundaries and the double curve of an immersion are added as further chains, and all of them are drawn as tapered ribbons with a broad-nib pen model, weight that grows on the shadow side and toward the viewer, and coherent hand wobble. Visibility is settled on the GPU: a hidden-line pass draws the occluded parts dashed, and a one-sided paper halo under each near contour cuts the lines behind it. Hatching is a set of streamlines of the principal-curvature line field, traced at build time in three nested densities (the second along the other principal direction, for cross-hatching); tone selects which family is inked and where each stroke feathers out. Highlights stay bare paper. The principal directions are ordered by signed curvature, not magnitude, so the two families stay continuous across the loci where κ₁ = −κ₂. Contour chains are lightly smoothed before inking. Strokes overshoot their ends a little in the manner of sketchy line rendering; the ink pooling at stroke starts and the ragged bleed into the paper grain are hand-tuned effects of this page (a widened ribbon whose fringe is gated by a fibre-like noise), not taken from a paper. Labels are hand-lettered, pinned to points of the surface with a leader line, and dimmed when their point is hidden.
G. K. Francis, A Topological Picture Book, Springer, 1987 — the style target: contour drawing with cusps, double curves, hidden lines, and sparing hatched bands.
P. Bénard, A. Hertzmann, “Line Drawings from 3D Models: A Tutorial,” Foundations and Trends in Computer Graphics and Vision 11(1–2), 2019 — the contour pipeline: smooth silhouettes as n·v = 0, chaining, visibility, stylization.
A. Hertzmann, “Introduction to 3D Non-Photorealistic Rendering: Silhouettes and Outlines,” SIGGRAPH 99 Course Notes — silhouettes from interpolated vertex normals (marching-triangles on n·v).
A. Hertzmann, D. Zorin, “Illustrating Smooth Surfaces,” SIGGRAPH 2000, pp. 517–526 — hatching along principal curvature directions, cross-hatching only in dark regions, blank highlights, undercuts.
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