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Interactive 3D Topological Surfaces Rendered in a Hand-Drawn Style
Key points
- Renders topological surfaces in a mid-century hand-drawn style.
- Uses strokes, not pixels, for drawing elements.
- Features GPU-based visibility and principal-curvature hatching.
- Includes effects like ink pooling and ragged bleed.
Interactive Hand-Drawn Topology
An interactive rendering project has been developed to visualize topological surfaces, drawing inspiration from the mid-century style of G. K. Francis's "A Topological Picture Book." Users can manipulate the 3D models by dragging to rotate and scrolling to zoom, with additional controls for rolling the model.
Stroke-Based Rendering Techniques
The rendering engine generates drawings using strokes rather than pixels. Silhouettes are determined by the zero set of n·v on the mesh, with interpolated normals ensuring smooth curves. Boundaries and double curves are added as chained elements. These lines are rendered as tapered ribbons, mimicking a broad-nib pen, with weight variations based on shadow and proximity to the viewer, and an intentional "hand wobble" effect.
GPU-Accelerated Visibility and Hatching
Visibility is managed on the GPU, employing a hidden-line pass to render occluded parts as dashed lines. A one-sided paper halo under near contours cuts lines behind them. Hatching is created by tracing streamlines of the principal-curvature line field at build time, available in three nested densities. Tone selection dictates which family of hatching is inked and where strokes feather out, while highlights remain uninked.
Stylistic Details and References
The principal directions for hatching are ordered by signed curvature to maintain continuity across loci where κ₁ = −κ₂. Contour chains undergo light smoothing before inking. Additional effects include strokes overshooting their ends, ink pooling at stroke starts, and a ragged bleed into the paper grain, which are custom-tuned. Labels are hand-lettered, pinned to surface points with leader lines, and dimmed when their corresponding point is hidden. The project references works by Francis, Bénard, Hertzmann, Zorin, Jobard, and Lefer for its stylistic and technical foundations.
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Reporting from
A new interactive rendering project visualizes topological surfaces in the style of G. K. Francis's "A Topological Picture Book." It uses GPU-accelerated techniques to create hand-hatched, stroke-based drawings with features like tapered ribbons, coherent hand wobble, and dynamic visibility.