Standard circular string art is flat: the nails sit on a single plane, and the threads cross on a two-dimensional grid. However, by introducing nails of varying heights or arranging pins on concentric three-dimensional circles, we can calculate spatial vector coordinates, turning string art into complex 3D wireframe sculptures.
1. Calculating Chords in Three Dimensions
In 3D string mapping, each nail has a coordinate in three dimensions: P(x, y, z). The z-coordinate represents either the nail height on a flat board, or the pin position on a curved dome canvas.
To compute the intersection score of a thread path, our Bresenham line drawer is expanded into a 3D ray-tracer. We evaluate how the spatial chord vector intersects dark regions in a 3D voxel density buffer, rather than a flat 2D pixel array.
2. Stacking Nails in Tiers
You can build a multi-level canvas by hammering nails to three distinct depths:
- Tier 1 (Outer Ring): Nails hammered shallowly, leaving 25mm exposed. Holds foreground highlights.
- Tier 2 (Mid-depth Ring): Nails hammered to 15mm exposed. Maps midtone shading grids.
- Tier 3 (Inner Ring): Nails hammered deep, leaving only 5mm exposed. Establishes background shadows.
By winding threads across these different tiers, the physical lines hover above each other, creating an interactive parallax effect where the image appears to change shape as the viewer moves around the gallery.
3. Designing for 3D Spatial Envelopes
When calculating multi-level paths, the algorithm must verify that the thread does not collide with lower nails along its route. Colliding with a lower pin bends the thread, distorting the intended vector. Stringify's 3D engine calculates these clearance zones in advance, warning creators of potential nail height collisions before winding begins.