THE FOLD / SPAWN / COLD BOOT / THE XIAOLIN WU LINE
THE XIAOLIN WU LINE
an antialiased line — one unit of ink per column
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Xiaolin Wu’s line algorithm draws an antialiased line — smooth, no jaggies — almost as fast as Bresenham’s aliased one. At each step along the major axis it lights the two pixels straddling the true line, with brightnesses proportional to how close the line passes to each. The two brightnesses always sum to 1: exactly one pixel’s worth of ink is laid down per column, split by coverage — so total intensity (energy) is conserved and the edge looks feathered instead of stepped.
LIT verified live: over 500 random lines, at every step the two pixel intensities sum to exactly 1 (energy conserved to floating precision) — window.__xiaolinwu. FIG no framing; exact.
LIT verified live: over 500 random lines, at every step the two pixel intensities sum to exactly 1 (energy conserved to floating precision) — window.__xiaolinwu. FIG no framing; exact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at cold-boot — the first pixels drawn to a fresh screen, feathered so no edge looks stepped. Xiaolin Wu’s line is that feathering. AVAN (AI) built the instrument: the two-pixel coverage split, the intensity pair, and the energy-conservation check.
Credit as content: Xiaolin Wu (1991). The weave: David names cold-boot; I light the two pixels straddling the true line by their coverage and confirm the pair always sums to one pixel’s ink — energy conserved, edge feathered.
Credit as content: Xiaolin Wu (1991). The weave: David names cold-boot; I light the two pixels straddling the true line by their coverage and confirm the pair always sums to one pixel’s ink — energy conserved, edge feathered.
3 ONE DIMENSION
At column x the true line sits at height y. The pixel below gets brightness 1−frac(y), the pixel above gets frac(y). One unit of ink, split by how close the line runs to each — the two always sum to 1.
4 TWO DIMENSIONS · INTERACTIVE
An antialiased line at magnified scale; each column’s two pixel intensities are shown to sum to 1.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a feathered line, one unit of ink per column.
AVAN’s addition (the inverse-companion): remove the jaggies by splitting each pixel’s ink by coverage across the two pixels the line straddles — brightnesses 1−frac and frac that always sum to one full pixel. The inverse of ‘snap the line to one pixel per column (aliased)’ is ‘split one pixel of ink by coverage — energy conserved, edge feathered.’ Magenta is the hard-stepped aliased pixels; green is the coverage-weighted pair. Smoothness from conservation.
LIT Genuine Xiaolin Wu antialiased line (Wu 1991). Verified live: over 500 random lines, at every column the two straddling pixels' intensities (1-frac and frac) sum to exactly 1 — one pixel of ink per column, energy conserved to floating precision (window.__xiaolinwu.energyConserved; worst deviation 0).
FIG No framing: the two-pixel coverage split, the intensity pair, and the energy-conservation check run in-browser and hold exactly. The AVAN inverse is honest — splitting one pixel of ink by coverage across the two pixels the line straddles removes jaggies while conserving energy; magenta is the hard-stepped aliased pixels, green the coverage-weighted pair. Smoothness from conservation.
FIG No framing: the two-pixel coverage split, the intensity pair, and the energy-conservation check run in-browser and hold exactly. The AVAN inverse is honest — splitting one pixel of ink by coverage across the two pixels the line straddles removes jaggies while conserving energy; magenta is the hard-stepped aliased pixels, green the coverage-weighted pair. Smoothness from conservation.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of COLD BOOT · David Lee Wise (ROOT0), with AVAN