How Multi-Head Processing Works

Multi-head printing loads N filaments at once and prints them in parallel, so colour changes happen at scheduled pauses rather than after every single run. Kromacut's job is to figure out the best way to group layers, assign filaments to nozzles, and arrange colors so the fewest pauses produce the most accurate result.

There are four main problems it solves, in order.

Glossary

• Run: a series of layers that all use the same filament.
• Window: A group of sequential runs, typically the number of runs equals the number of nozzles.
• DP: Display Program, synonymous with 'algorithm'.
• ΔE: The ΔE between an actual and a proposed layer configuration is the difference in errorFactor between the two.
• N: when N is referred to, you can assume that's equal to the nozzle count.
• K: the number of unique colors in a window
• Quality score: See ΔE
• ErrorFactor: The difference between the desired color, and the actual color that a series of layers will produce. Always a positive value, or 0.

1. Grouping Layers into Windows

Instead of swapping filament for every color change, the printer batches N consecutive color regions into a "window" and handles them all with the same N loaded filaments. It only pauses at window boundaries.

Before windows can be defined, Kromacut builds a run stack — a list of contiguous layer blocks where each block uses one filament. Colors are mapped to print heights by luminance (brighter = higher), then the full layer sequence is expanded at the printer's actual layer height. Where the filament index changes between layers, a new run starts.

Under the hood: selecting which runs become windows isn't just "take the first N, then the next N." Kromacut runs a dynamic programming pass over all candidate windows to find the non-overlapping subset that maximises a cumulative quality score. Each window gets an errorFactor — how well its N filaments cover the colours in that band — and the DP finds the combination of windows that maximises the total. Because windows are fixed-width (always N runs), the DP is O(n): the best previous non-overlapping window is always exactly N steps back, so there's no backtracking. The search also stops early once no remaining window improves the score by more than 0.01% — no point squeezing out tiny gains near the bottom of the pile. It will also end if no windows of >1 run long can be constructed.

Runs that don't land in any selected window are unclaimed and print with whatever filament was last loaded.

2. Assigning Filaments to Nozzles

Once windows are chosen and arranged appropriately, each window needs a filament assigned to each of its N nozzle slots. The goal is to match the target colors as closely as possible while reusing filaments across windows to minimize swaps.

Under the hood: this is split into two stages.

Stage 1 — what goes in each slot. For every window, Kromacut tries every possible combination of K filaments across the N layers — all K^N of them — and scores each one. The score is a perceptual color difference (more on that below) weighted by how many pixels in the frame use each color, so dominant colors matter more than rare ones. The top-scoring combination becomes that window's assignment.

Stage 2 — linking windows together. The per-window assignments are then threaded across the full print with a second DP. The state at each step is the N-tuple of currently loaded filament IDs. Moving from one window to the next costs one swap per nozzle slot that changes filament; idle slots carry their previous filament for free. The DP finds the sequence of assignments that minimises total swaps across the whole print.

One extra detail: individual runs inside a window can override the window-level consensus if a per-run slot assignment scores better. This lets two adjacent color regions in the same window use slightly different arrangements without forcing a full nozzle change.

3. Scoring Color Accuracy

FDM filaments are semi-translucent, so the color you see on a print isn't just the top filament — it's a blend of everything light passes through on its way in and out. The order filaments are stacked in directly changes the perceived color.

Under the hood: Kromacut models light transmission with:

T = 0.1 ^ (thickness / TD)

TD is the filament's transmission distance — the depth at which 10% of light still passes through. At one TD of thickness, 90% is absorbed; stack more layers and it drops fast. The perceived color at each depth is composited as:

result = filament_color × (1 − T) + background × T

This is evaluated layer by layer from the outside in, so the outer layers dominate and deeper layers contribute less and less.

Scoring uses ΔE in CIE Lab space (the CIE76 formula) rather than comparing raw RGB values. Lab is designed to match human perception, so a ΔE of 1 means a just-noticeable difference regardless of which part of the color spectrum you're in. This matters because two assignments with similar RGB error can look very different to a viewer — Kromacut optimises for what the eye sees.

For frontlit prints, the effective TD is multiplied by 0.1, compressing penetration depth to match how surface lighting works in practice.

4. Reducing Height Cliffs Between Columns (Spatial Variance)

The basic idea: when adjacent pixel columns are printed at very different heights, the side of the taller column is exposed to light at an angle rather than face-on. This bleeds color sideways and degrades the image near edges. The fix is to keep neighbouring columns close in height by grouping similar colors into the same print phase.

Under the hood: colors are sorted by luminance and divided into M = ⌈K/N⌉ bands, one per phase. The starting assignment is simple: band[i] = floor(colour_index / N) after sorting. This is a reasonable first guess but not necessarily optimal, so it's refined by a local search.

The search evaluates swapping pairs of colours between adjacent bands. The quality metric is:

Σ (for all pairs A, B) W(A,B) × (band[A] − band[B])²

where W(A,B) = 1 / (luminance_distance(A,B)² + 0.0001). The weight is high when two colours are close in luminance — those are the ones most likely to appear side-by-side in the image, so pulling them into the same band has the biggest impact on cliff height. Any swap that lowers the total is accepted; the search repeats until no improving swap exists.

Once phases are assigned, the support layers within each bar follow a rotation formula: support_index = phase × N + (column_position + phase) mod N. This spreads support layers across nozzle slots so no two adjacent columns in the same phase pull from the same head — keeping the number of distinct colours at any single layer level at exactly N, matching what the printer has loaded.