Predicting Stacked-Filament Color from Independently Measured Filament Properties

Abstract

Consumer multi-material fused deposition modeling (FDM) printers reproduce color images by stacking translucent filament layers; stack color must be predicted before printing. Existing workflows predict with a scalar transmission distance (TD) plus manual tuning, or with dense lookup tables (LUTs) per palette. We ask whether per-filament measurements alone predict arbitrary stack combinations. We present a forward model that composes nominal RGB, per-channel TD, an effective attenuation coefficient per filament, a shared monochromatic scattering prefactor, and stack geometry into stack color through a loss-allocation stacking rule; when only a scalar TD is available, the remaining coefficients are estimated on one printed plate, a LUT-free calibration of the same analytic model. Staircase-measured per-channel TDs predict 256-cell clear-filament permutation plates with no parameters fitted on the plates: 18.6 versus 47.2 CIEDE2000 color difference (ΔE00) at best, 42-60% reduction on all six plate/backing combinations. Eight scalars fitted on a plate of five arbitrary non-CMYWK filaments, RGB and per-channel TDs measured off-plate, explain 780 cells at 6.9 ΔE00 (white 5.3, black 8.5); a RAW replication reaches 5.5. A staircase, dual-backing plate, and phone camera supply these properties; a single-point optical filament sensor implies a 75x absorption scale across CMYW filaments and saturates on transparent ones, so it cannot deliver them. On ColorChecker targets across three prints, the model reaches 16.69 versus 30.92 ΔE00 for the community TD-table formula; coefficients are process-conditioned effective values in the sRGB-encoded domain, within which one shared model predicts arbitrary stacks from one measurement per filament.