🤖 AI Summary
This work addresses two types of chromatic artifacts—hue looping and neutral-axis deviation—that arise during OKLCH interpolation in low-saturation regions, noting that existing approaches only mitigate the latter. To resolve both issues simultaneously, the authors propose a continuously differentiable chroma-gated interpolation mechanism that smoothly blends between OKLCH and linear Oklab paths. Built upon the Oklab color space, the method employs a single-parameter gating function of Michaelis–Menten form, $w(C) = C^n / (C^n + \sigma^n)$, enabling differentiable fusion without requiring thresholds or endpoint detection. Experimental results demonstrate that, under default parameters, the approach reduces the average lateral deviation of hue trajectories by 49.5% and decreases chroma-weighted hue shift by 35.5%, offering a generic and backward-compatible solution for modern CSS color interpolation.
📝 Abstract
OKLCH -- the cylindrical (lightness, chroma, hue) form of Ottosson's Oklab color space -- is the interpolation space recommended by CSS Color 4 for gradients and color-mix(), and it is now broadly deployed. Its polar parameterization, however, casts color near the neutral axis in two ways: (1) an inter-hue detour between two chromatic endpoints that sweeps through an unintended hue (blue to yellow visibly passing through green), and (2) an off-line bow when one endpoint is achromatic. Existing remedies are uniformly two-valued -- a threshold switch that fires only at an achromatic endpoint -- so they address only (2); on chromatic pairs every one of them reduces to raw OKLCH, leaving the (1) inter-hue cast untreated. We introduce Continuous Oklab fallback (COFb), a one-parameter, differentiable chroma gate $w(C)=C^n/(C^n+σ^n)$ that continuously blends the OKLCH path toward the linear Oklab path as chroma falls. A single gate reduces the (1) cast that the two-valued family leaves untreated and unifies the handling of (1) and (2) without any endpoint test. We characterize a cast-hue trade-off frontier, adopt a default ($n=1$, the rational Michaelis-Menten form; $σ\approx0.19$ for a typical sRGB palette, from a normalization-independent cast-half criterion), and verify the gate's properties symbolically. At the default, COFb halves the inter-hue path detour (mean lateral deviation -49.5%, chroma-weighted hue excursion -35.5%). We also state the method's limits: on (2) alone the two-valued switch remains better, and like any Cartesian blend COFb does not preserve chroma. In deployment, COFb runs entirely in plain Oklab (a,b) to sRGB, so it serves as a fallback that delivers the same cast-reduced gradients where modern CSS color interpolation (color-mix(in oklch) and the like) is unavailable -- older engines, image and video pipelines, or GPU shaders.