Forward device models for multi-ink printing systems (i.e., ones that contain more than three colorants) relate ink amounts to predictions of either colorimetry or spectral reflectance. These models often have a large portion of their range (CIELAB values) that lack unique domain values (device ink amounts). This makes unique inversion of the forward model ill posed in these regions of color space. An approach is presented where direct computational techniques are applied to a tessellated version of a device's forward model to produce an inverse. This is accomplished using an isosurfacing technique that sequentially intersects m noncoincident planes in the m-dimensional range color space through the image of the model's device-code value n-dimensional domain tessellation. This computational approach results in (n-m)-dimensional piecewise-linear ink manifolds that define the mapping of the n-dimensional domain space (ink amounts) to a location in the m-dimensional range space (CIELAB). This process is generalizable to devices with any number of input inks, n ≥ m, provided the range space color is within the color gamut of the device.