A color space conversion technique uses a set of control lines in a first color space. Each control line includes several control points having predetermined values in a second color space. A planar region is identified among the set of control lines in the first color space. The planar region contains a number of target points that are to be interpolated from the first color space to the second color space. The planar region is partitioned into at least a first area and a quadrangular area. Target points in the quadrangular area correspond to a different set of colorants from the second color space than target points in the first area. A quadrangular interpolation is applied to the target points in the quadrangular area to determine corresponding values in the second color space based at least in part on the predetermined values of control points bounding the quadrangular area.