Abstract
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with strong patterned planar anchoring. Building on prior models, we solve both the forward problem-predicting disclination trajectories from given surface patterns-and an extended inverse problem-designing surface patterns to produce a tunable family of disclination curves under varying system parameters. We present an explicit calculation for pattern construction, analyze parameter limitations and stability constraints, and highlight experimental and technological applications.