🤖 AI Summary
To address reduced readability caused by symbol occlusion in information visualization of mixed numerical-categorical data, this paper proposes a differentiable geometric optimization method for symbol displacement. Within a rectangular canvas, unit-square symbols—each assigned a fixed y-coordinate—are displaced solely along the x-axis to maximize their minimum visible perimeter. We innovatively model symbol visibility as a differentiable geometric constraint, introduce topology-preserving adaptive displacement regularization, and formulate a gradient-based optimization framework that jointly incorporates spatial conflict detection and visibility awareness. Experiments on multi-scale map datasets demonstrate that our method increases average symbol visibility by 37.2%, reduces overlap rate by 61.5%, and satisfies real-time rendering requirements for interactive visualization.
