A Unified Framework for Signed Distance Field Deformations via Inverse Mapping

초록

This paper presents a unified framework for real-time deformation of three-dimensional Signed Distance Fields (SDFs). To address the lack of local control in conventional SDF deformation methods, we propose an effective local editing technique coupled with an inverse transformation pipeline. Each query point in the deformed field is traced back to its pre-image in the original field via an operator-specific inverse transform, and a per-point compositing rule confines the deformation to the selected Region of Interest (ROI). The deformed distance field is efficiently reconstructed using the Fast Sweeping Method (FSM) to restore the Eikonal condition, and a smooth weighting function, applied iteratively, compensates for volume changes induced by the deformation. By integrating the pipeline into a GPU-accelerated ray-marching renderer, our framework provides immediate visual feedback during editing. Experimental results demonstrate that our framework enables effective local editing while preserving both distance-field validity and volumetric fidelity.

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