Predicting Deformation Fields on 3D Stroke Clouds : Supplementary Material

Abstract

Deformation analysis is typically performed only after geometric modeling in design workflows, depriving designers of this physical insight during the early sketching phase, when the design has the highest optimization potential. To bridge this gap, we propose a physics-informed neural model that takes as input a 3D sketch stroke cloud and user-specified boundary conditions, and directly predicts the induced 3D deformation field on the stroke cloud without requiring reconstruction-and-simulation. To represent unstructured 3D sketches and user-annotated boundary conditions in a form suitable for learning, we use fVDB to encode stroke clouds into sparse voxel grids and leverage its differentiable splatting and sampling operators for bidirectional point–voxel mappings. Trained on our synthetic dataset of architectural thin-shell sketch–deformation pairs, our dual-head model predicts per-point displacement magnitudes and unit-length vectors, and is optimized using physics-informed loss terms inspired by stretching and bending as the two modes of deformation.