Collision Free Simplification for 2D Multi-Layered Shapes

Abstract

We propose a simplification-aware untangling algorithm for 2D layered shapes stacked on each other. While the shape undergoes simplification, our approach adjusts the vertex positions to prevent collision with other layers while simultaneously maintaining the correct relative ordering and offsets between the layers. The method features a field-based representation of the shapes and extends the concept of "implicit untangling" by incorporating interleaved shape preservation through a parameterized shape-matching technique. Our approach can be plugged on top of any existing vertex-decimation approach, leveraging its localized nature to accelerate the field evaluation. Furthermore, our method can seamlessly handle an arbitrary number of stacked layers, making it a versatile solution for stacked garment simplification.