Fast Physics-Based Modeling of Knots and Ties using Templates

Knots and ties are captivating elements of digital garments and accessories, but they have been notoriously challenging and computationally expensive to model manually. In this paper, we propose a physics-based modeling system for knots and ties using templates. The primary challenge lies in transforming cloth pieces into desired knot and tie configurations in a controllable, penetration-free manner, particularly when interacting with surrounding meshes. To address this, we introduce a pipe-like parametric knot template representation, defined by a Bézier curve as its medial axis and an adaptively adjustable radius for enhanced flexibility and variation. This representation enables customizable knot sizes, shapes, and styles while ensuring intersection-free results through robust collision detection techniques. Using the defined knot template, we present a mapping and penetration-free initialization method to transform selected cloth regions from UV space into the initial 3D knot shape. We further enable quasistatic simulation of knots and their surrounding meshes through a fast and reliable collision handling and simulation scheme. Our experiments demonstrate the system’s effectiveness and efficiency in modeling a wide range of digital knots and ties with diverse styles and shapes, including configurations that were previously impractical to create manually.