Interference detection and correction of 3D geometric structure of woven fabrics constructed by B-spline surface

Scientists and engineers require software to construct 3D geometric structures for fabrics accurately and rapidly. B-spline modelling technology has received special attention by the application developers for its flexibility in modelling the yarns of various cross-sections and central path. However, in the previous work, the interference among the yarns in various fabric structures might happen at the contact place between two yarns due to the complexity of the cross-sections in spite of accurate calculation of the interlacing points of a woven fabric. The paper proposes an algorithm based on AABB to detect the interferences among the yarns that are constructed by the shape-preserving quasi-uniform cubic B-spline surface, record all the possible interfered cross-sections, and modify the control points of the cross-sections where the interference takes place. Then, the yarns are reconstructed by the modified control mesh. The algorithm is tested and verified by imitating the geometric structure of fabric of 2/2 twill, 1/1 plain, and mock leno weave that are made of yarns of cross-sections of ellipse and racetrack, respectively. The corrected 3D geometrical structure of the fabrics that is saved in the file format of IGES can also be input to the 3D modeling software such as CATIA, indicating that the algorithm is beneficial for optimize a reasonable geometrical model based on an input woven fabric in seconds. The method also has the potential uses in optimizing the 3D geometric structure of knitted or braided fabrics that are comprised of yarns.