Contact detection between curved fibres: high order makes a difference

Computer Graphics has a long history in the design of effective algorithms for handling contact and friction between solid objects. For the sake of simplicity and versatility, most methods rely on low-order primitives such as line segments or triangles, both for the detection and the response stages. In this paper we carefully analyse, in the case of fibre systems, the impact of such choices on the retrieved contact forces. We highlight the presence of artifacts in the force response that are tightly related to the low-order geometry used for contact detection. Our analysis draws upon thorough comparisons between the high-order super-helix model and the low-order discrete elastic rod model. These reveal that when coupled to a low-order, segment-based detection scheme, both models yield spurious jumps in the contact force profile. Moreover, these artifacts are shown to be all the more visible as the geometry of fibres at contact is curved. In order to remove such artifacts we develop an accurate high-order detection scheme between two smooth curves, which relies on an efficient adaptive pruning strategy. We use this algorithm to detect contact between super-helices at high precision, allowing us to recover, in the range of wavy to highly curly fibres, much smoother force profiles during sliding motion than with a classical segment-based strategy. Furthermore, we show that our approach offers better scaling properties in terms of efficiency vs. precision compared to segment-based approaches, making it attractive for applications where accurate and reliable forces are desired. Finally, we demonstrate the robustness and accuracy of our fully high-order approach on a challenging hair combing scenario.