Real-time hair simulation with heptadiagonal decomposition on mass spring system

Simulating detailed dynamic hairs in real time is a challenging problem. Existing methods either simplify the strand dynamics or reduce the degrees of freedom at the cost of rich motion details. We present a real-time simulation for animating hair with high fidelity details. Our approach efficiently captures the inextensibility, bending and torsion strand mechanics, while presenting the stiction/repulsion and detailed real-time collision effects. To efficiently capture self-interactions, we factorize the phenomenon into a coarse, globally coupled volumetric, and detailed collision view. The coarse behaviors are solved with an Eulerian method via position-based density control, while detailed collisions are efficiently handled with temporal coherent link updates. We further provide a fast implicit integration via heptadiagonal matrix decomposition, which provides two to three orders of magnitude of acceleration to traditional methods. The efficiency and effectiveness of our method is validated by simulating variant motions of hair in various styles.