第5-2章 Physically Based Simulation_Cloth Simulation.pptVIP

(7) Fracture Tearing We can also allow springs to break One way is to define a length (or percentage of rest length) that will cause the spring to break This can also be combined with the plastic deformation, so that fracture occurs at the plastic limit Another option is to base the breaking on the force of the spring (this will include damping effects) It’s real easy to break individual springs, but it may require some real bookkeeping to update the cloth mesh connectivity properly… (8) Ropes Solids We can use this exact same scheme to simulate ropes, solids, and similar objects ? ? ? ? ? ? ? ? ? ? ? ? ? As real springs apply equal and opposite forces to two points, they obey conservation of momentum Our simple spring-damper implementation should actually guarantee conservation of momentum, due to the way we explicitly apply the equal and opposite forces (This assumes that everything says within reasonable floating point ranges and we don’t suffer from excessive round-off) 2.3.1 Conservation of Momentum 2.3 System Stability True linear springs also conserve energy, as the kinetic energy of motion can be stored in the deformation energy of the spring and later restored The dampers, however are specifically intended to remove kinetic energy from the system Our simple implementation using Euler integration is not guaranteed to conserve energy, as we never explicitly deal with it as a quantity 2.3.2 Conservation of Energy If we formulate the equations correctly and take small enough time steps, the system will hopefully conserve energy approximately In practice, we might see a gradual increase or decrease in system energy over time A gradual decrease of energy implies that the system damps out and might eventually come to rest. A gradual increase, however, it not so nice… 2.3.2 Conservation of Energy There are particle schemes that conserve energy, and other schemes that preserve momentum (and/or angular momentum) It’s possible to conserve all three, but it becomes s