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The Basics   Constraint  something that keeps an entity in the system from moving freely For our purposes, we will treat each discreet entity as one particle in a system Particles can be doors on hinges, bones in a skeleton, points on a piece of cloth, etc.   #Box Constraints $Box Constraints (cont)Confine P to extents of the box Recover from violations in position (last valid, rebound, wrap around) Simple, yet the basis for the rest of this*Spring ConstraintsuSeems like a reasonable choice for soft body dynamics (cloth) In practice, not very useful Unstable, quickly explodes+Stiff ConstraintsA special spring case does work Ball and Stick/Tinkertoy Particles stay a fixed distance apart Basically an infinitely stiff spring Simple Not as prone to explode/ k,Cloth SimulationNUse stiff springs Solving constraints by relaxation Solve with a linear system-Cloth SimulationZ .Cloth SimulationForces on our cloth/Cloth SimulationRelaxation is simple Infinitely rigid springs are stable Predetermine Ci distance between particles Apply forces (once per timestep) Calculate D for two particles If D != 0, move each particle half the distance If n = 2, you re done!9 " 9 G),F3g