PointBasedAnimationofElastic,PlasticandMeltingObjects.pptVIP

Point Based Animation of Elastic, Plastic and Melting Objects Outline Related Work Advantages Disadvantages Elasticity Model Simulation Loop Time Integration Surface Animation (省略) Result Related Work Desbrun Cani [95,96,99] Physics: Smoothed Particle Hydrodynamics (SPH) Surface: Implicit with suppressed distance blending Tonnesen [98] Physics: Lennard-Jones based forces Surface: Particles with orientation Advantages Disadvantages Advantages No volumetric mesh needed Natural adaptation to topological changes Disadvantages Difficulty of getting sharp fracture lines Neighboring Phyxels are not explicitly given Throughout this work we use Spatial Hashing [Teschner et al. 03] for fast neighbor search (when needed) Elasticity Model Continuum Elasticity Elastic Strain Estimation of Derivatives Discrete Energy Density Elastic Forces Continuum Elasticity Elastic Strain → Strain depends on the spatial derivatives of u(x) Estimation of Derivatives - 1 Estimation of Derivatives - 2 Discrete Energy Density -1 Strain from ?u Discrete Energy Density -2 Use Smoothed Particle Hydrodynamics (SPH) Method Mass of each Phyxel mi is fix during the simulation Distribute the mass around the Phyxel using a polynomial weighting kernel wij with compact support The density around Phyxel i is From which we compute the volume vi as Elastic Forces Estimate volume vi represented by phyxel i via SPH Simulation Loop Time Integration Verlet (Explicit) Time Stepping Newtons Second Law of Motion Result 彈性物體1、彈性物體2 * * Mark Pauly Andrew NealenMarc Alexa ETH Zürich TU Darmstadt Stanford Matthias MüllerRichard KeiserMarkus Gross 9555549 李盈璁 Reference configuration Deformed configuration = Elastic Memory Displacement (vector) field: u(x) = [ u(x,y,z) v(x,y,z) w(x,y,z) ]T u(x) x x+u(x) x’ u(x’) x’+u(x’) no strain strain u(x) Next: Compute spatial derivatives of the x component u Computation of the unknown u,x, u,y and u,z at xi by Linear approximation Minimize → WLS/MLS approximat