Dynamics and Forces External Force Gravity.pdfVIP

CPSC533D Animation Physics Final Project Cloth Simulation Xianglong (Steven) Chang Department of Computer Science University of British Columbia December 2005 Modeling Cloth model: - Mass-Spring model Collision geometry - Unit sphere sitting on the ground Collision type - Inelastic collision as in assignment 1 Time integration - Explicit Symplectic Euler Cloth Mesh A circle represented by triangle meshes with 362 vertices and 656 triangles. Mass of a vertex is 1/3 of the mass of triangles incident on the vertex. Mass around the spring is 1/3 of the mass of triangles incident on the edge Dynamics and Forces External Force Gravity: Fgravity m ⋅g Spring Forces Elastic spring force: ⎛x −x ⎞ x −x F −K ⎜ i j −1 ⎟ i j spring ⎜ L ⎟x −x ⎝ ⎠ i j Spring damping force: (v v ) U ⎛ − ⋅ ⎞ x −x ⎜ i j ⎟ i j F −D U U damp ⎜ ⎟ L x −x ⎝ ⎠ i j Dynamics and Forces (con’t.) Bending Forces (Bridson et al. “Simulation of …”) Elastic bending force: 2 E e e ( ( ) ( )) F k sin θ/ 2 −sin θ / 2 u i