an implicit frictional contact solver for adaptive cloth
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An Implicit Frictional Contact Solver for Adaptive Cloth Simulation Jie Li1, Gilles Daviet2, Rahul Narain1, Florence Bertails-Descoubes2, Matthew Overby1, George Brown1, Laurence Boissieux2 1 2 1 2 PREVIOUS WORK Traditional

  1. An Implicit Frictional Contact Solver for Adaptive Cloth Simulation Jie Li1, Gilles Daviet2, Rahul Narain1, Florence Bertails-Descoubes2, Matthew Overby1, George Brown1, Laurence Boissieux2 1 2 � 1

  2. � 2

  3. PREVIOUS WORK •Traditional methods •Implicit solver � 3 •[Erleben et al. 2007] •[Otaduy et al. 2009] •[Bridson et al. 2002] •[Provot 1997] •[Harmon et al. 2008] •[Daviet et al. 2011] •[Kaufman et al. 2008]

  4. � 4

  5. CLOTH DYNAMICS (WITHOUT CONTACTS) � 5

  6. SIGNORINI-COULOMB FRICTIONAL CONTACTS � 6

  7. LOCAL RELATIVE VELOCITY � 7

  8. LINEARIZED DYNAMICS WITH COULOMB FRICTION � 8

  9. DUAL APPROACH � 9

  10. TOWARDS A PRIMAL APPROACH � 10

  11. RESTRICTED SETTING � 11

  12. NODAL CONTACTS � 12

  13. SYSTEM WITH ORTHOGONAL EXTENSION � 13

  14. SOLVING THE PRIMAL SYSTEM � 14

  15. ORTHOGONAL EXTENSION FOR SELF CONTACTS � 15

  16. LAYERED CONTACTS � 16

  17. PIN CONSTRAINT � 17

  18. THE ISSUE WITH NODAL SOLVER In cloth mesh Strategy: Nodal solver Edge-Edge Edge-Edge Vertex-Face Vertex-Face Move the contact to the closest vertex. � 18

  19. MOVING CONTACTS INTRODUCES PROBLEMS Adaptive refinement Solution [Narain et al. 2012] � 19

  20. COHicdVDLSsNAFJ3UV62vqEs3g0VoF5ZECrpwUXDjzgr2AW0Ik+mkHZ1MwsykUNJ+lhs/w524caGIW7/ASZuFtvXAwOGce5h7jxcxKpVlvRi5ldW19Y38ZmFre2d3z9w/aMowFpg0cMhC0faQJIxy0lBUMdKOBEGBx0jLe7hK/daQCElDfqdGEXEC1OfUpxgpLbnmzbg7RCIaUJeWugFSA89P4olLy/AULnXuy2N4Cf9LjV2zaFWsKeAisTNSB nqrvnc7YU4DghXmCEpO7YVKSdBQlHMyKTQjSWJEH5AfdLRlKOASCeZHj6BJ1rpQT8U+nEFp+rvRI CKUeBpyfTLeW8l4rLvE6s/AsnoTyKFeF49pEfM6hCmLYIe1Q rNhIE4QF1btCPEACYaW7LugS7PmTF0nzrGJbFfu2WqxVszry4AgcgxKw TmogWtQBw2AwSN4Be/gw3gy3oxP42s2mjOyzCH4A+P7B9iHrZM=</latexit><latexit sha1_base64="Pj9cE6f PTDnsi6hLSLIxIvW0Zw=">A <latexit sha1_base64="Pj9cE6f PTDnsi6hLSLIxIvW0Zw=">A COHicdVDLSsNAFJ3UV62vqEs3g0VoF5ZECrpwUXDjzgr2AW0Ik+mkHZ1MwsykUNJ+lhs/w524caGIW7/ASZuFtvXAwOGce5h7jxcxKpVlvRi5ldW19Y38ZmFre2d3z9w/aMowFpg0cMhC0faQJIxy0lBUMdKOBEGBx0jLe7hK/daQCElDfqdGEXEC1OfUpxgpLbnmzbg7RCIaUJeWugFSA89P4olLy/AULnXuy2N4Cf9LjV2zaFWsKeAisTNSB nqrvnc7YU4DghXmCEpO7YVKSdBQlHMyKTQjSWJEH5AfdLRlKOASCeZHj6BJ1rpQT8U+nEFp+rvRI CKUeBpyfTLeW8l4rLvE6s/AsnoTyKFeF49pEfM6hCmLYIe1Q rNhIE4QF1btCPEACYaW7LugS7PmTF0nzrGJbFfu2WqxVszry4AgcgxKw TmogWtQBw2AwSN4Be/gw3gy3oxP42s2mjOyzCH4A+P7B9iHrZM=</latexit><latexit sha1_base64="Pj9cE6f PTDnsi6hLSLIxIvW0Zw=">A COHicdVDLSsNAFJ3UV62vqEs3g0VoF5ZECrpwUXDjzgr2AW0Ik+mkHZ1MwsykUNJ+lhs/w524caGIW7/ASZuFtvXAwOGce5h7jxcxKpVlvRi5ldW19Y38ZmFre2d3z9w/aMowFpg0cMhC0faQJIxy0lBUMdKOBEGBx0jLe7hK/daQCElDfqdGEXEC1OfUpxgpLbnmzbg7RCIaUJeWugFSA89P4olLy/AULnXuy2N4Cf9LjV2zaFWsKeAisTNSB nqrvnc7YU4DghXmCEpO7YVKSdBQlHMyKTQjSWJEH5AfdLRlKOASCeZHj6BJ1rpQT8U+nEFp+rvRI CKUeBpyfTLeW8l4rLvE6s/AsnoTyKFeF49pEfM6hCmLYIe1Q rNhIE4QF1btCPEACYaW7LugS7PmTF0nzrGJbFfu2WqxVszry4AgcgxKw TmogWtQBw2AwSN4Be/gw3gy3oxP42s2mjOyzCH4A+P7B9iHrZM=</latexit><latexit sha1_base64="Pj9cE6f PTDnsi6hLSLIxIvW0Zw=">A COHicdVDLSsNAFJ3UV62vqEs3g0VoF5ZECrpwUXDjzgr2AW0Ik+mkHZ1MwsykUNJ+lhs/w524caGIW7/ASZuFtvXAwOGce5h7jxcxKpVlvRi5ldW19Y38ZmFre2d3z9w/aMowFpg0cMhC0faQJIxy0lBUMdKOBEGBx0jLe7hK/daQCElDfqdGEXEC1OfUpxgpLbnmzbg7RCIaUJeWugFSA89P4olLy/AULnXuy2N4Cf9LjV2zaFWsKeAisTNSB nqrvnc7YU4DghXmCEpO7YVKSdBQlHMyKTQjSWJEH5AfdLRlKOASCeZHj6BJ1rpQT8U+nEFp+rvRI CKUeBpyfTLeW8l4rLvE6s/AsnoTyKFeF49pEfM6hCmLYIe1Q rNhIE4QF1btCPEACYaW7LugS7PmTF0nzrGJbFfu2WqxVszry4AgcgxKw TmogWtQBw2AwSN4Be/gw3gy3oxP42s2mjOyzCH4A+P7B9iHrZM=</latexit> ADAPTIVE REMESHING Obstacle metric (for each vertex close to obstacle) Distance to the The projection of the edge obstacle length in contact normal direction Remeshing metrics [Narain et al. 2012] •velocity | ϕ i ( u i ) − ϕ i ( u j ) | < | ϕ i ( u i ) | •curvature •distance to obstacle •etc. � 20

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