Cloth The Animation of Natural Phenomena Adrien Treuille
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1 Cloth The Animation of Natural Phenomena Adrien Treuille
2 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
3 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
![weft House, Breen [2000]](/docs-images/78/77041212/images/4-5.jpg "Cloth Animation")
4 What is cloth? 2 basic types: woven and knit We ll restrict to woven Warp vs. weft House, Breen [2000] Cloth Animation Christopher Twigg March 4, 2003
5 Warp and Weft source: Wikipedia
6 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
7 SIGGRAPH 2001 COURSE NOTES SE1 PHYSICALLY BASED MODELING
8 Stretch (Continuum Version)! x (u, v)!!x Su = "1!u SIGGRAPH 2001 COURSE NOTES E= SE11 1k 2 # 2 (Su 2 + Sv )du dv PHYSICALLY BASED MODELING
9 Shear (Continuum Version)! x (u, v)!! " " # $ "1 %x %x! = cos & i ' ( %u % v ) SIGGRAPH 2001 COURSE NOTES E = 12 k *! 2 du dv SE12 PHYSICALLY BASED MODELING
10 Bend (Continuum Version)! x (u, v) E = 12 k " (! u2 +! v2 )du dv SIGGRAPH 2001 COURSE NOTES SE13 PHYSICALLY BASED MODELING
11 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
12 Resitence To... Stretching Shearing Bending
13 Basic Model
14 Warp Srings
15 Weft Springs
16 Shear Springs
17 Bend Springs
18 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
19 Discretization SIGGRAPH 2001 COURSE NOTES SE14 PHYSICALLY BASED MODELING
20 Triangle Energy a c! a! v c u b! b First, compute the affine transformation T that maps: T : a " c! b " b! c " c! SIGGRAPH 2001 COURSE NOTES SE15 PHYSICALLY BASED MODELING
21 Triangle Stretch Energy a! a v u c b c! b! Su = T (uˆ ) " 1 Now compute the stretch energy. SIGGRAPH 2001 COURSE NOTES Estretch = 12 k (Su2 + Sv2 ) A SE16 PHYSICALLY BASED MODELING
22 Triangle Shear Energy a c! a! v c u b! b #1 " = cos (T (uˆ )it (vˆ )) Next compute the shear energy. SIGGRAPH 2001 COURSE NOTES Eshear = 12 k" 2 A SE17 PHYSICALLY BASED MODELING
23 Triangle Bend Energy a " v c b u d!= Finally compute the bend energy. SIGGRAPH 2001 COURSE NOTES SE18 " l perp Ebend = 2k (! 2 ) A PHYSICALLY BASED MODELING
24 A Note About Energy
25 Baraff, Witkin [1998] (5) Damping forces turn out to be important both for realism and numerical stability Damping forces should Act in direction of corresponding elastic force Be proportional to the velocity in that direction Hence, we derive (this should look familiar) where C(x) d = kdc (x) x Direction of force C(x) C(x) x C (x) = = t x t Cloth Animation Christopher Twigg March 4, 2003
26 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
27 Parameters Given stretch, shear, and bending constants... would you make a wrinkly t-shirt, How thick cloth, or non-uniform cloth?
28 Creating Clothes How could we create the 3D model the clothes for a character?
29 Non-flat Cloth Non-flat cloth is strange stuff: A baseball with no seams? Wrinkles give strength? Clothing cut out of a volume? Convexities that pop? Even 4 Triangles are over-constrained: 16 rest angles, 8 rest lengths. 24 constraints on 15 dofs dofs.. Must be consistent! SIGGRAPH 2001 COURSE NOTES SE10 PHYSICALLY BASED MODELING
30 Rest Mesh Options Model in 3D Clothing already on characters. Can directly craft desired 3D shape. Annotate warp/weft directions. Clothing probably will not locally flatten. Model in 2D Must put clothing on characters Hire a tailor to get the pattern right. Sew parts together. Clothing guaranteed to flatten locally. Greater realism. SIGGRAPH 2001 COURSE NOTES SE9 PHYSICALLY BASED MODELING
31 Real Cloth Overview Properties of Real Cloth Cloth Simulation Properties of Cloth sheet of fabric (4) parameter for stretching (1) (4) parameter for shearing (4) parameter for bending (4) how to set these properties wrinkles and crinkles (4) thickness (4) non-uniform (4) Spring-based Simulation mesh of springs (1) (2) Energy-based various forms of triangle energy Developable Surfaces Cloth Collisions interactions w/ itself (1) (2) (3) (4) interactions w/ rigid bodies (1) (3) friction (4) Advanced fluid flow affecting cloth (3) rendering / texturing of cloth (3) tearing (3) Group 1 Group 2 Group 3 Group 4 New!
32 Springs vs. Constraints Before Simulation Only Springs Stretch Constraints Stretch+Shear Constraints Source: Xavier Provot Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior
33 Avoiding stiffness (2) Popular for interactive applications Justification Biphasic spring model Displacement Iteration 1 Iteration 2 Iteration 3 (converged) Linear elastic region Force From Desbrun, Meyer, Barr [2000] Plausible dynamics Cloth Animation Christopher Twigg March 4, 2003
34 Developable Surfaces
35 Developable Surfaces is clo im ced (e. Ts Figure 2: Schematic of nonconforming variables, located at midpoints of edges between triangles. While continuous at these points, the surface may be discontinuous along the rest of each edge. and rendering. We therefore couple a ghost conforming mesh (with the usual vertex variables) to the simulation, used just for colanimating Developable Surfaces using Nonconforming Elements lisions and rendering. Elliot English University of British Columbia Robert Bridson University of British Columbia Mo app for by con acc can me am
36 Developable Surfaces
37 Question Cloth and Hair.. How can we detect collisions? Data structures? Algorithms? How do we handle collisions?
38 Course Evaluations
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