Sof oft-Bod ody y Dy Dyna namics cs Deformable Objects A - PowerPoint PPT Presentation

Deformable Physics Sof oft-Bod ody y Dy Dyna namics cs

Deformable Objects A difficult problem Lots of specific solutions but no accepted general best method Applies to: Soft bodies – incl. character animation Destruction Fluid simulation

Demo: Pixelux Digital Molecular Matter Used in LucasArts ’ "Star Wars: The Force Unleashed".

Soft Body Dynamics Visually Realistic physical simulations of motion and properties of deformable objects Shape and topology of objects changes Points within the object move relative to one another However shape has tendency to retain it’s shape to some degree: elastic vs plastic E.g. muscle, fat, hair, plants, clothing and fabric

Soft-body Physics Engines

Havok Cloth

PhysX

Bullet

Deformation in Graphics Two classes of deformation Geometric deformation Physically based deformation

Geometric Deformation

Solid Deformations Alan H. Barr, Global and Local Deformations of Solid Primitives, Computer Graphics (Proceedings of SIGGRAPH 84). 18(3), pp. 21-30, 1984. Hierarchical solid modeling transformation of surfaces Locally specified deformation by local/tangent transformation matrices Can be used for e.g. twisting, bending, tapering, … now mainstream

Free Form Deformations (FFD) Thomas W. Sederberg, Scott R. Parry, Free-Form Deformation of Solid Geometric Models, Computer Graphics (Proceedings of SIGGRAPH 86). 20(4), pp. 151-160, 1986. Global FFD Local FFD

Sabine Coquillart, Extended Free-Form Deformation: FFD A Sculpturing Tool for 3D Geometric Modeling,Computer Graphics (Proceedings of SIGGRAPH 90). 24(4), pp. 187-196, 1990.

William M. Hsu, John F. Hughes, Henry Kaufman, FFD Direct manipulation of free-form deformations, Computer Graphics (Proceedings of SIGGRAPH 92). 26(2), pp. 177-184, 1992. Working with control points can be awkward Apply (displacement) constraints directly to surface

Karan Singh, Eugene L. Fiume, Wires: A Wires Geometric Deformation Technique, Proceedings of SIGGRAPH 98. pp. 405-414, 1998.

Physically Based Deformation

Elastically Deformable Models Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. Elastically Deformable Models, ACM SIGGRAPH 87, 205-214, 1987. Major contribution to physically based deformable models in graphics Lagrangian derivation of eqns of motion       r r r E ( )        f ( r , t )       t t t t r ( a , t ): position of particle a at time Net externally applied forces time Net instantaneous potential energy Damping density Mass density of body at a

De Defor ormable le Ob Object ct Ap Approache oaches

Solutions from Engineering E.g. Finite element simulation Strive for accuracy Generally very slow Sometimes do not converge to a solution Don’t discern if the visual response is appealing – often provide other kinds of info: Visualization is somewhat different from computer graphics

Non-realtime Graphical Solutions E.g. Special effects in movies and commercials Faster solutions, but not fast enough. Animators don’t use techniques if the previews are too expensive. Not as accurate as engineering Focus on Appeal Recent interest in “controllable” simulations

Real-time Solutions Resolution Reduction Blobby and coarse look Details disappear Use specialized real-time techniques Physics low-res, appearance hi-res (shader effects) Reduction of dimension from 3d to 2d or 2.5d (height field fluids, BEM) Level of detail (LOD) No equation solving, procedural animation for specific effects

Interactive Physics requirements Solutions in Engineering and Off-line animation generally don’t fulfill the requirements of real -time physics Reality methods require: Efficiency Most of the time is going to be used in the rendering process (especially in games). Interactive responses Low latency Visual and haptic minimum frequency constrains Stability Must guarantee stability If the model blows up we lose immersion Realism Interactivity vs. accuracy Plausibility vs. accuracy

Taxonomy of Deformable Simulation We can categorise techniques based on: Phenomena they are meant to simulate Formulation of the solution Space Discretization method used Time Discretization methods used

Phenomena Being Simulated Elastic objects Plastic objects Fluids Liquids Smoke, clouds fire Cloth Hair

Formulation of solution Eulerian reference system attached to the space Lagrangian reference system attached to the object Semi-Lagrangian

Space Discretization Mesh based techniques A mesh joins the object nodes Large deformations are hard to simulate (fluids) Object boundary is explicitly calculated Mesh elements: segments, triangles, tetrahedrons, hexahedrons… Example: Mass-spring systems Meshless techniques No explicit mesh connecting particles Difficult to compute the object’s boundary (hard to draw) Suitable for large deformation: like fluids Example: SPH

Time Discretization Explicit     i 1 i i x x v t Current state depends only on past states      i 1 i 1 i v v m f t Faster Not unconditionally stable Implicit      i 1 i i 1 x x v t current state depends on past states       i 1 i 1 i 1 v v m f t and on the current state Requires solving a system of equations Generally slower Adds artificial damping (depending on the object properties) Unconditionally stable

Mass-spring Systems

Mass-spring Model Body modelled as point masses: masses connected by (weightless) springs Hooke’s Law fof Damped Spring Restoring force     f k ( x r ) spring spring Damping force (for now, lets just use viscous drag - effectively damps oscillation and other motions)   f k v drag drag

Basic deformable objects From erleben et al ch 8 Start with newtonian particle system        f m x x f / m For a particle system we know the accelerations acting on a particle at any time Assume Explicit Eurler Integration and that time is discretised as t i+1 = h + t i Second order Taylor approximation of position of particle at time t i+1 :        x x x    i 1 i i               x x f ( t i ) / m  i 1 i

Leads to instability if step-size is too high particle will diverge Not unconditionally stable

Verlet Integration Originated in molecular dynamics (central difference approximation: find x based on previous frame and next frame)      2 a x ( t h ) 2 x ( t ) x ( t h ) h ( t ) A velocity-free formulation (velocity implicitly represented by current and previous positions) in code (store current x and previous x): x = 2*x – x_prev + a *h^2; x_prev = x; not always accurate but fast and stable See; Jakobsen GDC 2001 talk: Advanced Character Physics http://www.floatingorigin.com/mirror/jacobson_01.shtml

Cloth Provot . X, “Deformation constraints in a mass-spring model to describe rigid cloth behaviour” Graphics Interface 2001, pp147-154 Springs chosen in a certain structure to model deformable dynamic properties verlet integration An adaptive technique; Dynamic inverse procedure applied to cap deformations for excessive deformation rates More detail on Verlet: http://wapedia.mobi/en/Verlet_integration

Mass-spring system for cloth Structural Springs between adjacent particles – resist stretching and compression. Usually relatively high k Shearing Springs connecting diagonal adjacent particles in a regular grid – relatively low k Bending Springs a.k.a flexion springs, prevent sharp ridges when folded: links every second or third particles. Usually very low k for cloth

Unstructured Meshes Regular grid is not always applicable For an unstructured mesh: Structural springs correspond to 1-neighbourhood Shearing and bending to a 2-neighbourhood 1 - neighbourhood 2 - neighbourhood

Implicit Integration David Baraff, Andrew Witkin The difference in the two methods is that the Large Steps in Cloth Simulation method’s step is based solely on forward Siggraph 1998 conditions at time t0 while the backward method’s step is written in terms of conditions at http://ai.stanford.edu/~latombe/cs99k/ the terminus of the step 2000/cloth.pdf itself.4

Integration Scheme Comparisons http://femto.cs.uiuc.edu/~sbond/code/SpringMass/

Deformable Solids Discretise object into 3d rectilinear grid (voxels) In addition to shearing diagonals we need spatial diagonals that counter volume loss Unstructured solid meshes can be voxelised Mesh points in between grid nodes are updated by trilinear interpolation Muller, M., Teschner, M., and Gross, M. Physically- Mesh Based Simulation of Objects Represented by coupling Surface Meshes. In Proceedings of the Computer Graphics international 2004.

Tetrahedral decomposition Split mesh up into tetrahedra Note that interior details are important (not just surface) Delauney tetrahedralization Springs between vertices and 2+ neighbourhoods depending on rigidity http://tetgen.berlios.de/