Unified Solver

A GPU-based unified particle solver for Unity, inspired by Macklin et al. 2014 (Unified Particle Physics for Real-Time Applications) and Macklin et al. 2019 (Small Steps in Physics Simulation).

All particle types — soft bodies, cloth, ropes, rigid bodies, fluids — share a single solver pipeline: predict, solve constraints, update velocities. The entire simulation runs on the GPU via compute shaders using XPBD with the Small Steps approach (n substeps, 1 iteration each).

Features

• XPBD Distance Constraints — structural, shear, and bend constraints with configurable compliance, damping, and breakable force thresholds
• Particle-Particle Collision — spatial hash based broadphase, Coulomb friction model (static + kinetic), max depenetration speed clamping
• Phase System — per-body collision filtering (Flex paper section 3/5). Particles sharing the same phase skip mutual collision
• World Colliders — sphere, capsule, and oriented box colliders with friction
• Cloth Simulation — procedural grid generator with structural + shear constraints, GPU-driven mesh rendering (vertex shader reads from particle buffer, no readback)
• Cube Generator — 3D particle grids with full constraint wiring (structural, shear, volume diagonals)
• GPU Instanced Rendering — particles rendered as instanced spheres directly from the compute buffer
• Successive Over-Relaxation — SOR factor for faster constraint convergence (Flex paper Eq. 13)
• Parallel Jacobi Solver — fixed-point atomic accumulation for lock-free parallel constraint solving

Demos

Architecture

SolverManager (singleton, orchestrator)
  |-- Compute Shader: UnifiedSolver.compute
  |     Kernels: Predict, ClearDeltas, SolveDistance, SolveContact,
  |              ApplyDeltas, SolveGround, SolveSphere, SolveCapsule,
  |              SolveBox, UpdateVelocity, ClearHash, BuildHash
  |
  |-- Generators: CubeGenerator, ClothGenerator
  |-- Colliders: SolverSphereCollider, SolverCapsuleCollider, SolverBoxCollider
  |-- Rendering: ParticleRenderer, ConstraintRenderer, ClothRenderer (shader)
  |-- Utility: PhaseManager, SolverData

Setup

1. Place the unified-solver folder in Assets/
2. Create a GameObject with SolverManager and assign the UnifiedSolver compute shader
3. Add generators (CubeGenerator, ClothGenerator) or spawn particles via the SolverManager.AddParticle() API
4. Add a ParticleRenderer with the particle material for sphere visualization
5. Add a ConstraintRenderer with the constraint material for constraint visualization
6. For cloth: assign a material using the UnifiedSolver/ClothRenderer shader

Roadmap

Note: The features listed below are not yet implemented. They represent planned future development milestones.

v0.3 — Cloth & Ropes

• RopeBody — chain of n particles with distance constraints between neighbors, configurable length, segment count, and fixed endpoints

No compute shader changes required — cloth and ropes use existing distance constraints + particle collision.

v0.4 — Shape Matching & Rigid Bodies

• SolveShapeMatch kernel — shape matching constraint (Flex paper Eq. 15-16), covariance matrix + polar decomposition per shape, stiffness parameter (1.0 = rigid, <1.0 = deformable)
• SoftBody — voxelized mesh with distance constraints + shape matching (stiffness < 1)
• RigidParticleBody — voxelized mesh with shape matching (stiffness = 1), SDF values per particle for collision normals (Flex paper section 5.1)

v0.5 — Fluids

• SolveDensity kernel — position-based fluids density constraint (Macklin & Mueller 2013, Flex paper Eq. 26-27), SPH kernels (Poly6 + Spiky), unilateral separation only
• FluidEmitter — spawns particles with fluid phase and configurable rest density
• FluidRenderer — screen-space ellipsoid splatting

References

• Macklin, M. et al. (2014). Unified Particle Physics for Real-Time Applications.
• Macklin, M. et al. (2019). Small Steps in Physics Simulation.
• Macklin, M. & Mueller, M. (2013). Position Based Fluids.