Overview
Position Based Fluids adapts position-based dynamics to fluid particles, correcting positions so local density stays near a target value.
SpecializedSource checked
Position Based Fluids
Simulates fluids by adjusting particle positions to satisfy density constraints.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Simulation
- Difficulty
- Advanced
- Family
- Particle Fluid Simulation
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
density constraintsmoothing kernelparticle neighborsposition correction
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(particles)
Average
O(iterations * particles * neighbors)
Worst
O(iterations * particles^2)
Space
O(particles)
When to Use
- Use when stable interactive fluid motion is more important than exact fluid physics.
- Use when interactive fluid effects is a central requirement.
When Not to Use
- Avoid when pressure, viscosity, or turbulence must be physically precise.
- Avoid when the timestep, constraints, or stability requirements exceed what the method can handle.
What It Does
- Computes particle fluid simulation within Particle Fluid Simulation workloads (O(iterations * particles * neighbors) time, O(particles) space).
- Works by Simulates fluids by adjusting particle positions to satisfy density constraints.
- Maintains key invariants across density constraint, smoothing kernel, particle neighbors.
Use Cases
- Interactive fluid effects
- Game water splashes
- Stable particle fluids
Inputs
- Fluid particles
- Smoothing radius
- Rest density
Outputs
- Updated particle positions
- Fluid surface samples
Key Formulas (1)
Density constraint
Ci = densityi / restdensity − 1
C_i = density_i / rest_density - 1Measures how far a particle's local density is above or below the target.
Pseudocode
- 1.Find neighbors for each particle
- 2.Estimate density from smoothing kernels
- 3.Compute constraint multipliers
- 4.Apply position corrections
- 5.Update velocities from corrected positions
Canonical Example
- Input
- clustered particles have density above target
- Output
- particles move apart
- Explanation
- Position corrections reduce local density error.
Implementation Notes
- Use a spatial hash or grid for neighbor lookup.
- Keep units, timestep size, and state variables explicit in tests.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Too few solver iterations makes fluid look compressible.
- Large timesteps can add energy, damp motion, or make constraints explode.
- Not defining boundary, empty, or degenerate inputs before implementation.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow fluid particles spreading out until local density constraints are satisfied.
Step 1 of 5: Find neighbors for each particle
simulation-stateNotes
Neighbor search is essential for interactive particle counts.
Sources (2)
What each reference supports for this entry.
Position Based Fluids
PaperOriginal position-based fluids reference for incompressibility constraints in a PBD solver.
Open sourceFluid Simulation for Computer Graphics
BookFluid-simulation reference supporting Position Based Fluids advection, incompressibility, particle-grid transfer, or numerical fluid update behavior.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageSpecializesPosition Based Dynamics
Position Based Fluids applies PBD constraints to fluid density behavior.
Variant ofSmoothed Particle Hydrodynamics
PBF adapts SPH-style neighborhood density estimates.
Related Algorithms
Tags
SimulationFluid SimulationParticlesConstraint Solving