Overview
A Verlet constraint solver predicts positions, then iteratively pulls constrained particles back to target distances.
CoreSource checked
Verlet Constraint Solver
Maintains distance constraints by repeatedly correcting Verlet-integrated particle positions.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Simulation
- Difficulty
- Intermediate
- Family
- Constraint Solver
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
verlet positiondistance constraintiterative correctionparticle system
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(constraints)
Average
O(iterations * constraints)
Worst
O(iterations * constraints)
Space
O(particles)
When to Use
- Use when physics simulation needs verlet position.
- Use when the input matches the assumptions behind constraint Solver.
When Not to Use
- Avoid when the time step, forces, or constraints make the system unstable for the chosen method.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Maintains distance constraints by repeatedly correcting Verlet-integrated particle positions
- Uses verlet position and distance constraint to guide the work.
- Produces updated state.
Use Cases
- Physics simulation
- Animation
- Interactive systems
Inputs
- Current state
- Forces or constraints
- Time step
Outputs
- Updated state
- Constraint corrections
- Collision results
Key Formulas (1)
Distance error
error = ||p2 − p1|| − restlength
error = ||p2 - p1|| - rest_lengthMeasures how far a particle pair is from the target distance.
Pseudocode
- 1.Prepare the inputs and state needed for Verlet Constraint Solver.
- 2.Apply the verlet position step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return updated state.
Canonical Example
- Input
- Verlet Constraint Solver input
- Output
- Updated state
- Explanation
- Verlet Constraint Solver applies verlet position to produce updated state.
Implementation Notes
- Use deterministic update ordering when reproducibility matters.
- Keep the verlet position step separate enough to test independently.
Common Pitfalls
- Changing the time step without retuning stiffness or damping can destabilize the simulation.
- Test boundary and adversarial cases, not only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow state updates, constraints, and error correction over simulation steps.
Step 1 of 4: Prepare the inputs and state needed for Verlet Constraint Solver.
simulation-mechanismNotes
Verlet Constraint Solver operates in O(iterations * constraints) time and O(particles) space within the Constraint Solver family. Key governing relation: error = ||p2 - p1|| - rest_length. Often compared with Verlet Integration and Position Based Dynamics.
Sources (1)
What each reference supports for this entry.
Fluid Simulation for Computer Graphics
BookFluid and simulation reference for state updates or fluid behavior in Verlet Constraint Solver.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageVerlet constraint solvers project positions to satisfy distance or collision constraints.
Often paired withVerlet Integration
Verlet solvers commonly alternate integration with constraint correction.
Related Algorithms
Tags
SimulationPhysicsConstraint ProjectionSpring System