Simulation
Algorithms that model how systems change over time or under uncertainty.
Simulation algorithms approximate motion, events, randomness, or interactions when direct calculation is hard or impossible.
Euler Integration
Approximates motion by stepping forward using the current rate of change.
Verlet Integration
Updates motion using current and previous positions.
Runge-Kutta Method
Approximates differential equations by sampling several slopes per step.
Monte Carlo Simulation
Estimates outcomes by running many random trials.
Cellular Automata
Updates grid cells from simple local rules.
Finite Difference Method
Approximates differential equations with differences on a grid.
N-Body Simulation
Simulates many bodies interacting through forces such as gravity.
Position Based Dynamics
Simulates motion by directly adjusting positions to satisfy constraints.
Semi-Implicit Euler
Updates velocity before position for a more stable Euler-style physics step.
Smoothed Particle Hydrodynamics
Simulates fluids with particles that estimate local density and pressure.
Rigid Body Dynamics
Simulates objects that translate and rotate while keeping their shape fixed.
Mass-Spring System
Simulates connected particles using spring forces between neighboring masses.
Cloth Simulation
Simulates fabric-like motion with connected particles, constraints, or continuum models.
Position Based Fluids
Simulates fluids by adjusting particle positions to satisfy density constraints.
Navier-Stokes Projection
Makes a fluid velocity field incompressible by subtracting pressure gradients.
Semi-Lagrangian Advection
Moves quantities through a velocity field by tracing backward from grid cells.
Vorticity Confinement
Adds small swirling forces back into fluid simulations to counter numerical damping.
Implicit Integration
Advances simulation state using equations evaluated at the future state for better stability.
Explicit Integration
Advances simulation state using derivatives evaluated at the current time.
Constraint Projection
Enforces simulation constraints by projecting invalid state back onto the allowed manifold.
Verlet Constraint Solver
Maintains distance constraints by repeatedly correcting Verlet-integrated particle positions.
Broad Phase Collision Detection
Quickly finds possible colliding object pairs before exact collision tests.
Narrow Phase Collision Detection
Performs precise collision tests for candidate pairs found by broad phase.
Sweep and Prune
Reduces collision candidates by sorting bounding-box intervals along one or more axes.
GJK Collision Detection
Tests convex shapes for intersection using support points of their Minkowski difference.
Expanding Polytope Algorithm
Computes penetration depth and contact normal after GJK detects convex overlap.
Sequential Impulse Solver
Approximates rigid-body contact and joint constraints by applying clamped impulses one constraint at a time.
Boids Flocking
Simulates flocking from local separation, alignment, and cohesion rules.
Lattice Boltzmann Method
Simulates fluids by evolving particle distribution functions on a lattice.
Particle-in-Cell
Combines moving particles with a grid used to solve field quantities.
Finite Element Method
Approximates continuum behavior by solving equations over mesh elements.
Finite Volume Fluid Simulation
Simulates fluids by conserving quantities across cell boundaries.
Impulse-Based Collision Response
Impulse-Based Collision Response advances physical or agent state under forces, constraints, or collisions.
Penalty Method Collision Response
Penalty Method Collision Response advances physical or agent state under forces, constraints, or collisions.
Continuous Collision Detection
Continuous Collision Detection advances physical or agent state under forces, constraints, or collisions.
Stable Fluids
Stable Fluids advances physical or agent state under forces, constraints, or collisions.
FLIP Fluid Simulation
FLIP Fluid Simulation advances physical or agent state under forces, constraints, or collisions.
MPM Simulation
MPM Simulation advances physical or agent state under forces, constraints, or collisions.
Verlet Cloth Simulation
Verlet Cloth Simulation advances physical or agent state under forces, constraints, or collisions.
Projective Dynamics
Projective Dynamics advances physical or agent state under forces, constraints, or collisions.
Shape Matching Simulation
Shape Matching Simulation advances physical or agent state under forces, constraints, or collisions.
Position Based Rigid Bodies
Position Based Rigid Bodies advances physical or agent state under forces, constraints, or collisions.
Barnes-Hut Simulation
Approximates many-body forces by grouping distant bodies in a spatial tree.
Fast Multipole Method
Fast Multipole Method addresses approximate n-body simulation by expanding far-field interactions and translating multipole summaries.
Verlet Neighbor List
Caches nearby particle pairs so neighbor searches can be reused across several simulation steps.