Physical Simulation
The physical forces that sculpt form across time—Eulerian Navier-Stokes atmospheric smoke, SPH/FLIP ocean waves, unconditionally stable XPBD cloth, and FEM hyperelastic soft bodies.
Indexed Physical Solvers (6)
Eulerian Grids vs. Lagrangian Particles vs. XPBD ConstraintsEulerian Navier-Stokes Fluid Solver (Smoke & Gas)
The mathematical physics of volumetric atmosphere. Solves pressure Poisson equations across 3D voxel grids to simulate hyper-realistic smoke plumes, fire explosions, and swirling vortex rings.
\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla)\mathbf{u} = -\frac{1}{\rho}\nabla p + \nu \nabla^2 \mathbf{u} + \mathbf{f}, \quad \nabla \cdot \mathbf{u} = 0Lagrangian Liquid Solvers (SPH, FLIP & APIC)
Simulating water droplets, ocean waves, and violent splashing. Tracks millions of moving water particles and transfers velocities to background grids for sharp, volume-preserving liquid meshing.
\frac{D\mathbf{v}}{Dt} = -\frac{1}{\rho}\nabla P + \mathbf{g} + \frac{\mu}{\rho}\nabla^2 \mathbf{v} + \frac{\sigma}{\rho}\kappa \mathbf{n}Extended Position Based Dynamics (XPBD Cloth & Hair)
The modern standard for real-time and offline garment simulation. Directly projects vertex positions to satisfy stretching, shearing, and bending constraints without numerical blow-up.
C_j(\mathbf{x}) = 0, \quad \Delta \mathbf{x} = -\frac{w_i}{\sum w_k + \frac{\tilde{\alpha}}{\Delta t^2}} C(\mathbf{x}) \nabla C(\mathbf{x})Mass-Spring & Particle Dynamics
Millions of independent point masses governed by vector force fields, turbulence, collision surfaces, and emitter rules. Perfect for rain, sparks, dust motes, and magic FX.
m_i \frac{d^2 \mathbf{x}_i}{dt^2} = \mathbf{F}_{\text{gravity}} + \mathbf{F}_{\text{drag}} + \mathbf{F}_{\text{noise}} + \sum_{j} \mathbf{F}_{\text{spring}}(i,j)Rigid Body Dynamics & Destruction Solvers
Calculating massive structural collapse, tumbling bricks, and vehicle crashes. Enforces hard contact constraints, friction cones, and inertia tensors across thousands of solid objects.
M \dot{\mathbf{v}} = \mathbf{f} + \mathbf{J}^T \boldsymbol{\lambda}, \quad \mathbf{I} \dot{\boldsymbol{\omega}} + \boldsymbol{\omega} \times (\mathbf{I}\boldsymbol{\omega}) = \boldsymbol{\tau} + \mathbf{J}_{\text{rot}}^T \boldsymbol{\lambda}Soft Body Mechanics (FEM & Material Point Method)
Simulating volumetric squish, flesh tearing, snow compaction, and muscle contraction. Uses continuum solid mechanics and hyperelastic strain tensors for cinema-grade organic realism.
\nabla \cdot \boldsymbol{\sigma} + \rho \mathbf{b} = \rho \ddot{\mathbf{u}}, \quad \boldsymbol{\sigma} = \frac{1}{J} \frac{\partial \Psi}{\partial \mathbf{F}} \mathbf{F}^T