StableShape
Algorithm Framework
The core of the StableShape algorithm includes two main components: the StableFluid class and the ParticleSystem class. The StableFluid class manages velocity and density fields, resolving the Navier-Stokes equations through methods like diffusion, advection, and pressure projection. These methods ensure the stability of fluid dynamics simulation.
The ParticleSystem class operates on a mesh of particles connected by springs, allowing for tension calculations and mesh reconstruction. By treating mesh vertices as particles influenced by a stable velocity field, this framework achieves realistic fluid behavior simulation.
From Field to Morphology
The project explores the transformation from scalar fields to morphology. In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. Examples of scalar fields are electric or magnetic fields, containing values for each point on a 2D plane. In the fluid case, our scalar field represents fluid density.
In three dimensions, the equipotential space of a scalar field is two-dimensional, that is, equipotential surfaces. We can use these equipotential surfaces to represent three-dimensional fluid, which differs from a 2D height field. Here, any equipotential surface is a three-dimensional closed body, equivalent to a contour line.
Morphogenesis Methods
StableShape offers two methods for generating morphology: the VDB method and the mesh method. The VDB method uses the Dendro plugin to convert density points to volumes. The mesh method employs the particle system to process meshes. Through these two methods, complex fluid forms can be evolved from simple primitive shapes.
The project utilizes the Grasshopper interface for interactive design, including components such as grid construction, VDB processing, StableFluid solver, and ParticleSystem solver. This workflow allows designers to directly manipulate and observe the evolution of forms in real-time.
Implementation Process
The implementation process of the fluid solver includes four main steps: initialization, adding density, updating the velocity field, and updating the density field. In each time step, the algorithm resolves the Navier-Stokes equations through diffusion, projection, and advection operations, ensuring physical accuracy and numerical stability of the fluid simulation.
The mesh solver processes the particle system, including mesh topology processing, particle movement, tension application, and mesh reconstruction. Through these steps, the system can generate fluid forms that evolve over time, providing new possibilities for architectural and design exploration.
