Soft-body dynamics
Soft-body dynamics is a field of computer graphics that focuses on visually realistic physical simulations of the motion and properties of deformable objects (or soft bodies).
While the relative distances of points are not fixed, the body is expected to retain its shape to some degree (unlike a fluid).
In this approach, the body is modeled as a set of point masses (nodes) connected by ideal weightless elastic springs obeying some variant of Hooke's law.
The nodes may either derive from the edges of a two-dimensional polygonal mesh representation of the surface of the object, or from a three-dimensional network of nodes and edges modeling the internal structure of the object (or even a one-dimensional system of links, if for example a rope or hair strand is being simulated).
Applying Newton's second law to the point masses including the forces applied by the springs and any external forces (due to contact, gravity, air resistance, wind, and so on) gives a system of differential equations for the motion of the nodes, which is solved by standard numerical schemes for solving ODEs.
This is a more physically accurate approach, which uses the widely used finite element method to solve the partial differential equations which govern the dynamics of an elastic material.
Pixelux (developers of the Digital Molecular Matter system) use a finite-element-based approach for their soft bodies, using a tetrahedral mesh and converting the stress tensor directly into node forces.
[19] Deformation can also be handled by a traditional rigid-body physics engine, modeling the soft-body motion using a network of multiple rigid bodies connected by constraints, and using (for example) matrix-palette skinning to generate a surface mesh for rendering.
[21] Via rendering effects, this can produce a visually plausible emulation of textiles and clothing, used in a variety of contexts in video games, animation, and film.
Cloth simulators are generally based on mass-spring models, but a distinction must be made between force-based and position-based solvers.
To create high resolution cloth with a realistic stiffness is not possible however with simple explicit solvers (such as forward Euler integration), unless the timestep is made too small for interactive applications (since as is well known[citation needed], explicit integrators are numerically unstable for sufficiently stiff systems).
Therefore, implicit solvers must be used,[22] requiring solution of a large sparse matrix system (via e.g. the conjugate gradient method), which itself may also be difficult to achieve at interactive frame rates.
This system is solved sequentially and iteratively, by directly moving nodes to satisfy each constraint, until sufficiently stiff cloth is obtained.
Pixar has presented a method which uses a global topological analysis of mesh intersections in configuration space to detect and resolve self-interpenetration of cloth.
To do collision detection efficiently, primitives which are certainly not colliding must be identified as soon as possible and discarded from consideration to avoid wasting time.
In contrast, a fluid assumes the shape of whatever vessel contains it, as the particles are bound together by relatively weak forces.
