Abstract: In one embodiment of the present invention, a position-based dynamics (PBD) framework provides realistic modeling and simulation for elastic rods. In particular, the twisting and bending physics of elastic rods is incorporated into the PBD framework. In operation, an elastic rod model generator represents the center line of an elastic rod as a polyline of points connected via edges. For each edge, the elastic rod model generator adds a ghost point to define the orientation of a material frame that encodes the twist of the edge. Subsequently, a PBD simulator solves for positions of both points and ghost points that, together, represent the evolving position and torsion of the elastic rod. Advantageously, the ghost points enable more realistic animation of deformable objects (e.g., curly hair) than conventional PBD frameworks. Further, unlike force based methods, elastic rod simulation in the PBD framework performs acceptably in environments where speed is critical.

Abstract: In one embodiment, a dynamic effects subsystem automatically generates a dynamic effects animation. A graphical user interface enables an animator to sketch applied energies that influence graphical objects. Each applied energy includes flow particles that are associated with velocity fields. Over time, a dynamic effects engine moves the flow particles and the associated velocity fields along a overall direction associated with the applied energy. To generate each frame included in the dynamic effects animation, the dynamic effect engine computes samples of the graphical objects, computes the influences of the velocity fields on the samples, and updates the positions of the samples based on the influences of the velocity fields. Notably, the applied energies and the flow particles enable the animator to effectively and interactively control the automated animation operations of the dynamic effects engine.

Abstract: In one embodiment of the present invention, a position-based dynamics (PBD) framework provides realistic modeling and simulation for elastic rods. In particular, the twisting and bending physics of elastic rods is incorporated into the PBD framework. In operation, an elastic rod model generator represents the center line of an elastic rod as a polyline of points connected via edges. For each edge, the elastic rod model generator adds a ghost point to define the orientation of a material frame that encodes the twist of the edge. Subsequently, a PBD simulator solves for positions of both points and ghost points that, together, represent the evolving position and torsion of the elastic rod. Advantageously, the ghost points enable more realistic animation of deformable objects (e.g., curly hair) than conventional PBD frameworks. Further, unlike force based methods, elastic rod simulation in the PBD framework performs acceptably in environments where speed is critical.

Abstract: In one embodiment of the present invention, a position-based dynamics (PBD) framework provides realistic modeling and simulation for elastic rods. In particular, the twisting and bending physics of elastic rods is incorporated into the PBD framework. In operation, an elastic rod model generator represents the center line of an elastic rod as a polyline of points connected via edges. For each edge, the elastic rod model generator adds a ghost point to define the orientation of a material frame that encodes the twist of the edge. Subsequently, a PBD simulator solves for positions of both points and ghost points that, together, represent the evolving position and torsion of the elastic rod. Advantageously, the ghost points enable more realistic animation of deformable objects (e.g., curly hair) than conventional PBD frameworks. Further, unlike force based methods, elastic rod simulation in the PBD framework performs acceptably in environments where speed is critical.

Abstract: In one embodiment, a dynamic effects subsytem automatically generates a dynamic effects animation. A graphical user interface enables an animator to sketch applied energies that influence graphical objects. Each applied energy includes flow particles that are associated with velocity fields. Over time, a dynamic effects engine moves the flow particles and the associated velocity fields along a overall direction associated with the applied energy. To generate each frame included in the dynamic effects animation, the dynamic effect engine computes samples of the graphical objects, computes the influences of the velocity fields on the samples, and updates the positions of the samples based on the influences of the velocity fields. Notably, the applied energies and the flow particles enable the animator to effectively and interactively control the automated animation operations of the dynamic effects engine.

Abstract: In one embodiment of the present invention, a position-based dynamics (PBD) framework provides realistic modeling and simulation for elastic rods. In particular, the twisting and bending physics of elastic rods is incorporated into the PBD framework. In operation, an elastic rod model generator represents the center line of an elastic rod as a polyline of points connected via edges. For each edge, the elastic rod model generator adds a ghost point to define the orientation of a material frame that encodes the twist of the edge. Subsequently, a PBD simulator solves for positions of both points and ghost points that, together, represent the evolving position and torsion of the elastic rod. Advantageously, the ghost points enable more realistic animation of deformable objects (e.g., curly hair) than conventional PBD frameworks. Further, unlike force based methods, elastic rod simulation in the PBD framework performs acceptably in environments where speed is critical.

Abstract: In one embodiment of the present invention, a position-based dynamics (PBD) framework provides realistic modeling and simulation for elastic rods. In particular, the twisting and bending physics of elastic rods is incorporated into the PBD framework. In operation, an elastic rod model generator represents the center line of an elastic rod as a polyline of points connected via edges. For each edge, the elastic rod model generator adds a ghost point to define the orientation of a material frame that encodes the twist of the edge. Subsequently, a PBD simulator solves for positions of both points and ghost points that, together, represent the evolving position and torsion of the elastic rod. Advantageously, the ghost points enable more realistic animation of deformable objects (e.g., curly hair) than conventional PBD frameworks. Further, unlike force based methods, elastic rod simulation in the PBD framework performs acceptably in environments where speed is critical.

Abstract: A system is described that treats a solver as an ordered sequence of steps involving the different objects that have to be simulated and relationships between them. Tasks and the order of the tasks are obtained from each object and relationship. The tasks are merged into a sorted list. The solver traverses the list and passing each task to a corresponding object and relationship where the objects are interleaved during processing. The object or relationship then executes the task.

Abstract: The present invention is a particle position solver that allows particles to reach an end of a fixed time, time step in an invalid state and which are then pushed toward a valid state. This allows the solver to continue the simulation while the simulation results move toward a valid behavior. Particle collision calculations are simplified by adopting a non-sequential model ignoring some collisions or combining them. The speed of the simulation is also improved by performing some operations outside the solver calculation loop and by using specialized data structures.

Abstract: A method, computer readable storage, and apparatus for improving subdivision schemes for subdivision surfaces. The present method can correct distortion from the base mesh caused by prior art subdivision and smoothing schemes. In one embodiment, the method includes: (a) subdividing a curve having original vertices producing additional vertices; (b) smoothing the curve into smoothed vertices comprising smoothed original vertices and smoothed additional vertices; and (c) adjusting positions of the smoothed vertices.

Abstract: The present invention is a particle position solver that allows particles to reach an end of a fixed time, time step in an invalid state and which are then pushed toward a valid state. This allows the solver to continue the simulation while the simulation results move toward a valid behavior. Particle collision calculations are simplified by adopting a non-sequential model ignoring some collisions or combining them. The speed of the simulation is also improved by performing some operations outside the solver calculation loop and by using specialized data structures.

Abstract: A method, computer readable storage, and apparatus for improving subdivision schemes for subdivision surfaces. The present method can correct distortion from the base mesh caused by prior art subdivision and smoothing schemes. In one embodiment, the method includes: (a) subdividing a curve having original vertices producing additional vertices; (b) smoothing the curve into smoothed vertices comprising smoothed original vertices and smoothed additional vertices; and (c) adjusting positions of the smoothed vertices.

Abstract: A method and computer program product are presented for converting an arbitrary mesh to a subdivision surface. Where the subdivision surface is to have an odd degree d=2m+1 on the regular part of the mesh, the method includes the steps of subdividing the mesh in a linear fashion, then iteratively smoothing the subdivided mesh m times. Where the subdivision surface is to have an even degree d=2m on the regular part of the mesh, the method includes the steps of subdividing the mesh, calculating the dual of the subdivided mesh, and iteratively smoothing the dual m−1 times. In either case, the resulting subdivision surfaces generalize uniform tensor product B-spline surfaces of any degree to meshes of arbitrary topology. The method uses subdivision rules that involve direct neighbors.

Abstract: A computer-based method for determining a property of a location on a computer surface model where the location is described by a set of parameters and the surface model is described by a set of control vertices having a corresponding set of subdivision rules, and the control vertices admit a parameterization of regular sets of control vertices, includes receiving input specifying coordinates of control vertices that describe the surface model, projecting the specified coordinates of the control vertices into an eigenspace derived from a matrix representation of the subdivision rules to produce a set of projected control vertices, determining which of a hierarchically nested set of regular tiles of the surface model contains the location, and evaluating the location as a function of a valence of one of the control vertices, the determined nested tile, and the set of projected control vertices. The evaluated location is stored in a computer memory.

Abstract: The present invention is a method for performing computer graphic simulation of a fluid in motion. The method takes input data and calculates the velocity of the fluid at a plurality of points at successive time intervals. The velocity values are sent to an animator module which produces a geometrical description of the scene. This geometrical description is then sent to a renderer module, which calculates an image using the geometrical description. The animation is then displayed on an output device. In an embodiment of the invention, scalar quantities such as temperature and density are calculated as well and sent to the renderer module, where they are used in calculating the image. The process of calculating velocity and scalar fields comprises solution of the Navier-Stokes equations, is easy to implement, and allows a user to interact in real-time with three-dimensional fluids on a graphics workstation.

Abstract: The invention provides a method for performing computer graphic simulation of an anisotropic surface reflecting light towards a viewer. First, the data necessary to calculate the amount of light reflected from each point of the anisotropic surface toward the viewer is obtained. This data includes a statistical description of the surface, as well as information about the light and its directions of incidence and reflection. The data is then sent to a renderer, which calculates the amount of light reflected from each point of the anisotropic surface toward the viewer. An image is then created, based on the calculated values. The calculation step is performed with the aid of a model that is derived from wave physics. The model also relies on a statistical, probabilistic description of the anisotropic surface, a description which treats the height of any given point on the surface as a random variable.

Abstract: A method for simulating and rendering hair. A simulator calculates the motion dynamics of a hair. The simulator includes a particle system that emits particles from a surface and a normalization module that normalizes the trajectory of each of the particles to a fixed length to form a set of normalized segments. The simulator outputs a list of normalized segments that are passed to a renderer. The renderer performs a variety of tasks, including fuzzy segment generation and self-shadowing, that results in an image being displayed on a display device. That is, the renderer takes three-dimensional spacial information, applies a light to this information and renders this information as a two-dimensional image.