Abstract: The use of power diagrams in accordance with embodiments of the invention enable particle based fluid simulation. One embodiment includes a processor, a memory containing a model of a fluid, where the fluid is broken into a set of cells each defining a volume with boundaries that are relative to a distance of a set of points, where the process is configured by the power particle application to: calculate a plurality of forces acting on the set of cells, move the set of cells within the model of the fluid based upon the plurality of forces, and update the model of the fluid with a new set of cells.

Abstract: The use of power diagrams in accordance with embodiments of the invention enable particle based fluid simulation. One embodiment includes a processor, a memory containing a model of a fluid, where the fluid is broken into a set of cells each defining a volume with boundaries that are relative to a distance of a set of points, where the process is configured by the power particle application to: calculate a plurality of forces acting on the set of cells, move the set of cells within the model of the fluid based upon the plurality of forces, and update the model of the fluid with a new set of cells.

Abstract: A method for deriving barycentric coordinates for a point p within an n-sided polygon is provided wherein, for a particular coordinate wj, corresponding to the vertex qj, the method embodies a formula which depends only on the edge pqj, and the two adjacent angles ?j and ?j. Similarly, a method is provided for deriving weights wij for expressing a vertex qi in a mesh representation of an object surface in terms of its one-ring neighbors qj, ?j?N(i). For a particular vertex qj, and neighbor vertex qj, this method embodies a formula which depends only on the edge qiqj, and the two adjacent angles ?j and ?j. A method of parameterizing a mesh representation of an object surface using the latter formula is also provided. This method begins with the step of computing the weights wij in 3D space (in contrast to parameter space) for each of the vertices in the mesh representation. For a vertex i, i?[1 . . . n], the weights wij allow the vertex i to be expressed in terms of its one-ring neighbors j?N(i).

Abstract: A method of updating in real-time the locations and velocities of mass points of a two- or three-dimensional object represented by a mass-spring system. A modified implicit Euler integration scheme is employed to determine the updated locations and velocities. In an optional post-integration step, the updated locations are corrected to preserve angular momentum. A processor readable medium and a network server each tangibly embodying the method are also provided. A system comprising a processor in combination with the medium, and a system comprising the server in combination with a client for accessing the server over a computer network, are also provided.

Abstract: A method for deriving barycentric coordinates for a point p within an n-sided polygon is provided wherein, for a particular coordinate wj, corresponding to the vertex qj, the method embodies a formula which depends only on the edge pqj, and the two adjacent angles &dgr;J and &ggr;j. Similarly, a method is provided for deriving weights wij for expressing a vertex qi in a mesh representation of an object surface in terms of its one-ring neighbors qj, ∀j&egr;N(i). For a particular vertex qj, and neighbor vertex qj, this method embodies a formula which depends only on the edge qiqj, and the two adjacent angles &dgr;j and &ggr;j. A method of parameterizing a mesh representation of an object surface using the latter formula is also provided. This method begins with the step of computing the weights wij in 3D space (in contrast to parameter space) for each of the vertices in the mesh representation. For a vertex i, i&egr;[1 . . .