California Institute of Technology

Mathieu Desbrun

Alan H Barr

Mark Meyer

Fernando Ferrari De Goes

Peter Schroeder

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.

Particle-based simulation through power diagrams

A method for deriving barycentric coordinates for a point p within an n-sided polygon is provided wherein, for a particular coordinate w, corresponding to the vertex q, the method embodies a formula which depends only on the edge pq, and the two adjacent angles &#x3b4;and &#x3b3;. Similarly, a method is provided for deriving weights wfor expressing a vertex qin a mesh representation of an object surface in terms of its one-ring neighbors q, &#x2200;j&#x3b5;N(i). For a particular vertex q, and neighbor vertex q, this method embodies a formula which depends only on the edge qq, and the two adjacent angles &#x3b4;and &#x3b3;. 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 winD space (in contrast to parameter space) for each of the vertices in the mesh representation. For a vertex i, i&#x3b5;[. . . n], the weights wallow the vertex i to be expressed in terms of its one-ring neighbors j&#x3b5;N(i). The method then proceeds to parameterizing the mesh representation responsive to the weights w.

Methods for computing barycentric coordinates generalized to irregular n-gons and applications of the same

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.

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Pasadena, CA, United States of America

Mathieu Desbrun