California Institute of Technology

Mark Meyer

Alan H Barr

Mathieu Desbrun

Peter Schroeder

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

Mark Meyer