California Institute of Technology

Other

Alan H Barr

David B Kirk

Marcel Gavriliu

Mathieu Desbrun

Mark Meyer

Peter Schroeder

David E Breen

Joel Carranza

Brooke P Anderson

Douglas A Kerns

Denis Zorin

A method of identifying one or more regions of the domain of a function that do not contain solutions is described along with a related subdivision method. These methods may be employed in the context of branch and bound methods that use interval analysis to search for solutions of functions. The one or more regions of the function domain that do not contain solutions are identified using a cropping formula derived from one or more components (low order and high order) of a Taylor Form inclusion function. A Corner Taylor Form inclusion function is also described which might be used to identify the output range of a function.

Efficient method of identifying non-solution or non-optimal regions of the domain of a function

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 extracting a mesh representation of a surface from a volumetric representation of at least a portion of an object is provided. A surface is derived from the volumetric representation. A seed point on the surface is then selected, and a neighborhood of the seed point is grown over at least a portion of the surface. These selection and growing steps are iteratively repeated until the entire surface is substantially completely covered. Seed points are then selectively connected to form polygons which comprise the mesh representation.

Method of deriving mesh surface representation from volume representation

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.

Real-time, interactive animation of deformable two- and three-dimensional objects

An imaging system which corrects perceptual distortion in wide angle picture balances between direct view distortion and linear perspective distortion. The two kinds of distortion are balanced according to a transformation ratio. The balancing can be expressed as: and .phi.=.o slashed. where .rho. and .phi. are the transformed polar coordinates corresponding to the original polar coordinates r and .o slashed., .lambda. is the transformation ratio defining the amount of each transform to be used, and R is the size of the new image. This can also be effected by a lens having the transfer characteristic whereby B=tan .beta./K; where K is between 1 and 2.

Imaging system for correction of perceptual distortion in wide angle

The multiplier which includes built-in adjustments to improve circuit performance. More specifically, the multiplier is a compensated multiplier to increase the accuracy and precision of computation using analog very large scale integrated (VLSI) circuits and consists of adjustable parameters which allow for the improvement of the linear range of behavior as well as the cancellation of input offsets. A differential multiplier is further described in which adjustable parameters in addition to the four inputs to the multiplier compensate for offsets and non-linearities to result in a highly accurate analog multiplier.

Compensated analog multipliers

A circuit and method for executing real time constraint solution permits real time control of computational tasks using analog very large scale integrated (VLSI) circuits. The constraints of a computation or task are first defined as a function or set of functions. The function(s) are used to produce an error measure function which described how well the constraint(s) is/are stisfied. Analog gradient descent techniques are then used to minimize the error measure function and produce an improved output of the task and optionally adjust the performance of the task. As this is performed in analog VLSI, the constraint solution can be performed continuously and continually in real time, without the limitations of discrete optimization as implemented using digital processing.

Method and apparatus for real-time constraint solution

A circuit and method for estimating gradients of a target function using noise injection and correlation is provided. In one embodiment, an input signal is combined with an input noise signal and the combined signal is input to a circuit which computes the output of the target function. An amplified noise signal and output signal of the target function are input to a multiplier which performs a correlation of the inputs. The output of the multiplier is processed by a low-pass filter which generates the gradient. The circuit and method can be expanded to N-dimensions. Furthermore, in a alternate embodiment, a differentiator is coupled between the multiplier and amplifier and the multiplier and the output of the target function to differentiate the two signals prior to input to the multiplier. In other embodiments, the circuit may be used to compute gradient-like signals, wherein each component of the gradient is individually scaled by a different value. The output of the circuit can then be used in other descent algorithms. In addition, varying the scale of the noise signal over a time schedule, an annealing style of optimization can be implemented. This prevents the gradient process from stopping at local minima while descending to the global minimum of the function.

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Pasadena, CA, United States of America

Alan H Barr