31 results about "Low-discrepancy sequence" patented technology

A discrete pattern, formed by dots discretely arranged in two dimensions, is provided wherein the dots are generated in a low discrepancy sequence. The dots are preferably generated in a discrete pattern wherein the square of discrepancy D satisfies the formula,

D≦0.13N^−1.15  (1)

Further, the method provides for generation of, and the appartus provides implementation of, a discrete pattern even when the filling factor rapidly changes by automatically generating or deleting dots.

A system, method and program product for searching and classifying patterns in a VLSI design layout. A method is provided that includes generating a target vector using a two dimensional (2D) low discrepancy sequence; identifying layout regions in a design layout; generating a feature vector for a layout region; comparing a subset of sequence values in the target vector with sequence values in the feature vector as an initial filter, wherein the system for comparing determines that the layout region does not contain a match if a comparison of the subset of sequence values in the target vector with sequence values in the feature vector falls below a threshold; and outputting search results.

A computer graphics system generates pixel values for pixels in an image of objects in a scene, using strictly-deterministic low-discrepancy sequences, as sample points for evaluating integrals which are used to simulate a number of computer graphic techniques, including soft shadows generated for scenes illuminated by a light source having a finite extent, such as a disk, simulation of depth of field; motion blur; and jittering. The computer graphics system uses the low-discrepancy sequence to generate sample points. The low discrepancy sequences ensure that the sample points are evenly distributed over a respective region or time interval, thereby reducing error in the image which can result from clumping of such sample points which can occur in the Monte Carlo technique. The invention facilitates the generation of images of improved quality when using the same number of sample points at the same computational cost as in the Monte Carlo technique.

A computer graphics system generates a pixel value for a pixel in an image, the pixel being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer graphics system being configured to generate the pixel value for an image using a selected ray-tracing methodology in which simulated rays are shot from respective ones of a plurality of subpixels in the pixel, each subpixel having coordinates (s_x,s_y) in the image plane The computer graphics system comprises a sample point generator and a function evaluator. The sample point generator is configured to map subpixel coordinates (s_x,s_y) onto strata coordinates (j,k):=(s_x mod 2ⁿ,s_y mod 2ⁿ), from which a ray is to be shot, in accordance with $x_i=\left(s_x+\frac{\sigma \left(k\right)}{2^n},s_y+\frac{\sigma \left(j\right)}{2^n}\right)$

where “i” is an instance number for the ray generated as i=j2ⁿ+σ(k), where integer permutation σ(k):=2ⁿΦ_b(k) for 0≦k<2ⁿ for selected “n,” where Φ_b(x) is a radical inverse function given by ${\Phi }_b:N_0\to I$$x=\sum _{j=0}^{\infty }{a}_j\left(x\right)b^j\mapsto \sum _{j=0}^{\infty }{a}_j\left(x\right)b^{-j-1},\mathrm{where}{\left(a_j\right)}_{j=0}^{\infty }$

is the representation of “x” in a selected integer base “b”. The function evaluator is configured to evaluate a selected function using the strata coordinates generated by the sample point generator, the value generated by the function evaluator corresponding to the pixel value.

Random number generating method for generating random numbers in accordance with multivariate non-normal distributions based on the Yuan and Bentler method I on computer. The method includes application steps for applying n-dimensional multivariate non-normal distributions to n-dimensional experience distribution by using computer and steps for generating random numbers including pseudo-random numbers, quasi-random numbers, low discrepancy sequences, and physical random numbers by methods including additive generator method, M-sequence, generalized feedback shift-register method, and Mersenne Twister, and excluding congruential method, by using computer. The application steps use predetermined relationship equations for the third and fourth order moments to perform application associated with the third and fourth order moments of the empirical distributions. Moreover, by using random numbers generation method, parameters are estimated by maximum likelihood method. Furthermore, the random number generation method and the parameters estimation method are applied to simulation of financial field, semiconductor ion implantation, and the like.

A system and method for generating sample points that can generate the sample points in parallel. The sample points can be used in processing in parallel, with the results subsequently collected and used as necessary in subsequent rendering operations. Sample points are generated using a coarse Halton sequence, which makes use of coarse radical inverse values Φ_b^i,M(j) as follows:

Φ_b^i,M(j)=Φ_b(jM+i)

where base “b” is preferably a prime number, but not a divisor of “M,” and “i” is an integer. Using this definition, the s-dimensional coarse Halton sequence U_S^CHal,i,M, which may be used to define sample points for use in evaluating integrals, is defined as

U_s^CHal,i,M=(Φ_b1^i,M(j), . . . , Φ_{b<sub2>s</sub2>}^i,M(j))

where b₁, . . . , b_s are the first “s” prime numbers that are not divisors of “M.” Each value of “i” defines a subsequence that is a low-discrepancy sequence, and so can be used in connection with processing. Similarly, the union of all subsequences for all values of “i” between “zero” and “M−1” is also a low-discrepancy sequence, so results of processing using the coarse Halton sequences for all such values of “i” can be collected together and used in the same manner as if the results had been generated using a Halton sequence to define the sample points.

The invention discloses a path integral method for X-ray Monte Carlo simulation. The path integral method for the X-ray Monte Carlo simulation comprises the following steps: step a, a low-difference sequence with the length of m in a [0,1] 3n dimension is generated, wherein the n is the scattering times and the m is the number of samples; step b, scattering point sequences geometrically matched with a motif are generated through an isomorphic mapping of the low-difference sequence; step c, m photon paths are formed by the scattering point sequences on each detector grid point; step d, the probability density of passing through the photon paths to reach the detector grid points is determined; step e, the probability density is weighted and summed to obtain the scattering intensity of each detector grid point. According to the path integral method for the X-ray Monte Carlo simulation, errors caused by discontinuity on a boundary are eliminated, variances of the samples are lowered, calculation is finished with fewer samples under given accuracy, and the calculated amount is greatly reduced.

The invention provides a method for renormalization of X-ray multiple scattering simulation. The method comprises a first step of generating a low-difference sequence with the length of m in [0,1]<3n> space, enabling n to be scattering times and be a positive integer larger than 1, and enabling m to be the sample number; a second step of generating a scattering point sequence matched with the geometrical shape of a die body by performing isomorphic mapping transformation on the low-difference sequence; a third step of forming m photon paths for each detector grid point through the scattering point sequence; a fourth step of performing renormalization processing on each photon path among the m photon paths; a fifth step of determining the probability density of photons reaching the detector grid points through n-time scattering along each photon path after renormalization processing; and a sixth step of obtaining scattering intensity of each detector grid point according to the probability density of the photons through n-time scattering along each photon path after renormalization processing. The method can improve multiple scattering simulation efficiency and eliminate errors caused by die body edge incontinuity.

Data objects of a geospatial data set are arranged in a low-discrepancy sequence spanning over a pre-defined interval, and assigned to N computing units based on in which sub-interval within the pre-defined interval the point, to which the data object belongs, falls. A subset of the data objects that have been distributed over the N computing units is subjected to processing operations by computer readable instructions loaded on each of the N computing units.

A computer graphics system generates a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer graphics system comprising a photon map generator, a sample point generator and a function evaluator. The photon map generator is configured to a plurality of photon maps, each photon map being associated with a respective point in time during a time interval. The sample point generator is configured to generate a set of sample points in accordance with a selected low-discrepancy sequence, each sample point representing a respective point in time during the time interval. The function evaluator is configured to generate at least one value representing an evaluation of a selected function using selected ones of the photon maps associated with respective ones of the points in time associated with the sample points generated by the sample point generator, the value generated by the function evaluator corresponding to the pixel value.

A system and method for scanning for an object within a region using a Low Discrepancy Sequence scanning scheme. The system may comprise a computer which includes a CPU and a memory medium which is operable to store one or more programs executable by the CPU to perform the method. The method may: 1) calculate a Low Discrepancy Sequence of points in the region; 2) generate a motion control trajectory from the Low Discrepancy Sequence of points (e.g., by generating a Traveling Salesman Path (TSP) from the Low Discrepancy Sequence of points and then re-sampling the TSP to produce a sequence of motion control points comprising the motion control trajectory); 3) scan the region along the motion control trajectory to determine one or more characteristics of the object in response to the scan. The method may also generate output indicating the one or more characteristics of the object.

A scanning system and method for scanning for an object within a region, or for locating a point within a region. Embodiments of the invention include a method for scanning for an object within a region using a Low Discrepancy Curve (LDC) scanning scheme. The method may: 1) generate a Low Discrepancy Sequence (LDS) of points in the region; 2) calculate an LDC in the region based on the LDS of points; and 3) scan the region along the LDC to determine one or more characteristics of the object in response to the scan. In calculating the LDC in the region based on the LDS of points, the method may connect sequential pairs of the LDS with contiguous orthogonal line segments (each parallel to a respective axis of the region), then sample the segments, generating points which may be used to generate the LDC, such as by a curve fit.

A method and renderer for a progressive computation of a light transport simulation are provided. The method includes the steps of employing a low discrepancy sequence of samples; and scrambling an index of the low discrepancy sequence independently per region using a hash value based on coordinates of a respective region, wherein for each set of a power-of-two number of the samples, the scrambling is a permutation.