Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: A method of performing stretch-driven mesh parameterization. A method of performing stretch-driven mesh parameterization comprising, computing a spectral analysis to parameterize a mesh, and iterating a stretch optimization calculation to further optimize the initial parameterization.

Abstract: Systems and methods are provided for providing a fine-to-coarse look ahead in connection with parametrization in a graphics system. The use of a variety of parametrization metrics may be supplemented and improved by the fine-to-coarse look ahead techniques of the invention. First, the metric of a parametrization is minimized using a coarse-to-fine hierarchical solver, and then accelerated with a fine-to-coarse propagation. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail at all levels of detail in the progressive mesh sequence.

Abstract: Real-time processing includes per-point transfer matrices forming a high-dimensional surface signal that is compressed using clustered principal component analysis (CPCA). CPCA partitions multiple samples into fewer clusters, each cluster approximating the signal as an affine subspace. Further, source radiance is input to a processor, which approximates source radiance using spherical harmonic basis to produce a set of source radiance coefficients. A graphics processing unit (GPU) processes the source radiance coefficients through the transfer matrix model for each cluster. The result of such processing is the exit radiance, which parameterizes the radiance leaving the surface of the object at each point, thus producing the shading for each point of the virtual object in real time.

Abstract: Forward mapping is provided, which accumulates and resolves over all samples forward mapped to each pixel bin. During accumulation and resolution of each of the samples, since a point sample from a forefront object and a point sample from an occluded object may be received by the same bin, wherein only the former should be accumulated and resolved according to the accumulation and resolution process, a Z-range, or Z-interval, is assigned to each sample instead of the conventional Z-value. The Z-range is a function of the Z-value. Analysis of the overlapping of these Z-ranges then determines which samples are to be accumulated and resolved together according to the accumulation and resolution process, and which are not.

Abstract: Systems and methods are provided for optimizing a parametrization scheme in accordance with information about the surface signal. A surface parametrization is created to store a given surface signal into a texture image. The signal-specialized metric of the invention minimizes signal approximation error, i.e., the difference between the original surface signal and its reconstruction from the sampled texture. A signal-stretch parametrization metric is derived based on a Taylor expansion of signal error. For fast evaluation, the metric of the invention is pre-integrated over the surface as a metric tensor. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail. Compared to traditional geometric parametrizations, the number of texture samples can often be reduced by a significant factor for a desired signal accuracy.

Abstract: The described systems and methods are directed at interactively rendering graphics using precomputed radiance transfer (PRT). A reflectance matrix that represents the reflectance of a particular object to be rendered is determined. Source lighting associated with the object is represented using basis functions. The reflectance matrix is factored into view and light components. A raw transfer matrix is determined based, in part, from the factored reflectance matrix and the source lighting. The raw transfer matrix is partitioned to obtain transfer matrices, which are used to render the object. The described systems and methods are capable of rendering glossy objects with well-defined shadows.

Abstract: Systems and methods are provided for providing a fine-to-coarse look ahead in connection with parametrization in a graphics system. The use of a variety of parametrization metrics may be supplemented and improved by the fine-to-coarse look ahead techniques of the invention. First, the metric of a parametrization is minimized using a coarse-to-fine hierarchical solver, and then accelerated with a fine-to-coarse propagation. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail at all levels of detail in the progressive mesh sequence.

Abstract: Systems and methods are provided for variable source rate sampling in connection with image rendering, which accumulate and resolve over all samples forward mapped to each pixel bin. In accordance with the invention, the textured surface to be rendered is sampled, or oversampled, at a variable rate that reflects variations in frequency among different regions, taking into account any transformation that will be applied to the surface prior to rendering and the view parameters of the display device, thus ensuring that each bin of the rendering process receives at least a predetermined minimum number of samples. A variety of image processing applications are contemplated wherein variable rate source sampling, and accumulation and resolution of forward mapped point samples can be applied, ranging from 3-D graphics applications to applications wherein images recorded in a recording/storage environment are mapped to the arbitrary requirements of a display environment.

Abstract: Reduction of aliasing artifacts along discontinuity edges of a rendered polygon mesh is achieved by overdrawing the edges as antialiased lines. The discontinuity edges are oriented consistently and blended as they approach silhouettes in the mesh to avoid popping at the edge, thereby achieving a temporal smoothness at the silhouettes. This temporal smoothness is balanced with a competing desire to maintain spatial sharpness by utilizing an asymmetric blending technique. To further improve results, the discontinuity edges can be sorted by depth prior to overdrawing them. These processes are effective at reducing the temporal artifact known as “crawling jaggies”.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: Systems and methods are provided for variable source rate sampling in connection with image rendering, which accumulate and resolve over all samples forward mapped to each pixel bin. In accordance with the invention, the textured surface to be rendered is sampled, or oversampled, at a variable rate that reflects variations in frequency among different regions, taking into account any transformation that will be applied to the surface prior to rendering and the view parameters of the display device, thus ensuring that each bin of the rendering process receives at least a predetermined minimum number of samples. A variety of image processing applications are contemplated wherein variable rate source sampling, and accumulation and resolution of forward mapped point samples can be applied, ranging from 3-D graphics applications to applications wherein images recorded in a recording/storage environment are mapped to the arbitrary requirements of a display environment.

Abstract: Systems and methods for forward mapping are provided, which accumulate and resolve over all samples forward mapped to each pixel bin. The invention uses a pixel, or sub-pixel, binning approach that accumulates and resolves over all samples, and performs particularly well compared to prior architectures in areas that have higher frequency content, solving the minification antialiasing problem and producing a high quality result. A filter determines the value(s) to assign to each pixel based upon accumulation and resolution, e.g., taking the mean, taking the median, taking the mode, taking the minimum, taking the maximum, applying a least squares fit or applying some other function, of all of the sample points that fall within the pixel bin(s), rather than assigning a value by selecting only the point sample that corresponds to the center of the pixel.

Abstract: Systems and methods are provided for providing a fine-to-coarse look ahead in connection with parametrization in a graphics system. The use of a variety of parametrization metrics may be supplemented and improved by the fine-to-coarse look ahead techniques of the invention. First, the metric of a parametrization is minimized using a coarse-to-fine hierarchical solver, and then accelerated with a fine-to-coarse propagation. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail at all levels of detail in the progressive mesh sequence.

Abstract: Systems and methods are provided for optimizing the geometric stretch of a parametrization scheme. Given an arbitrary mesh, the systems and methods construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. The systems and methods minimize geometric stretch, i.e., small texture distances mapped onto large surface distances, to balance sampling rates over all locations and directions on the surface. The systems and methods also minimize texture deviation, i.e., “slippage” error based on parametric correspondence, to obtain accurate textured mesh approximations. The technique(s) begin by partitioning the mesh into charts using planarity and compactness heuristics. Then, the technique(s) proceed by creating a stretch-minimizing parametrization within each chart, and by resizing the charts based on the resulting stretch. Then, the technique(s) simplify the mesh while respecting the chart boundaries.

Abstract: Systems and methods are provided for optimizing a parametrization scheme in accordance with information about the surface signal. A surface parametrization is created to store a given surface signal into a texture image. The signal-specialized metric of the invention minimizes signal approximation error, i.e., the difference between the original surface signal and its reconstruction from the sampled texture. A signal-stretch parametrization metric is derived based on a Taylor expansion of signal error. For fast evaluation, the metric of the invention is pre-integrated over the surface as a metric tensor. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail. Compared to traditional geometric parametrizations, the number of texture samples can often be reduced by a significant factor for a desired signal accuracy.

Abstract: Systems and methods are provided for diffusing clipping error in a computing system. When a data set contains values which are to be restricted to a range, and the data set includes one or more values which are beyond the range, the invention provides methodology that is an improvement over clipping extraneous values to the range or squeezing the values to the range. Advantageously, systems and methods are provided for distributing or diffusing error to neighboring samples of the data set, thereby spreading localized error, and minimizing the effects associated with remapping the data set to the restrictive range.

Abstract: Reduction of aliasing artifacts along discontinuity edges of a rendered polygon mesh is achieved by overdrawing the edges as antialiased lines. The discontinuity edges are oriented consistently and blended as they approach silhouettes in the mesh to avoid popping at the edge, thereby achieving a temporal smoothness at the silhouettes. This temporal smoothness is balanced with a competing desire to maintain spatial sharpness by utilizing an asymmetric blending technique. To further improve results, the discontinuity edges can be sorted by depth prior to overdrawing them. These processes are effective at reducing the temporal artifact known as “crawling jaggies”.