Game and movie studios are switching to physically based rendering en masse, but physically accurate filter convolution is difficult to do quickly enough to update reflection probes in real-time. Cubemap filtering has also become a bottleneck in the content processing pipeline. We have developed a two-pass filtering algorithm that is specialized for isotropic reflection kernels, is several times faster than existing algorithms, and produces superior results. The first pass uses a quadratic b-spline recurrence that is modified for cubemaps. The second pass uses lookup tables to determine optimal sampling in terms of placement, mipmap level, and coefficients. Filtering a full 1282 cubemap on an NVIDIA GeForce GTX 980 takes between 160 µs and 730 µs with out method, depending on the desired quality.

Abstract Our method approximates exact texture filtering for arbitrary scales and translations of an image while taking into account the performance characteristics of modern GPUs. Our algorithm is fast because it accesses textures with a high degree of spatial locality. Using bilinear samples guarantees that the texels we read are in a regular pattern and that we use a hardware accelerated path. We control the texel weights by manipulating the u, v parameters of each sample and the blend factor between the samples. Our method is similar in quality to Cardinality‐Constrained Texture Filtering [ MS13 ] but runs two times faster.

Abstract We present a method of analytically rasterizing shapes that have curved boundaries and linear color gradients using piecewise polynomial prefilters. By transforming the convolution of filters with the image from an integral over area into a boundary integral, we find closed‐form expressions for rasterizing shapes. We show that a polynomial expression can be used to rasterize any combination of polynomial curves and filters. Our rasterizer also handles rational quadratic boundaries, which allows us to evaluate circles and ellipses. We apply our technique to rasterizing vector graphics and show that our derivation gives an efficient implementation as a scanline rasterizer.

We present a method to create high-quality sampling filters by combining a prescribed number of texels from several resolutions in a mipmap. Our technique provides fine control over the number of texels we read per texture sample so that we can scale quality to match a memory bandwidth budget. Our method also has a fixed cost regardless of the filter we approximate, which makes it feasible to approximate higher-quality filters such as a Lánczos 2 filter in real-time rendering. To find the best set of texels to represent a given sampling filter and what weights to assign those texels, we perform a cardinality-constrained least-squares optimization of the most likely candidate solutions and encode the results of the optimization in a small table that is easily stored on the GPU. We present results that show we accurately reproduce filters using few texel reads and that both quality and speed scale smoothly with available bandwidth. When using four or more texels per sample, our image quality exceeds that of trilinear interpolation.

Abstract We present a method of generating mipmaps that takes into account the distortions due to the parameterization of a surface. Existing algorithms for generating mipmaps assume that the texture is isometrically mapped to the surface and ignore the actual surface parameterization. Our method correctly downsamples warped textures by assigning texels weights proportional to their area on a surface. We also provide a least‐squares approach to filtering over these warped domains that takes into account the postfilter used by the GPU. Our method improves texture filtering for most models but only modifies mipmap generation, requires no modification of art assets or rasterization algorithms, and does not affect run‐time performance.

Abstract We present a method for analytically calculating an anti‐aliased rasterization of arbitrary polygons or fonts bounded by Bézier curves in 2D as well as oriented triangle meshes in 3D. Our algorithm rasterizes multiple resolutions simultaneously using a hierarchical wavelet representation and is robust to degenerate inputs. We show that using the simplest wavelet, the Haar basis, is equivalent to performing a box‐filter to the rasterized image. Because we evaluate wavelet coefficients through line integrals in 2D, we are able to derive analytic solutions for polygons that have Bézier curve boundaries of any order, and we provide solutions for quadratic and cubic curves. In 3D, we compute the wavelet coefficients through analytic surface integrals over triangle meshes and show how to do so in a computationally efficient manner.

Abstract We propose a method for calculating deformations of models by deforming a low‐resolution mesh and adding details while ensuring that the details we add satisfy a set of constraints. Our method builds a low‐resolution representation of a mesh by using edge collapses and performs an as‐rigid‐as‐possible deformation on the simplified mesh. We then add back details by reversing edge‐collapses so that the shape of the mesh is locally preserved. While adding details, we deform the mesh to match the predicted positions of constraints so that constraints on the full‐resolution mesh are met. Our method operates on meshes with arbitrary triangulations, satisfies constraints over the full‐resolution mesh and converges quickly.

Abstract We present a method for calculating the boundary of objects from Discrete Indicator Functions that store 2‐material volume fractions with a high degree of accuracy. Although Marching Cubes and its derivatives are effective methods for calculating contours of functions sampled over discrete grids, these methods perform poorly when contouring non‐smooth functions such as Discrete Indicator Functions. In particular, Marching Cubes will generate surfaces that exhibit aliasing and oscillations around the exact surface. We derive a simple solution to remove these problems by using a new function to calculate the positions of vertices along cell edges that is efficient, easy to implement, and does not require any optimization or iteration. Finally, we provide empirical evidence that the error introduced by our contouring method is significantly less than is introduced by Marching Cubes.

Abstract We provide a simple method that extracts an isosurface that is manifold and intersection‐free from a function over an arbitrary octree. Our method samples the function dual to minimal edges, faces, and cells, and we show how to position those samples to reconstruct sharp and thin features of the surface. Moreover, we describe an error metric designed to guide octree expansion such that flat regions of the function are tiled with fewer polygons than curved regions to create an adaptive polygonalization of the isosurface. We then show how to improve the quality of the triangulation by moving dual vertices to the isosurface and provide a topological test that guarantees we maintain the topology of the surface. While we describe our algorithm in terms of extracting surfaces from volumetric functions, we also show that our algorithm extends to generating manifold level sets of co‐dimension 1 of functions of arbitrary dimension.

Abstract We propose a new family of barycentric coordinates that have closed‐forms for arbitrary 2D polygons. These coordinates are easy to compute and have linear precision even for open polygons. Not only do these coordinates have linear precision, but we can create coordinates that reproduce polynomials of a set degree m as long as degree m polynomials are specified along the boundary of the polygon. We also show how to extend these coordinates to interpolate derivatives specified on the boundary.

Abstract We present a streaming method for reconstructing surfaces from large data sets generated by a laser range scanner using wavelets. Wavelets provide a localized, multiresolution representation of functions and this makes them ideal candidates for streaming surface reconstruction algorithms. We show how wavelets can be used to reconstruct the indicator function of a shape from a cloud of points with associated normals. Our method proceeds in several steps. We first compute a low‐resolution approximation of the indicator function using an octree followed by a second pass that incrementally adds fine resolution details. The indicator function is then smoothed using a modified octree convolution step and contoured to produce the final surface. Due to the local, multiresolution nature of wavelets, our approach results in an algorithm over 10 times faster than previous methods and can process extremely large data sets in the order of several hundred million points in only an hour.