Common acoustic sources, like voices or musical instruments, exhibit strong frequency and directional dependence. When transported through complex environments, their anisotropic radiated field undergoes scattering, diffraction, and occlusion before reaching a directionally-sensitive listener. We present the first wave-based interactive auralization system that encodes and renders a complete reciprocal description of acoustic wave fields in general scenes. Our method renders directional effects at freely moving and rotating sources and listeners and supports any tabulated source directivity function and head-related transfer function. We represent a static scene's global acoustic transfer as an 11-dimensional bidirectional impulse response (BIR) field, which we extract from a set of wave simulations. We parametrically encode the BIR as a pair of radiating and arriving directions for the perceptually-salient initial ( direct ) response, and a compact 6 × 6 reflections transfer matrix capturing indirect energy transfer with scene-dependent anisotropy. We render our encoded data with an efficient and scalable algorithm - integrated in the Unreal Engine ™ - whose CPU performance is agnostic to scene complexity and angular source/listener resolutions. We demonstrate convincing effects that depend on detailed scene geometry, for a variety of environments and source types.

Extended stochastic sources, like falling rain or a flowing waterway, provide an immersive ambience in virtual environments. In complex scenes, the rendered sound should vary naturally with listener position, differing not only in overall loudness but also in texture, to capture the indistinct murmur of a faraway brook versus the bright babbling of one up close. Modeling an ambient sound as a collection of random events such as individual raindrop impacts or water bubble oscillations, this variation can be seen as a change in the statistical distribution of events heard by the listener: the arrival rate of nearby, louder events relative to more distant or occluded, quieter ones. Reverberation and edge diffraction from scene geometry multiply and mix events more extensively compared to an empty scene and introduce salient spatial variation in texture. We formalize the notion of acoustic texture by introducing the event loudness density (ELD), which relates the rapidity of received events to their loudness. To model spatial variation in texture, the ELD is made a function of listener location in the scene. We show that this ELD field can be extracted from a single wave simulation for each extended source and rendered flexibly using a granular synthesis pipeline, with grains derived procedurally or from recordings. Our system yields believable, realtime changes in acoustic texture as the listener moves, driven by sound propagation in the scene.

Precomputed sound propagation samples acoustics at discrete scene probe positions to support dynamic listener locations. An offline 3D numerical simulation is performed at each probe and the resulting field is encoded for runtime rendering with dynamic sources. Prior work place probes on a uniform grid, requiring high density to resolve narrow spaces. Our adaptive sampling approach varies probe density based on a novel "local diameter" measure of the space surrounding a given point, evaluated by stochastically tracing paths in the scene. We apply this measure to layout probes so as to smoothly adapt resolution and eliminate undersampling in corners, narrow corridors and stairways, while coarsening appropriately in more open areas. Coupled with a new runtime interpolator based on radial weights over geodesic paths, we achieve smooth acoustic effects that respect scene boundaries as both the source or listener move, unlike existing visibility-based solutions. We consistently demonstrate quality improvement over prior work at fixed cost.

Convincing audio for games and virtual reality requires modeling directional propagation effects. The initial sound's arrival direction is particularly salient and derives from multiply-diffracted paths in complex scenes. When source and listener straddle occluders, the initial sound and multiply-scattered reverberation stream through gaps and portals, helping the listener navigate. Geometry near the source and/or listener reveals its presence through anisotropic reflections. We propose the first precomputed wave technique to capture such directional effects in general scenes comprising millions of polygons. These effects are formally represented with the 9D directional response function of 3D source and listener location, time, and direction at the listener, making memory use the major concern. We propose a novel parametric encoder that compresses this function within a budget of ~100MB for large scenes, while capturing many salient acoustic effects indoors and outdoors. The encoder is complemented with a lightweight signal processing algorithm whose filtering cost is largely insensitive to the number of sound sources, resulting in an immediately practical system.

Ambient sounds arise from a massive superposition of chaotic events distributed over a large area or volume, such as waves breaking on a beach or rain hitting the ground. The directionality and loudness of these sounds as they propagate in complex 3D scenes vary with listener location, providing cues that distinguish indoors from outdoors and reveal portals and occluders. We show that ambient sources can be approximated using an ideal notion of spatio-temporal incoherence and develop a lightweight technique to capture their global propagation effects. Our approach precomputes a single FDTD simulation using a sustained source signal whose phase is randomized over frequency and source extent. It then extracts a spherical harmonic encoding of the resulting steady-state distribution of power over direction and position in the scene using an efficient flux density formulation. The resulting parameter fields are smooth and compressible, requiring only a few MB of memory per extended source. We also present a fast binaural rendering technique that exploits phase incoherence to reduce filtering cost.

We investigate the expressiveness of the microfacet model for isotropic bidirectional reflectance distribution functions (BRDFs) measured from real materials by introducing a non-parametric factor model that represents the model’s functional structure but abandons restricted parametric formulations of its factors. We propose a new objective based on compressive weighting that controls rendering error in high-dynamic-range BRDF fits better than previous factorization approaches. We develop a simple numerical procedure to minimize this objective and handle dependencies that arise between microfacet factors. Our method faithfully captures a more comprehensive set of materials than previous state-of-the-art parametric approaches yet remains compact (3.2KB per BRDF). We experimentally validate the benefit of the microfacet model over a naïve orthogonal factorization and show that fidelity for diffuse materials is modestly improved by fitting an unrestricted shadowing/masking factor. We also compare against a recent data-driven factorization approach [Bilgili et al. 2011] and show that our microfacet-based representation improves rendering accuracy for most materials while reducing storage by more than 10 ×.

We present a novel method for capturing real-world, spatially-varying surface reflectance from a small number of object views ( k ). Our key observation is that a specific target's reflectance can be represented by a small number of custom basis materials ( N ) convexly blended by an even smaller number of non-zero weights at each point ( n ). Based on this sparse basis/sparser blend model, we develop an SVBRDF reconstruction algorithm that jointly solves for n , N , the basis BRDFs, and their spatial blend weights with an alternating iterative optimization, each step of which solves a linearly-constrained quadratic programming problem. We develop a numerical tool that lets us estimate the number of views required and analyze the effect of lighting and geometry on reconstruction quality. We validate our method with images rendered from synthetic BRDFs, and demonstrate convincing results on real objects of pre-scanned shape and lit by uncontrolled natural illumination, from very few or even a single input image.

We present a novel method to generate high-quality simplicial meshes with specified anisotropy. Given a surface or volumetric domain equipped with a Riemannian metric that encodes the desired anisotropy, we transform the problem to one of functional approximation. We construct a convex function over each mesh simplex whose Hessian locally matches the Riemannian metric, and iteratively adapt vertex positions and mesh connectivity to minimize the difference between the target convex functions and their piecewise-linear interpolation over the mesh. Our method generalizes optimal Delaunay triangulation and leads to a simple and efficient algorithm. We demonstrate its quality and speed compared to state-of-the-art methods on a variety of domains and metrics.

The acoustic wave field in a complex scene is a chaotic 7D function of time and the positions of source and listener, making it difficult to compress and interpolate. This hampers precomputed approaches which tabulate impulse responses (IRs) to allow immersive, real-time sound propagation in static scenes. We code the field of time-varying IRs in terms of a few perceptual parameters derived from the IR's energy decay. The resulting parameter fields are spatially smooth and compressed using a lossless scheme similar to PNG. We show that this encoding removes two of the seven dimensions, making it possible to handle large scenes such as entire game maps within 100MB of memory. Run-time decoding is fast, taking 100 μ s per source. We introduce an efficient and scalable method for convolutionally rendering acoustic parameters that generates artifact-free audio even for fast motion and sudden changes in reverberance. We demonstrate convincing spatially-varying effects in complex scenes including occlusion/obstruction and reverberation, in our system integrated with Unreal Engine 3 ™ .

Masonry structures must be compressively self-supporting; designing such surfaces forms an important topic in architecture as well as a challenging problem in geometric modeling. Under certain conditions, a surjective mapping exists between a power diagram , defined by a set of 2D vertices and associated weights, and the reciprocal diagram that characterizes the force diagram of a discrete self-supporting network. This observation lets us define a new and convenient parameterization for the space of self-supporting networks. Based on it and the discrete geometry of this design space, we present novel geometry processing methods including surface smoothing and remeshing which significantly reduce the magnitude of force densities and homogenize their distribution.

We exploit the falloff of acuity in the visual periphery to accelerate graphics computation by a factor of 5-6 on a desktop HD display (1920x1080). Our method tracks the user's gaze point and renders three image layers around it at progressively higher angular size but lower sampling rate. The three layers are then magnified to display resolution and smoothly composited. We develop a general and efficient antialiasing algorithm easily retrofitted into existing graphics code to minimize "twinkling" artifacts in the lower-resolution layers. A standard psychophysical model for acuity falloff assumes that minimum detectable angular size increases linearly as a function of eccentricity. Given the slope characterizing this falloff, we automatically compute layer sizes and sampling rates. The result looks like a full-resolution image but reduces the number of pixels shaded by a factor of 10-15. We performed a user study to validate these results. It identifies two levels of foveation quality: a more conservative one in which users reported foveated rendering quality as equivalent to or better than non-foveated when directly shown both, and a more aggressive one in which users were unable to correctly label as increasing or decreasing a short quality progression relative to a high-quality foveated reference. Based on this user study, we obtain a slope value for the model of 1.32-1.65 arc minutes per degree of eccentricity. This allows us to predict two future advantages of foveated rendering: (1) bigger savings with larger, sharper displays than exist currently (e.g. 100 times speedup at a field of view of 70° and resolution matching foveal acuity), and (2) a roughly linear (rather than quadratic or worse) increase in rendering cost with increasing display field of view, for planar displays at a constant sharpness.

We introduce a new method to synthesize mechanical toys solely from the motion of their features. The designer specifies the geometry and a time-varying rotation and translation of each rigid feature component. Our algorithm automatically generates a mechanism assembly located in a box below the feature base that produces the specified motion. Parts in the assembly are selected from a parameterized set including belt-pulleys, gears, crank-sliders, quick-returns, and various cams (snail, ellipse, and double-ellipse). Positions and parameters for these parts are optimized to generate the specified motion, minimize a simple measure of complexity, and yield a well-distributed layout of parts over the driving axes. Our solution uses a special initialization procedure followed by simulated annealing to efficiently search the complex configuration space for an optimal assembly.

Recent work defines vector graphics using diffusion between colored curves. We explore higher-order fairing to enable more natural interpolation and greater expressive control. Specifically, we build on thin-plate splines which provide smoothness everywhere except at user-specified tears and creases (discontinuities in value and derivative respectively). Our system lets a user sketch discontinuity curves without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth interpolation subject to the outlines. We refine the representation with novel contour and slope curves, which anisotropically constrain interpolation derivatives. Compound curves further increase editing power by expanding a single curve into multiple offsets of various basic types (value, tear, crease, slope, and contour). The vector constraints are discretized over an image grid, and satisfied using a hierarchical solver. We demonstrate interactive authoring on a desktop CPU.

We present a simple, fast solution for reflectance acquisition using tools that fit into a pocket. Our method captures video of a flat target surface from a fixed video camera lit by a hand-held, moving, linear light source. After processing, we obtain an SVBRDF. We introduce a BRDF chart , analogous to a color "checker" chart, which arranges a set of known-BRDF reference tiles over a small card. A sequence of light responses from the chart tiles as well as from points on the target is captured and matched to reconstruct the target's appearance. We develop a new algorithm for BRDF reconstruction which works directly on these LDR responses, without knowing the light or camera position, or acquiring HDR lighting. It compensates for spatial variation caused by the local (finite distance) camera and light position by warping responses over time to align them to a specular reference. After alignment, we find an optimal linear combination of the Lambertian and purely specular reference responses to match each target point's response. The same weights are then applied to the corresponding (known) reference BRDFs to reconstruct the target point's BRDF. We extend the basic algorithm to also recover varying surface normals by adding two spherical caps for diffuse and specular references to the BRDF chart. We demonstrate convincing results obtained after less than 30 seconds of data capture, using commercial mobile phone cameras in a casual environment.

Manifold bootstrapping is a new method for data-driven modeling of real-world, spatially-varying reflectance, based on the idea that reflectance over a given material sample forms a low-dimensional manifold. It provides a high-resolution result in both the spatial and angular domains by decomposing reflectance measurement into two lower-dimensional phases. The first acquires representatives of high angular dimension but sampled sparsely over the surface, while the second acquires keys of low angular dimension but sampled densely over the surface. We develop a hand-held, high-speed BRDF capturing device for phase one measurements. A condenser-based optical setup collects a dense hemisphere of rays emanating from a single point on the target sample as it is manually scanned over it, yielding 10 BRDF point measurements per second. Lighting directions from 6 LEDs are applied at each measurement; these are amplified to a full 4D BRDF using the general (NDF-tabulated) microfacet model. The second phase captures N =20-200 images of the entire sample from a fixed view and lit by a varying area source. We show that the resulting N -dimensional keys capture much of the distance information in the original BRDF space, so that they effectively discriminate among representatives, though they lack sufficient angular detail to reconstruct the SVBRDF by themselves. At each surface position, a local linear combination of a small number of neighboring representatives is computed to match each key, yielding a high-resolution SVBRDF. A quick capture session (10-20 minutes) on simple devices yields results showing sharp and anisotropic specularity and rich spatial detail.

We present a method for real-time sound propagation that captures all wave effects, including diffraction and reverberation, for multiple moving sources and a moving listener in a complex, static 3D scene. It performs an offline numerical simulation over the scene and then applies a novel technique to extract and compactly encode the perceptually salient information in the resulting acoustic responses. Each response is automatically broken into two phases: early reflections (ER) and late reverberation (LR), via a threshold on the temporal density of arriving wavefronts. The LR is simulated and stored in the frequency domain, once per room in the scene. The ER accounts for more detailed spatial variation, by recording a set of peak delays/amplitudes in the time domain and a residual frequency response sampled in octave frequency bands, at each source/receiver point pair in a 5D grid. An efficient run-time uses this precomputed representation to perform binaural sound rendering based on frequency-domain convolution. Our system demonstrates realistic, wave-based acoustic effects in real time, including diffraction low-passing behind obstructions, sound focusing, hollow reverberation in empty rooms, sound diffusion in fully-furnished rooms, and realistic late reverberation.

Abstract We present a real‐time method for rendering global illumination effects from large area and environmental lights on dynamic height fields. In contrast to previous work, our method handles inter‐reflections (indirect lighting) and non‐diffuse surfaces. To reduce sampling, we construct one multi‐resolution pyramid for height variation to compute direct shadows, and another pyramid for each indirect bounce of incident radiance to compute inter‐reflections. The basic principle is to sample the points blocking direct light, or shedding indirect light, from coarser levels of the pyramid the farther away they are from a given receiver point. We unify the representation of visibility and indirect radiance at discrete azimuthal directions (i.e., as a function of a single elevation angle) using the concept of a “casting set” of visible points along this direction whose contributions are collected in the basis of normalized Legendre polynomials. This analytic representation is compact, requires no precomputation, and allows efficient integration to produce the spherical visibility and indirect radiance signals. Sub‐sampling visibility and indirect radiance, while shading with full‐resolution surface normals, further increases performance without introducing noticeable artifacts. Our method renders 512×512 height fields (> 500K triangles) at 36Hz.

We describe a technique for real-time rendering of dynamic, spatially-varying BRDFs in static scenes with all-frequency shadows from environmental and point lights. The 6D SVBRDF is represented with a general microfacet model and spherical lobes fit to its 4D spatially-varying normal distribution function (SVNDF). A sum of spherical Gaussians (SGs) provides an accurate approximation with a small number of lobes. Parametric BRDFs are fit on-the-fly using simple analytic expressions; measured BRDFs are fit as a preprocess using nonlinear optimization. Our BRDF representation is compact, allows detailed textures, is closed under products and rotations, and supports reflectance of arbitrarily high specularity. At run-time, SGs representing the NDF are warped to align the half-angle vector to the lighting direction and multiplied by the microfacet shadowing and Fresnel factors. This yields the relevant 2D view slice on-the-fly at each pixel, still represented in the SG basis. We account for macro-scale shadowing using a new, nonlinear visibility representation based on spherical signed distance functions (SSDFs). SSDFs allow per-pixel interpolation of high-frequency visibility without ghosting and can be multiplied by the BRDF and lighting efficiently on the GPU.

Abstract We present a new, real‐time method for rendering soft shadows from large light sources or lighting environments on dynamic height fields. The method first computes a horizon map for a set of azimuthal directions. To reduce sampling, we compute a multi‐resolution pyramid on the height field. Coarser pyramid levels are indexed as the distance from caster to receiver increases. For every receiver point and every azimuthal direction, a smooth function of blocking angle in terms of log distance is reconstructed from a height difference sample at each pyramid level. This function's maximum approximates the horizon angle. We then sum visibility at each receiver point over wedges determined by successive pairs of horizon angles. Each wedge represents a linear transition in blocking angle over its azimuthal extent. It is precomputed in the order‐4 spherical harmonic (SH) basis, for a canonical azimuthal origin and fixed extent, resulting in a 2D table. The SH triple product of 16D vectors representing lighting, total visibility, and diffuse reflectance then yields the soft‐shadowed result. Two types of light sources are considered; both are distant and low‐frequency. Environmental lights require visibility sampling around the complete 360 ° azimuth, while key lights sample visibility within a partial swath. Restricting the swath concentrates samples where the light comes from (e.g. 3 azimuthal directions vs. 16‐32 for a full swath) and obtains sharper shadows. Our GPU implementation handles height fields up to 1024 × 1024 in real‐time. The computation is simple, local, and parallel, with performance independent of geometric content.

We present a new technique for the visual modeling of spatiallyvarying anisotropic reflectance using data captured from a single view. Reflectance is represented using a microfacet-based BRDF which tabulates the facets' normal distribution (NDF) as a function of surface location. Data from a single view provides a 2D slice of the 4D BRDF at each surface point from which we fit a partial NDF. The fitted NDF is partial because the single view direction coupled with the set of light directions covers only a portion of the "half-angle" hemisphere. We complete the NDF at each point by applying a novel variant of texture synthesis using similar, overlapping partial NDFs from other points. Our similarity measure allows azimuthal rotation of partial NDFs, under the assumption that reflectance is spatially redundant but the local frame may be arbitrarily oriented. Our system includes a simple acquisition device that collects images over a 2D set of light directions by scanning a linear array of LEDs over a flat sample. Results demonstrate that our approach preserves spatial and directional BRDF details and generates a visually compelling match to measured materials.

We present a new, general, and real-time technique for soft global illumination in low-frequency environmental lighting. It accumulates over relatively few spherical proxies which approximate the light blocking and re-radiating effect of dynamic geometry. Soft shadows are computed by accumulating log visibility vectors for each sphere proxy as seen by each receiver point. Inter-reflections are computed by accumulating vectors representing the proxy's unshadowed radiance when illuminated by the environment. Both vectors capture low-frequency directional dependence using the spherical harmonic basis. We also present a new proxy accumulation strategy that splats each proxy to receiver pixels in image space to collect its shadowing and indirect lighting contribution. Our soft GI rendering pipeline unifies direct and indirect soft effects with a simple accumulation strategy that maps entirely to the GPU and outperforms previous vertex-based methods.

Previous methods for soft shadows numerically integrate over many light directions at each receiver point, testing blocker visibility in each direction. We introduce a method for real-time soft shadows in dynamic scenes illuminated by large, low-frequency light sources where such integration is impractical. Our method operates on vectors representing low-frequency visibility of blockers in the spherical harmonic basis. Blocking geometry is modeled as a set of spheres; relatively few spheres capture the low-frequency blocking effect of complicated geometry. At each receiver point, we compute the product of visibility vectors for these blocker spheres as seen from the point. Instead of computing an expensive SH product per blocker as in previous work, we perform inexpensive vector sums to accumulate the log of blocker visibility. SH exponentiation then yields the product visibility vector over all blockers. We show how the SH exponentiation required can be approximated accurately and efficiently for low-order SH, accelerating previous CPU-based methods by a factor of 10 or more, depending on blocker complexity, and allowing real-time GPU implementation.

Precomputed radiance transfer (PRT) captures realistic lighting effects from distant, low-frequency environmental lighting but has been limited to static models or precomputed sequences. We focus on PRT for local effects such as bumps, wrinkles, or other detailed features, but extend it to arbitrarily deformable models. Our approach applies zonal harmonics (ZH) which approximate spherical functions as sums of circularly symmetric Legendre polynomials around different axes. By spatially varying both the axes and coefficients of these basis functions, we can fit to spatially varying transfer signals. Compared to the spherical harmonic (SH) basis, the ZH basis yields a more compact approximation. More important, it can be trivially rotated whereas SH rotation is expensive and unsuited for dense per-vertex or per-pixel evaluation. This property allows, for the first time, PRT to be mapped onto deforming models which re-orient the local coordinate frame. We generate ZH transfer models by fitting to PRT signals simulated on meshes or simple parametric models for thin membranes and wrinkles. We show how shading with ZH transfer can be significantly accelerated by specializing to a given lighting environment. Finally, we demonstrate real-time rendering results with soft shadows, inter-reflections, and subsurface scatter on deforming models.

We present a novel technique for large deformations on 3D meshes using the volumetric graph Laplacian. We first construct a graph representing the volume inside the input mesh. The graph need not form a solid meshing of the input mesh's interior; its edges simply connect nearby points in the volume. This graph's Laplacian encodes volumetric details as the difference between each point in the graph and the average of its neighbors. Preserving these volumetric details during deformation imposes a volumetric constraint that prevents unnatural changes in volume. We also include in the graph points a short distance outside the mesh to avoid local self-intersections. Volumetric detail preservation is represented by a quadric energy function. Minimizing it preserves details in a least-squares sense, distributing error uniformly over the whole deformed mesh. It can also be combined with conventional constraints involving surface positions, details or smoothness, and efficiently minimized by solving a sparse linear system.We apply this technique in a 2D curve-based deformation system allowing novice users to create pleasing deformations with little effort. A novel application of this system is to apply nonrigid and exaggerated deformations of 2D cartoon characters to 3D meshes. We demonstrate our system's potential with several examples.

We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of per-point weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results per-point (on the GPU). Since the output of the matrix is lower-dimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.

Radiance transfer represents how generic source lighting is shadowed and scattered by an object to produce view-dependent appearance. We generalize by rendering transfer at two scales. A macro-scale is coarsely sampled over an object's surface, providing global effects like shadows cast from an arm onto a body. A meso-scale is finely sampled over a small patch to provide local texture. Low-order (25D) spherical harmonics represent low-frequency lighting dependence for both scales. To render, a coefficient vector representing distant source lighting is first transformed at the macro-scale by a matrix at each vertex of a coarse mesh. The resulting vectors represent a spatially-varying hemisphere of lighting incident to the meso-scale. A 4D function, called a radiance transfer texture (RTT), then specifies the surface's meso-scale response to each lighting basis component, as a function of a spatial index and a view direction. Finally, a 25D dot product of the macro-scale result vector with the vector looked up from the RTT performs the correct shading integral. We use an id map to place RTT samples from a small patch over the entire object; only two scalars are specified at high spatial resolution. Results show that bi-scale decomposition makes preprocessing practical and efficiently renders self-shadowing and interreflection effects from dynamic, low-frequency light sources at both scales.

We present a new, real-time method for rendering diffuse and glossy objects in low-frequency lighting environments that captures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object's surface representing transfer of arbitrary, low-frequency incident lighting into transferred radiance which includes global effects like shadows and interreflections from the object onto itself. At run-time, these transfer functions are applied to actual incident lighting. Dynamic, local lighting is handled by sampling it close to the object every frame; the object can also be rigidly rotated with respect to the lighting and vice versa. Lighting and transfer functions are represented using low-order spherical harmonics. This avoids aliasing and evaluates efficiently on graphics hardware by reducing the shading integral to a dot product of 9 to 25 element vectors for diffuse receivers. Glossy objects are handled using matrices rather than vectors. We further introduce functions for radiance transfer from a dynamic lighting environment through a preprocessed object to neighboring points in space. These allow soft shadows and caustics from rigidly moving objects to be cast onto arbitrary, dynamic receivers. We demonstrate real-time global lighting effects with this approach.

Static environment maps fail to capture local reflections including effects like selfreflections and parallax in the reflected imagery. We instead propose parameterized environment maps (PEMs), a set of per-view environment maps which accurately reproduce local reflections at each viewpoint as computed by an offline ray tracer. Even with a small set of viewpoint samples, PEMs support plausible movement away from and between the pre-rendered viewpoint samples while maintaining local reflections. They also make use of environment maps supported in graphics hardware to provide real-time exploration of the pre-rendered space. In addition to parameterization by viewpoint, our notion of PEMextends to general, multidimensional parameterizations of the scene, including relative motions of objects and lighting changes. Our contributions include a technique for inferring environment maps providing a close match to ray-traced imagery. We also explicitly infer and encode all MIPMAP levels of the PEMs to achieve higher accuracy. We propose layered environment maps that separate local and distant reflected geometry. We explore several types of environment maps including finite spheres, ellipsoids, and boxes that better approximate the environmental geometry. We demonstrate results showing faithful local reflections in an interactive viewer.

Given an arbitrary mesh, we present a method to construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. Our method considers two important goals simultaneously. It minimizes texture stretch (small texture distances mapped onto large surface distances) to balance sampling rates over all locations and directions on the surface. It also minimizes texture deviation (“slippage” error based on parametric correspondence) to obtain accurate textured mesh approximations. The method begins by partitioning the mesh into charts using planarity and compactness heuristics. It creates a stretch-minimizing parametrization within each chart, and resizes the charts based on the resulting stretch. Next, it simplifies the mesh while respecting the chart boundaries. The parametrization is re-optimized to reduce both stretch and deviation over the whole PM sequence. Finally, the charts are packed into a texture atlas. We demonstrate using such atlases to sample color and normal maps over several models.

Approximating detailed with coarse, texture-mapped meshes results in polygonal silhouettes. To eliminate this artifact, we introduce silhouette clipping, a framework for efficiently clipping the rendering of coarse geometry to the exact silhouette of the original model. The coarse mesh is obtained using progressive hulls, a novel representation with the nesting property required for proper clipping. We describe an improved technique for constructing texture and normal maps over this coarse mesh. Given a perspective view, silhouettes are efficiently extracted from the original mesh using a precomputed search tree. Within the tree, hierarchical culling is achieved using pairs of anchored cones. The extracted silhouette edges are used to set the hardware stencil buffer and alpha buffer, which in turn clip and antialias the rendered coarse geometry. Results demonstrate that silhouette clipping can produce renderings of similar quality to high-resolution meshes in less rendering time.

We present an efficient algorithm for visibility sorting a set of moving geometric objects into a sequence of image layers which are composited to produce the final image.Instead of splitting the geometry as in previous visibility approaches, we detect mutual occluders and resolve them using an appropriate image compositing expression or merge them into a single layer.Such an algorithm has many applications in computer graphics; we demonstrate two: rendering acceleration using image interpolation and visibility-correct depth of field using image blurring.We propose a new, incremental method for identifying mutually occluding sets of objects and computing a visibility sort among these sets.Occlusion queries are accelerated by testing on convex bounding hulls; less conservative tests are also discussed.Kd-trees formed by combinations of directions in object or image space provide an initial cull on potential occluders, and incremental collision detection algorithms are adapted to resolve pairwise occlusions, when necessary.Mutual occluders are further analyzed to generate an image compositing expression; in the case of nonbinary occlusion cycles, an expression can always be generated without merging the objects into a single layer.Results demonstrate that the algorithm is practical for real-time animation of scenes involving hundreds of objects each comprising hundreds or thousands of polygons.

For decades, animated cartoons and movie special effects have factored the rendering of a scene into layers that are updated independently and composed in the final display.We apply layer factorization to real-time computer graphics.The layers allow targeting of resources, whether the ink and paint artists of cartoons or the graphics pipeline as described here, to those parts of the scene that are most important.To take advantage of frame-to-frame coherence, we generalize layer factorization to apply to both dynamic geometric objects and terms of the shading model, introduce new ways to trade off fidelity for resource use in individual layers, and show how to compute warps that reuse renderings for multiple frames.We describe quantities, called fiducials, that measure the fidelity of approximations to the original image.Layer update rates, spatial resolution, and other quality parameters are determined by geometric, photometric, visibility, and sampling fiducials weighted by the content author's preferences.We also compare the fidelity of various types of reuse warps and demonstrate the suitability of the affine warp.Using Talisman, a hardware architecture with an efficient layer primitive, the work presented here dramatically improves the geometric complexity and shading quality of scenes rendered in real-time.

We present a new method for accelerating walkthroughs of geometrically complex static scenes. As a preprocessing step, our method constructs a BSP-tree that hierarchically partitions the geometric primitives in the scene. In the course of a walkthrough, images of nodes at various levels of the hierarchy are cached for reuse in subsequent frames. A cached image is applied as a texture map to a single quadrilateral that is drawn instead of the geometry contained in the corresponding node. Visual artifacts are kept under control by using an error metric that quantifies the discrepancy between the appearance of the geometry contained in a node and the cached image. The new method is shown to achieve significant speedups for a walkthrough of a complex outdoor scene, with little or no loss in rendering quality. 1 Introduction Interactive visualization of extremely complex geometric environments is becoming an increasingly important application of computer graphics. Advances in the throughp...

Article An interactive tool for placing curved surfaces without interpenetration Share on Author: John M. Snyder Microsoft Corporation, 1 Microsoft Way, Redmond WA Microsoft Corporation, 1 Microsoft Way, Redmond WAView Profile Authors Info & Claims SIGGRAPH '95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniquesSeptember 1995 Pages 209–218https://doi.org/10.1145/218380.218444Online:15 September 1995Publication History 30citation589DownloadsMetricsTotal Citations30Total Downloads589Last 12 Months6Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We present an efficient and robust algorithm for finding points of collision between time-dependent parametric and implicit surfaces. The algorithm detects simultaneous collisions at multiple points of contact. When the regions of contact form curves or surfaces, it returns a finite set of points uniformly distributed over each contact region. Collisions can be computed for a very general class of surfaces: those for which inclusion functions can be constructed. Included in this set are the familiar kinds of surfaces and time behaviors encountered in computer graphics. We use a new interval approach for constrained minimization to detect collisions, and a tangency condition to reduce the dimensionality of the search space. These approaches make interval methods practical for multi-point collisions between complex surfaces. An interval Newton method based on the solution of the interval linear equation is used to speed convergence to the collision time and location. This method is mor...

This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are required: SOLVE, which computes solutions to a system of constraints, and MINIMIZE, which computes the global minimum of a function, subject to a system of constraints. We present algorithms for SOLVE and MINIMIZE using interval analysis as the conceptual framework. Crucial to the technique is the creation of "inclusion functions" for each constraint and function to be minimized. Inclusion functions compute a bound on the range of a function, given a similar bound on its domain, allowing a branch and bound approach to constraint solution and constrained minimization. Inclusion functions also allow the MINIMIZE algorithm to compute global rather than local minima, unlike many other numerica...

article Free Access Share on Generative modeling: a symbolic system for geometric modeling Authors: John M. Snyder California Institute of Technology, Pasadena, CA California Institute of Technology, Pasadena, CAView Profile , James T. Kajiya California Institute of Technology, Pasadena, CA California Institute of Technology, Pasadena, CAView Profile Authors Info & Claims ACM SIGGRAPH Computer GraphicsVolume 26Issue 2July 1992 pp 369–378https://doi.org/10.1145/142920.134094Published:01 July 1992Publication History 47citation952DownloadsMetricsTotal Citations47Total Downloads952Last 12 Months38Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

An approach to ray tracing complex models containing mathematically defined surfaces is presented. Parametric and implicit surfaces, and boolean combinations of these, are first tessellated into triangles. The resulting triangles from many such surfaces are organized in a hierachy of lists and 3D grids, allowing efficient calculation of ray/model intersections.The technique has been used to ray trace models containing billions of traiangles and surfaces never before ray traced. The organizing scheme developed is also independently useful for efficiently ray tracing any complex model, whether or not it contains surface tessellations.