Abstract Although modern path tracers are successfully being applied to many rendering applications, there is considerable interest to push them towards ever‐decreasing sampling rates. As the sampling rate is substantially reduced, however, even Monte Carlo (MC) denoisers–which have been very successful at removing large amounts of noise–typically do not produce acceptable final results. As an orthogonal approach to this, we believe that good importance sampling of paths is critical for producing better‐converged, path‐traced images at low sample counts that can then, for example, be more effectively denoised. However, most recent importance‐sampling techniques for guiding path tracing (an area known as “path guiding”) involve expensive online (per‐scene) training and offer benefits only at high sample counts. In this paper, we propose an offline, scene‐independent deep‐learning approach that can importance sample first‐bounce light paths for general scenes without the need of the costly online training, and can start guiding path sampling with as little as 1 sample per pixel. Instead of learning to “overfit” to the sampling distribution of a specific scene like most previous work, our data‐driven approach is trained a priori on a set of training scenes on how to use a local neighborhood of samples with additional feature information to reconstruct the full incident radiance at a point in the scene, which enables first‐bounce importance sampling for new test scenes. Our solution is easy to integrate into existing rendering pipelines without the need for retraining, as we demonstrate by incorporating it into both the Blender/Cycles and Mitsuba path tracers. Finally, we show how our offline, deep importance sampler (ODIS) increases convergence at low sample counts and improves the results of an off‐the‐shelf denoiser relative to other state‐of‐the‐art sampling techniques.

Regression-based algorithms have shown to be good at denoising Monte Carlo (MC) renderings by leveraging its inexpensive by-products (e.g., feature buffers). However, when using higher-order models to handle complex cases, these techniques often overfit to noise in the input. For this reason, supervised learning methods have been proposed that train on a large collection of reference examples, but they use explicit filters that limit their denoising ability. To address these problems, we propose a novel, supervised learning approach that allows the filtering kernel to be more complex and general by leveraging a deep convolutional neural network (CNN) architecture. In one embodiment of our framework, the CNN directly predicts the final denoised pixel value as a highly non-linear combination of the input features. In a second approach, we introduce a novel, kernel-prediction network which uses the CNN to estimate the local weighting kernels used to compute each denoised pixel from its neighbors. We train and evaluate our networks on production data and observe improvements over state-of-the-art MC denoisers, showing that our methods generalize well to a variety of scenes. We conclude by analyzing various components of our architecture and identify areas of further research in deep learning for MC denoising.

This paper introduces a new computational method to solve differential equations on subdivision surfaces. Our approach adapts the numerical framework of Discrete Exterior Calculus (DEC) from the polygonal to the subdivision setting by exploiting the refin-ability of subdivision basis functions. The resulting Subdivision Exterior Calculus (SEC) provides significant improvements in accuracy compared to existing polygonal techniques, while offering exact finite-dimensional analogs of continuum structural identities such as Stokes' theorem and Helmholtz-Hodge decomposition. We demonstrate the versatility and efficiency of SEC on common geometry processing tasks including parameterization, geodesic distance computation, and vector field design.

Subspace deformable body simulations can be very fast, but can behave unrealistically when behaviors outside the prescribed subspace such as novel external collisions, are encountered. We address this limitation by presenting a fast, flexible new method that allows full space computation to be activated in the neighborhood of novel events while the rest of the body still computes in a subspace. We achieve this using a method we call subspace condensation , a variant on the classic static condensation precomputation. However, instead of a precomputation, we use the speed of subspace methods to perform the condensation at every frame. This approach allows the full space regions to be specified arbitrarily at runtime, and forms a natural two-way coupling with the subspace regions. While condensation is usually only applicable to linear materials, the speed of our technique enables its application to non-linear materials as well. We show the effectiveness of our approach by applying it to a variety of articulated character scenarios.

We present a new approach to clothing simulation using low-dimensional linear subspaces with temporally adaptive bases. Our method exploits full-space simulation training data in order to construct a pool of low-dimensional bases distributed across pose space. For this purpose, we interpret the simulation data as offsets from a kinematic deformation model that captures the global shape of clothing due to body pose. During subspace simulation, we select low-dimensional sets of basis vectors according to the current pose of the character and the state of its clothing. Thanks to this adaptive basis selection scheme, our method is able to reproduce diverse and detailed folding patterns with only a few basis vectors. Our experiments demonstrate the feasibility of subspace clothing simulation and indicate its potential in terms of quality and computational efficiency.

About the Speaker Tony DeRose is currently a Senior Scientist and lead of the Research Group at Pixar Animation Studios. He received a BS in Physics in from the University of California, Davis, and a Ph.D. in Computer Science from the University of California, Berkeley. From 1986 to 1995 Dr. DeRose was a Professor of Computer Science and Engineering at the University of Washington. In 1998, he was a major contributor to the Oscar (c) winning short film "Geri's game", in 1999 he received the ACM SIGGRAPH Computer Graphics Achievement Award, and in 2006 he received a Scientific and Technical Academy Award (c) for his work on surface representations. In addition to his research interests, Tony is also involved in a number of initiatives to help make math, science, and engineering education more inspiring and relevant for middle and high school students. One such initiative is the Young Makers Program (youngmakers.org) that supports youth in building ambitious hands-on projects of their own choosing.

Current multitouch frameworks require application developers to write recognition code for custom gestures; this code is split across multiple event-handling callbacks. As the number of custom gestures grows it becomes increasingly difficult to 1) know if new gestures will conflict with existing gestures, and 2) know how to extend existing code to reliably recognize the complete gesture set. Proton is a novel framework that addresses both of these problems. Using Proton, the application developer declaratively specifies each gesture as a regular expression over a stream of touch events. Proton statically analyzes the set of gestures to report conflicts, and it automatically creates gesture recognizers for the entire set. To simplify the creation of complex multitouch gestures, Proton introduces gesture tablature, a graphical notation that concisely describes the sequencing of multiple interleaved touch actions over time. Proton contributes a graphical editor for authoring tablatures and automatically compiles tablatures into regular expressions. We present the architecture and implementation of Proton, along with three proof-of-concept applications. These applications demonstrate the expressiveness of the framework and show how Proton simplifies gesture definition and conflict resolution.

Proton++ is a declarative multitouch framework that allows developers to describe multitouch gestures as regular expressions of touch event symbols. It builds on the Proton framework by allowing developers to incorporate custom touch attributes directly into the gesture description. These custom attributes increase the expressivity of the gestures, while preserving the benefits of Proton: automatic gesture matching, static analysis of conflict detection, and graphical gesture creation. We demonstrate Proton++'s flexibility with several examples: a direction attribute for describing trajectory, a pinch attribute for detecting when touches move towards one another, a touch area attribute for simulating pressure, an orientation attribute for selecting menu items, and a screen location attribute for simulating hand ID. We also use screen location to simulate user ID and enable simultaneous recognition of gestures by multiple users. In addition, we show how to incorporate timing into Proton++ gestures by reporting touch events at a regular time interval. Finally, we present a user study that suggests that users are roughly four times faster at interpreting gestures written using Proton++ than those written in procedural event-handling code commonly used today.

We present a novel method for high-performance GPU-based rendering of Catmull-Clark subdivision surfaces. Unlike previous methods, our algorithm computes the true limit surface up to machine precision, and is capable of rendering surfaces that conform to the full RenderMan specification for Catmull-Clark surfaces. Specifically, our algorithm can accommodate base meshes consisting of arbitrary valence vertices and faces, and the surface can contain any number and arrangement of semisharp creases and hierarchically defined detail. We also present a variant of the algorithm which guarantees watertight positions and normals, meaning that even displaced surfaces can be rendered in a crack-free manner. Finally, we describe a view-dependent level-of-detail scheme which adapts to both the depth of subdivision and the patch tessellation density. Though considerably more general, the performance of our algorithm is comparable to the best approximating method, and is considerably faster than Stam's exact method.

Set construction is the process of selecting and positioning virtual geometric objects to create a virtual environment used in a computer-animated film. Set construction artists often have a clear mental image of the set composition, but find it tedious to build their intended sets with current mouse and keyboard interfaces. We investigate whether multitouch input can ease the process of set construction. Working with a professional set construction artist at Pixar Animation Studios, we designed and developed Eden, a fully functional multitouch set construction application. In this paper, we describe our design process and how we balanced the advantages and disadvantages of multitouch input to develop usable gestures for set construction. Based on our design process and the user experiences of two set construction artists, we present a general set of lessons we learned regarding the design of a multitouch interface.

Abstract Procedural noise functions are widely used in computer graphics, from off‐line rendering in movie production to interactive video games. The ability to add complex and intricate details at low memory and authoring cost is one of its main attractions. This survey is motivated by the inherent importance of noise in graphics, the widespread use of noise in industry and the fact that many recent research developments justify the need for an up‐to‐date survey. Our goal is to provide both a valuable entry point into the field of procedural noise functions, as well as a comprehensive view of the field to the informed reader. In this report, we cover procedural noise functions in all their aspects. We outline recent advances in research on this topic, discussing and comparing recent and well‐established methods. We first formally define procedural noise functions based on stochastic processes and then classify and review existing procedural noise functions. We discuss how procedural noise functions are used for modelling and how they are applied to surfaces. We then introduce analysis tools and apply them to evaluate and compare the major approaches to noise generation. We finally identify several directions for future work.

In this paper we consider the problem of creating and controlling volume deformations used to articulate characters for use in high-end applications such as computer generated feature films. We introduce a method we call harmonic coordinates that significantly improves upon existing volume deformation techniques. Our deformations are controlled using a topologically flexible structure, called a cage, that consists of a closed three dimensional mesh. The cage can optionally be augmented with additional interior vertices, edges, and faces to more precisely control the interior behavior of the deformation. We show that harmonic coordinates are generalized barycentric coordinates that can be extended to any dimension. Moreover, they are the first system of generalized barycentric coordinates that are non-negative even in strongly concave situations, and their magnitude falls off with distance as measured within the cage.

Noise functions are an essential building block for writing procedural shaders in 3D computer graphics. The original noise function introduced by Ken Perlin is still the most popular because it is simple and fast, and many spectacular images have been made with it. Nevertheless, it is prone to problems with aliasing and detail loss. In this paper we analyze these problems and show that they are particularly severe when 3D noise is used to texture a 2D surface. We use the theory of wavelets to create a new class of simple and fast noise functions that avoid these problems.

The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the severe topological restrictions that NURBS impose. In order to move beyond these restrictions, we have recently introduced subdivision surfaces into our production environment. Subdivision surfaces are not new, but their use in high-end CG production has been limited.

Multiresolution analysis and wavelets provide useful and efficient tools for representing functions at multiple levels of detail. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation, and numerical analysis. In this article, we present a new class of wavelets, based on subdivision surfaces, that radically extends the class of representable functions. Whereas previous two-dimensional methods were restricted to functions difined on R 2 , the subdivision wavelets developed here may be applied to functions defined on compact surfaces of arbitrary topological type. We envision many applications of this work, including continuous level-of-detail control for graphics rendering, compression of geometric models, and acceleration of global illumination algorithms. Level-of-detail control for spherical domains is illustrated using two examples: shape approximation of a polyhedral model, and color approximation of global terrain data.

Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and level-of-detail control of complex meshes in a unified and theoretically sound way. We extend previous work on multiresolution analysis of meshes in two ways. First, we show how to perform multiresolution analysis of colored meshes by separately analyzing shape and color. Second, we describe efficient algorithms and data structures that allow us to incrementally construct lower resolution approximations to colored meshes from the geometry and color wavelet coefficients at interactive rates. We have integrated these algorithms in a prototype mesh viewer that supports progressive transmission, dynamic display at a constant frame rate independent of machine characteristics and load, and interactive choice of tradeoff between the amount of detail in geometry and color. The viewer operates as a helper application to Netscape, and can therefore be used to rapidly browse and di...

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...

We show how importance-driven refinement and a wavelet basis can be combined to provide an efficient solution to the global illumination problem with glossy and diffuse reflections. Importance is used to focus the computation on the interactions having the greatest impact on the visible solution. Wavelets are used to provide an efficient representation of radiance, importance, and the transport operator. We discuss a number of choices that must be made when constructing a finite element algorithm for glossy global illumination. Our algorithm is based on the standard wavelet decomposition of the transport operator and makes use of a four-dimensional wavelet representation for spatially and angularly varying radiance distributions. We use a final gathering step to improve the visual quality of the solution. Features of our implementation include support for curved surfaces as well as texture-mapped anisotropic emission and reflection functions.

In computer graphics and geometric modeling, shapes are often represented by triangular meshes.With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace.Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit.Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems.Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity.Unfortunately, meshes encountered in practice typically do not meet this requirement.In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form.The method is based on the approximation of an arbitrary initial mesh M by a mesh M J that has subdivision connectivity and is guaranteed to be within a specified tolerance.The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain.We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches.

We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering—the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data.

Toolglass™ widgets are new user interface tools that can appear, as though on a transparent sheet of glass, between an application and a traditional cursor.They can be positioned with one hand while the other positions the cursor.The widgets provide a rich and concise vocabulary for operating on application objects.These widgets may incorporate visual filters, called Magic Lens™ filters, that modify the presentation of application objects to reveal hidden information, to enhance data of interest, or to suppress distracting information.Together, these tools form a see-through interface that offers many advantages over traditional controls.They provide a new style of interaction that better exploits the user's everyday skills.They can reduce steps, cursor motion, and errors.Many widgets can be provided in a user interface, by designers and by users, without requiring dedicated screen space.In addition, lenses provide rich context-dependent feedback and the ability to view details and context simultaneously.Our widgets and lenses can be combined to form operation and viewing macros, and can be used over multiple applications.

We describe an efficient method for constructing a smooth surface that interpolates the vertices of a mesh of arbitrary topological type. Normal vectors can also be interpolated at an arbitrary subset of the vertices. The method improves on existing interpolation techniques in that it is fast, robust and general. Our approach is to compute a control mesh whose Catmull-Clark subdivision surface interpolates the given data and minimizes a smoothness or "fairness" measure of the surface. Following Celniker and Gossard, the norm we use is based on a linear combination of thin-plate and membrane energies. Even though Catmull-Clark surfaces do not possess closed-form parametrizations, we show that the relevant properties of the surfaces can be computed efficiently and without approximation. In particular, we show that (1) simple, exact interpolation conditions can be derived, and (2) the fairness norm and its derivatives can be computed exactly, without resort to numerical integration.

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices.Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data.We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).

The electronic encyclopedia exploratorium (E/sup 3/) is a vision of a future computer system-an electronic book describing how thing work. Typical articles in E/sup 3/ will describe such mechanisms as compression refrigerators, engines, telescopes, and mechanical linkages. Each article will provide simulations, three-dimensional animated graphics that the user can manipulate, laboratory areas that allow a user to modify the device or experiment with related artifacts, and a facility for asking questions and receiving customized, computer-generated English-language explanations. Some of the foundational technology is discussed, focusing on topics in artificial intelligence, graphics, and user interfaces. The initial prototype system and the technical lessons learned from it, as well as the second prototype currently under construction, are described.>

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions F and G , compute a representation of the function H = F o G . We examine this problem in detail for the case when F and G are given in either Be´zier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.

B-spline surfaces, although widely used, are incapable of describing surfaces of arbitrary topology. It is not possible to model a general closed surface or a surface with handles as a single non-degenerate B-spline. In practice such surfaces are often needed. In this paper, we present generalizations of biquadratic and bicubic B-spline surfaces that are capable of capturing surfaces of arbitrary topology (although restrictions are placed on the connectivity of the control mesh). These results are obtained by relaxing the sufficient but not necessary smoothness constraints imposed by B-splines and through the use of an n-sided generalization of Bezier surfaces called S-patches.

In this paper we introduce a class of surface patch representations, called S-patches, that unify and generalize triangular and tensor product Bézier surfaces by allowing patches to be defined over any convex polygonal domain; hence, S-patches may have any number of boundary curves. Other properties of S-patches are geometrically meaningful control points, separate control over positions and derivatives along boundary curves, and a geometric construction algorithm based on de Casteljau's algorithm. Of special interest are the regular S-patches, that is, S-patches defined on regular domain polygons. Also presented is an algorithm for smoothly joining together these surfaces with C k continuity.

In this paper, we analyze planar parametric cubic curves to determine conditions for loops, cusps, or inflection points. By expressing the curve to be analyzed as a linear combination of control points, it can be transformed such that three of the control points are mapped to specific locations on the plane. We call this image curve the canonical curve . Affine maps do not affect inflection points, cusps, or loops, so the analysis can be applied to the canonical curve instead of the original one. Since the first three points are fixed, the canonical curve is completely characterized by the position of its fourth point. The analysis therefore reduces to observing which region of the canonical plane the fourth point occupies. We demonstrate that for all parametric cubes expressed in this form, the boundaries of these regions are tonics and straight lines. Special cases include Bézier curves, B-splines, and Beta-splines. Such a characterization forms the basis for an easy and efficient solution to this problem.

This paper describes two algorithms for solving the following general problem: Given two polynomial maps f: R n ↦ R N and S R N ↦ R d in Bézier simplex form, find the composition map S = S ° f in Bézier simplex form (typically, n ≤ N ≤ d ≤ 3). One algorithm is more appropriate for machine implementation, while the other provides somewhat more geometric intuition. The composition algorithms can be applied to the following problems: evaluation, subdivision, and polynomial reparameterization of Bézier simplexes; joining Bézier curves with geometric continuity of arbitrary order; and the determination of the control nets of Bézier curves and triangular Bézier surface patches after they have undergone free-form deformations.

Catmull-Rom splines have local control, can be either approximating or interpolating, and are efficiently computable. Experience with Beta-splines has shown that it is useful to endow a spline with shape parameters , used to modify the shape of the curve or surface independently of the defining control vertices. Thus it is desirable to construct a subclass of the Catmull-Rom splines that has shape parameters. We present such a class, some members of which are interpolating and others approximating. As was done for the Beta-spline, shape parameters are introduced by requiring geometric rather than parametric continuity. Splines in this class are defined by a set of control vertices and a set of shape parameter values. The shape parameters may be applied globally, affecting the entire curve, or they may be modified locally, affecting only a portion of the curve near the corresponding joint. We show that this class results from combining geometrically continuous (Beta-spline) blending functions with a new set of geometrically continuous interpolating functions related to the classical Lagrange curves . We demonstrate the practicality of several members of the class by developing efficient computational algorithms. These algorithms are based on geometric constructions that take as input a control polygon and a set of shape parameter values and produce as output a sequence of Bézier control polygons that exactly describes the original curve. A specific example of shape design using a low-degree member of the class is given.