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Convergence Estimation of Markov-Chain Monte Carlo Rendering
We present a theoretical framework for estimating the convergence of Markov-Chain Monte Carlo (MCMC) rendering algorithms. Our theory considers both the variance and the correlation between samples, allowing for quantitative analyses of the convergence properties of MCMC estimators. With our theoretical framework, we devise a Monte Carlo (MC) algorithm capable of accurately estimating the expected MSE of an MCMC rendering algorithm. By adopting an efficient rejection sampling scheme, our MC-based MSE estimator yields a lower standard deviation compared to directly measuring the MSE by running the MCMC rendering algorithm multiple times. Moreover, we demonstrate that modifying the target distribution of the Markov chain by roughening the specular BRDF might lead to faster convergence on some scenarios. This finding suggests that our estimator can serve as a potential guide for selecting the target distribution.Eurographics Symposium on RenderingSampling and Guidin
A no-API Approach to an Introductory Computer Graphics Course
Many introductory computer graphics courses rely on the use of an established, GPU-inspired API to assist students in completing their programming assignments. However, as GPUs become more advanced, so too do the APIs used to interface with them, and as such, the complexity of using these modern APIs can sometimes overshadow the learning of basic graphics concepts that assignments are meant to illustrate. In this paper, we present an introductory course in computer graphics that takes an alternate approach whereby students do not make use of any API, instead creating their own rasterization engine written from scratch using an OpenGL-like shader-based architecture. We present the syllabus, course structure, and assignments for the course and share our observations on student learning from sections offered over the past several years.Eurographics 2025 - Education PapersEducation
Reviewer #2: ''Why didn't you use UMAP?''
t-SNE and UMAP are both popular Dimensionality Reduction (DR) techniques. Over recent years, UMAP has gained popularity, but there has been some debate on the difference between the two, and whether a preference for UMAP is justified. We apply a recently defined framework to gain new insights by analyzing these two techniques in two phases: how they model the relationships in the high-dimensional space (relationship phase) and how they create the embedding (mapping phase). Our findings suggest that the main difference lies in the UMAP mapping phase, and not in how the relationships are modeled.EuroVis 2025 - PostersPoster
World-Space Direct and Indirect Lighting Sample Reuse with Persistent Reservoirs
In the context of hardware-accelerated real-time ray tracing, existing spatiotemporal resampling techniques are still constrained by screen-space dependencies, which may lead to reuse failures. To address this issue, we propose a world-space resampling method based on a hybrid spatial structure that combines uniform grids and octrees. This persistent structure, which remains unchanged with respect to camera motion, can efficiently partition scenes while preserving geometric details. Our method begins with generating initial light samples, then remaps these samples to the spatial structure. Spatial reuse occurs entirely within individual spatial nodes. For direct illumination, we determine the spatial node of each shading point and select the world-space reservoir from that node to obtain a light sample. For indirect illumination, we trace a BRDF ray and use the world-space reservoir within the spatial node at the hit point to improve the NEE. This unified approach enables joint sample reuse for both direct and indirect illumination. Our experiments show that the proposed method achieves 20-70% reduction in RelMSE compared to screen-space ReSTIR and previous world-space methods under equal-time comparison, with 2× faster convergence rates and superior temporal stability under rapid camera motion.Pacific Graphics Conference Papers, Posters, and DemosLighting & Renderin
Voronoi Cell Interface-Based Parameter Sensitivity Analysis for Labeled Samples
Varying the input parameters of simulations or experiments often leads to different classes of results. Parameter sensitivity analysis in this context includes estimating the sensitivity to the individual parameters, that is, to understand which parameters contribute most to changes in output classifications and for which parameter ranges these occur. We propose a novel visual parameter sensitivity analysis approach based on Voronoi cell interfaces between the sample points in the parameter space to tackle the problem. The Voronoi diagram of the sample points in the parameter space is first calculated. We then extract Voronoi cell interfaces which we use to quantify the sensitivity to parameters, considering the class label information of each sample's corresponding output. Multiple visual encodings are then utilized to represent the cell interface transitions and class label distribution, including stacked graphs for local parameter sensitivity. We evaluate the approach's expressiveness and usefulness with case studies for synthetic and real-world datasets.Computer Graphics ForumDimensionality Reduction and High-Dimensional Dat
Multiphysics Simulation Methods in Computer Graphics
Physics simulation is a cornerstone of many computer graphics applications, ranging from video games and virtual reality to visual effects and computational design. The number of techniques for physically-based modeling and animation has thus skyrocketed over the past few decades, facilitating the simulation of a wide variety of materials and physical phenomena. This report captures the state-of-the-art of multiphysics simulation for computer graphics applications. Although a lot of work has focused on simulating individual phenomena, here we put an emphasis on methods developed by the computer graphics community for simulating various physical phenomena and materials, as well as the interactions between them. These include combinations of discretization schemes, mathematical modeling frameworks, and coupling techniques. For the most commonly used methods we provide an overview of the state-of-the-art and deliver valuable insights into the various approaches. A selection of software frameworks that offer out-of-the-box multiphysics modeling capabilities is also presented. Finally, we touch on emerging trends in physics-based animation that affect multiphysics simulation, including machine learning-based methods which have become increasingly popular in recent years.Computer Graphics ForumState of the Art Reports442sta
State-of-the-art Report in Sketch Processing
Sketches are a powerful and natural form of communication and are used in numerous systems for modelling, animation, shape retrieval, and editing. Despite their popularity, rough sketches - whether raster or vector, 2D or 3D - are often too complex and imprecise to be used directly and thus need special processing. For instance, many downstream applications, such as shape reconstruction, have strict requirements for cleanliness and accuracy of the input sketch. Alternatively, if a drawing is the final result, users might want to further process the sketch through tasks such as vectorization, beautification, cleanup, flat colorization, and more. In this state-of-the-art report, we identify core geometrical and topological challenges shared by many processing methods, such as identifying endpoints, strokes, and junctions. Building upon that analysis, we then survey sketch processing methods in each task category. Furthermore, we outline the commonly used sketch datasets and promising avenues for future research in sketch processing.Computer Graphics ForumState of the Art Reports442sta
MatAIRials: Isotropic Inflatable Metamaterials for Freeform Surface Design
Inflatable pads, such as those used as mattresses or protective equipment, are structures made of two planar membranes sealed according to periodic patterns, typically parallel lines or dots. In this work, we propose to treat these inflatables as metamaterials. By considering novel sealing patterns with 6-fold symmetry, we are able to generate a family of inflatable materials whose macroscale contraction is isotropic and can be modulated by controlling the parameters of the seals. We leverage this property of our inflatable materials family to propose a simple and effective algorithm based on conformal mapping that allows us to design the layout of inflatable structures that can be fabricated flat and whose inflated shapes approximate those of given target freeform surfaces.Computer Graphics ForumFabrication44
3D Shape Analysis: From Classical Optimisation Methods to Feature Learning for Shape Matching
The field of 3D shape analysis is concerned with the extraction of ''useful'' information from geometric data. Shape analysis has a high relevance for a wide range of applications, such as autonomous driving, biomedicine, or augmented/virtual reality. A core task of 3D shape analysis is shape matching, i.e. identifying correspondences between given shapes. While traditional shape matching methods rely on optimising a task-specific objective function, modern shape matching oftentimes involves datadriven components. We will first introduce traditional methods for shape matching, starting with the linear assignment problem and the quadratic assignment problem. We then present product graph formalisms in different settings, including 2D to 2D, 2D to 3D or shape to image, and 3D to 3D shape matching. We then discuss recent developments in learning-based shape correspondence methods, from learning shape correspondence with topological data structures to spectral approaches that provide efficient structure and circumvent annotations altogether. Furthermore, we discuss the practical relevance of these methods to application domains in image-to-image and shape-to-image correspondence, medical imaging and surgical navigation, and discuss how recent developments in foundation models play a role in shape analysis. Finally, the tutorial will conclude by addressing the challenges of shape matching, including handling partial shapes, and will explore potential future directions in the field.Eurographics 2025 - TutorialsTutorial