Vinícius Silva

Pontifícia Universidade Católica do Rio de Janeiro · Instituto Tecgraf

We present MR-Net, a general architecture for multiresolution sinusoidal neural networks, and a framework for imaging applications based on this architecture. We extend sinusoidal networks, and we build an infrastructure to train networks to represent signals in multiresolution. Our coordinate-based networks, namely L-Net, M-Net, and S-Net, are con...

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towa...

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows ter...

We present MR-Net, a general architecture for multiresolution neural networks, and a framework for imaging applications based on this architecture. Our coordinate-based networks are continuous both in space and in scale as they are composed of multiple stages that progressively add finer details. Besides that, they are a compact and efficient repre...

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows te...

This book explores the visualization of three-dimensional non-Euclidean spaces using ray- tracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. The content of this book serves both ex...

We introduce MIP-plicits, a novel approach for rendering 3D and 4D Neural Implicits that divide the problem into macro and meso components. We rely on the iterative nature of the sphere tracing algorithm, the spatial continuity of the Neural Implicit representation, and the association of the network architecture complexity with the details it can...

Global illumination is a collection of algorithms in computer graphics that are employed to mimic realistic lighting in 3D scenes. The complexity of these algorithms depends on the indirect illumination, which does not directly come from the light sources (direct illumination), but from reflections on other surfaces at the scene. Computing reflecti...

This chapter explores the Riemannian ray tracing (introduced in Chapter 5) in non-isotropic geometries to render inside views of the most non-trivial Thurston geometries: Nil, Sol, and SL2(R)~. These Riemannian manifolds are fundamental in the Geometrization conjecture as we saw in Section 2.6.

A 3D visualization algorithm renders an image of a 3D scene according to a view specification. The input of the algorithm is a scene description composed of ambient three-dimensional space, 3D shapes placed in this ambient space, and a viewpoint, among other parameters. The output is a 2D view. In that sense, the rendering process transforms geomet...

Riemannian ray tracing was defined in Chapter 5 to visualize classical non-Euclidean spaces. This chapter focuses on Riemannian metric constructions in ℝ3 to explore special effects like warping, mirages, and deformations. We investigate the possibility of using graphs of functions and diffeomorphism to produce such effects. For these, their Rieman...

We present some expressive output images from our implementation (given in Chapter 5) of the algorithm in GPU using RTX. This chapter consider examples of 3-manifolds and orbifolds modeled by the classical geometries. For visualizations using classical rasterization techniques, see Weeks [Wee02].

In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization of relevant three-dimensional manifolds in the context of the Geometrization Conjecture.

This survey presents methods that use neural networks for implicit representations of 3D geometry-neural implicit functions. We explore the different aspects of neural implicit functions for shape modeling and synthesis. We aim to provide a theoretical analysis of 3D shape reconstruction using deep neural networks and introduce a discussion between...

A manifold is a topological space that is locally Euclidean. Manifolds are important because they arise naturally in a variety of mathematical and physical applications as global objects with simpler local structure. In this paper we propose a technique for immersive visualization of relevant three-dimensional manifolds in the context of the Geomet...

This chapter describes how to use intersection and closest-hit shaders to implement real-time visualizations of complex fractals using distance functions. The Mandelbulb and Julia sets are used as examples.

NVIDIA's RTX platform has been changing, and extending possibilities for real-time computer graphics applications. It's still a long way to fully understand and optimize its use, and this task is itself a fertile field for scientific progress. However, another path is to explore the platform as an expansion of paradigms for other problems. For exam...

NVIDIA's RTX platform has been changing, and extending possibilities for real-time computer graphics applications. It's still a long way to fully understand and optimize its use, and this task is itself a fertile field for scientific progress. However, another path is to explore the platform as an expansion of paradigms for other problems. For exam...

This chapter describes how to use intersection and closest-hit shaders to implement real-time visualizations of complex fractals using distance functions. The Mandelbulb and Julia Sets are used as examples.

A couple of years after its launch, NVidia RTX is established as the standard low-level real-time ray tracing platform. From the start, it came with support for both triangle and procedural primitives. However, the workflow to deal with each primitive type is different in essence. Every triangle geometry uses a built-in intersection shader, resulti...

These images are inside views of famous 3-manifolds, with their geometries modeled by Thurston geometries. Such spaces date back to the famous Thurston geometrization conjecture, proved in 2003 by Grigori Perelman. The theorem states that every compact 3D manifold decomposes into pieces whose geometry is modeled by Thurston geometries. The even mor...

This paper presents a novel path tracer algorithm for immersive visualization of Riemannian manifolds. To do this, we introduce Riemannian illumination, a generalization of classical Computer Graphics illumination models. In this context, global light transport is expressed by extending the rendering equation to Riemannian manifolds. Using Monte Ca...

In this work, we propose a novel ray tracing model for immersive visualization of Riemannian manifolds. To do this we introduce Riemannian ray tracing, a generalization of the classic Computer Graphics concept. Specifically, our model is capable of interactive real-time VR visualizations of Nil, Sol, and SL2(R), Thurston’s most nontrivial geometrie...

Rendering large point clouds ordinarily requires building a hierarchical data structure for accessing the points that best represent the object for a given viewing frustum and level-of-detail. The building of such data structures frequently represents a large portion of the cost of the rendering pipeline both in terms of time and space complexity,...

This paper presents a system for immersive visualization of the Classical Non-Euclidean spaces using real-time ray tracing. It exploits the capabilities of the latest generation of GPU's based on the NVIDIA's Turing architecture in order to develop new methods for intuitive exploration of landscapes featuring non-trivial geometry and topology in vi...

Local and global illumination were recently defined in Riemannian manifolds to visualize classical Non-Euclidean spaces. This work focuses on Riemannian metric construction in $\mathbb{R}^3$ to explore special effects like warping, mirages, and deformations. We investigate the possibility of using graphs of functions and diffeomorphism to produce s...

This paper presents a path tracer algorithm to compute the global illumination of non-Euclidean manifolds. We use the 3D torus as an example.

NVidia RTX platform has been changing and extending the possibilities for real time Computer Graphics applications. It is the first time in history that retail graphics cards have full hardware support for ray tracing primitives. It still a long way to fully understand and optimize its use and this task itself is a fertile field for scientific prog...

This paper presents a system for immersive visualization of Non-Euclidean spaces using real-time ray tracing. It exploits the capabilities of the new generation of GPU’s based on the NVIDIA’s Turing architecture in order to develop new methods for intuitive exploration of landscapes featuring non-trivial geometry and topology in virtual reality. P...

We present a \real-time" ray tracing algorithm to immersive visualization of manifolds with their geometries locally modeled by Nil, Sol, and SL2(R) geometries: Thurston's three most nontrivial geometries.

This paper presents a system for immersive visualization of Non-Euclidean spaces using real-time ray tracing. It exploits the capabilities of the new generation of GPU’s based on the NVIDIA’s Turing architecture in order to develop new methods for intuitive exploration of landscapes featuring nontrivial geometry and topology in virtual reality.

Rendering large point clouds ordinarily requires building a hierarchical data structure for accessing the points that best represent the object for a given viewing frustum and level-of-detail. The building of such data structures frequently represents a large portion of the cost of the rendering pipeline both in terms of time and space complexity,...

This study presents the results of research in dynamic load balancing for Continuous Collision Detection (CCD) using Bounding Volumes Hierarchies (BVHs) on Graphics Processing Units (GPUs). Hierarchy traversal is a challenging problem for GPU computing, since the work load of traversal has a very dynamic nature. Current research resulted in methods...