Quadric tracing : a geometric method for accelerated sphere tracing of implicit surfaces

Sphere tracing is a common raytracing technique used for rendering implicit surfaces defined by a signed distance function (SDF). However, these distance functions are often expensive to compute, prohibiting several real-time applications despite recent efforts to accelerate it. This paper presents a method to precompute a slightly augmented distance field that hugely accelerates rendering. This novel method called quadric tracing supports two configurations: (i) accelerating raytracing without losing precision, so the original SDF is still needed; (ii) entirely replacing the SDF and tracing an interpolated surface. Quadric tracing can offer 20% to 100% speedup in rendering static scenes and thereby amortizing the slowdown caused by the complexity of the geometry

Footvector representation of curves and surfaces

This paper proposes a foot mapping-based representation of curves and surfaces which is a geometric generalization of signed distance functions. We present a first-order characterization of the footvector mapping in terms of the differential geometric invariants of the represented shape and quantify the dependence of the spatial partial derivatives of the footvector mapping with respect to the principal curvatures at the footpoint. The practical applicability of foot mapping representations is highlighted by several fast iterative methods to compute the exact footvector mapping of the offset surface of CSG trees. The set operations for footpoint mappings are higher-order functions that map a tuple of functions to a single function, which poses a challenge for GPU implementations. We propose a code generation framework to overcome this that transforms CSG trees to the GLSL shader code

Synchronized-tracing of implicit surfaces

Implicit surfaces are known for their ability to represent smooth objects of arbitrary topology thanks to hierarchical combinations of primitives using a structure called a blobtree. We present a new tile-based rendering pipeline well suited for modeling scenarios, i.e., no preprocessing is required when primitive parameters are updated. When using approximate signed distance fields, we rely on compact, smooth CSG operators - extended from standard bounded operators - to compute a tight volume of interest for all primitives of the blobtree. The pipeline relies on a low-resolution A-buffer storing the primitives of interest of a given screen tile. The A-buffer is then used during ray processing to synchronize threads within a subfrustum. This allows coherent field evaluation within workgroups. We use a sparse bottom-up tree traversal to prune the blobtree on-the-fly which allows us to decorrelate field evaluation complexity from the full blobtree size. The ray processing itself is done using the sphere-tracing algorithm. The pipeline scales well to surfaces consisting of thousands of primitives

Valós idejű egysugaras puhaárnyék-számító algoritmusok távolságfüggvényekkel definiált felületekhez

A háromdimenziós színterek valószerű megjelenítésének egyik fontos eleme azárnyékok alkalmazása. Segítségükkel a színteret alkotó geometriák önmagukban vett és egymáshoz viszonyított tulajdonságai is egyértelműsödnek. A dolgozat célja olyan területtel rendelkező fényforrások által vetett valószerű, puha árnyékok kiszámítását végző algoritmusok konstruálása, amelyek távolságfüggényekkel definiált felületekkel működnek, a reprezentáció speciális tulajdonságait felhasználva a minél hatékonyabb képszintézis megvalósítására. Számításigény tekintetében a legnagyobb kihívást a térfogattal rendelkező fényforrások jelentik, melyekhez valósidejű megoldást mutatunk be. Fontos eredmény továbbá, hogy a dolgozatban bemutatott puha árnyékot számító adaptív algoritmus az approximált integrál maximális hibájával paraméterezhet

Modelado de geometría mediante "Signed Distance Functions" y desarrollo de algoritmos para su intersección

Aunque la representación más común de la geometría en entornos de ray tracing sean las mallas de triángulos, existen otras formas de representar geometrías complejas. Una de estas representaciones alternativas son las SDFs (Signed Distance Functions). Estas funciones devuelven la distancia con signo a la superficie desde cualquier punto en el espacio (para cada punto p, f(p)=0 en la superficie, f(p)0 en el exterior). Su naturaleza geométrica permite una manipulación de la geometría mucho más directa que la basada en polígonos: se modifica directamente la ecuación implícita de los volúmenes, en lugar de modificar individualmente los vértices de los polígonos. En este trabajo, presentamos una librería para la definición y manipulación de geometría mediante SDFs. Mostramos distintos ejemplos de estas funciones y sus capacidades, así como algunas aplicaciones al margen de la representación de geometría. El código implementado se ha integrado con el renderer Mitsuba2 para sintetizar escenas avanzadas con estas geometrías.Pese a todas las ventajas que ofrecen las SDFs para representar geometría, estas complican en cierta medida la intersección con las superficies. Durante los años, se han desarrollado diversos métodos para abordar este problema. En este trabajo, se han implementado tanto algunos de los algoritmos más populares de este tipo (Sphere Tracing y Enhanced Sphere Tracing), como otros métodos nuevos diseñados para este proyecto (Newton Marching y Forward Newton Marching), basados en el método de Newton para intersectar más rápidamente superficies planas. Se han comparado todos los métodos experimentalmente, y se han analizado las capacidades y limitaciones de los nuevos algoritmos. Se muestra también la posibilidad que ofrecen los nuevos algoritmos de intersectar geometría definida por otro tipo de funciones derivables (no necesariamente SDFs).<br /

Visual-auditory visualisation of dynamic multi-scale heterogeneous objects.

The multi-scale phenomena analysis is an area of active research that is connecting simulations with experiments to get a correct insight into the compound dynamic structure. Visualisation is a challenging task due to a large amount of data and a wide range of complex data representations. The analysis of dynamic multi-scale phenomena requires a combination of geometric modelling and rendering techniques for the analysis of the changes in the internal structure in the case of data coming from different sources of various nature. Moreover, the area often addresses the limitations of solely visual data representation and considers the introduction of other sensory stimuli as a well-known tool to enhance visual analysis. However, there is a lack of software tools allowing perform an advanced real-time analysis of heterogeneous phenomena properties. The hardware-accelerated volume rendering allows getting insight into the internal structure of complex multi-scale phenomena. The technique is convenient for detailed visual analysis and highlights the features of interest in complex structures and is an area of active research. However, the conventional volume visualisation is limited to the use of transfer functions that operate on homogeneous material and, as a result, does not provide flexibility in geometry and material distribution modelling that is crucial for the analysis of heterogeneous objects. Moreover, the extension to visual-auditory analysis emphasises the necessity to review the entire conventional volume visualisation pipeline. The multi-sensory feedback highly depends on the use of modern hardware and software advances for real-time modelling and evaluation. In this work, we explore the aspects of the design of visual-auditory pipelines for the analysis of dynamic multi-scale properties of heterogeneous objects that can allow overcoming well-known problems of complex representations solely visual analysis. We consider the similarities between light and sound propagation as a solution to the problem. The approach benefits from a combination of GPU accelerated ray-casting, geometry, optical and auditory properties modelling. We discuss how the modern GPU techniques application in those areas allows introducing a unified approach to the visual-auditory analysis of dynamic multi-scale heterogeneous objects. Similarly to the conventional volume rendering technique based on light propagation, we model auditory feedback as a result of initial impulse propagation through 3D space and its digital representation as a sampled sound wave obtained with the ray-casting procedure. The auditory stimuli can complement visual ones in the analysis of the dynamic multi-scale heterogeneous object. We propose a framework that facilitates the design of dynamic multi-scale heterogeneous objects visual-auditory pipeline and discuss the framework application for two case studies. The first is a molecular phenomena study that is a result of molecular dynamics simulation and quantum simulation. The second explores microstructures in digital fabrication with an arbitrary irregular lattice structure. For considered case studies, the visual-auditory techniques facilitate the interactive analysis of both spatial structure and internal multi-scale properties of volume nature in complex heterogeneous objects. A GPU-accelerated framework for visual-auditory analysis of heterogeneous objects can be applied and extend beyond this research. Thus, to specify the main direction of such extension from the point of view of the potential users, strengthen the value of this research as well as to evaluate the vision of the application of the techniques described above, we carry out a preliminary evaluation. The user study aims to compare our expectations on the visual-auditory approach with the views of the potential users of this system if it is implemented as a software product. A preliminary evaluation study was carried out with limitations imposed by 2020/2021 restrictions. However, it confirms that the main direction for the visual-auditory analysis of heterogeneous objects has been identified correctly and visual and auditory stimuli can complement each other in the analysis of both volume and spatial distribution properties of heterogeneous phenomena. The user reviews also highlight the necessary enhancements that should be introduced to the approach in terms of the design of more complex user interfaces and consideration of additional application cases. To provide a more detailed picture on evaluation results and recommendations introduced, we also identify the key factors that define the user vision of the approach further enhancement and its possible application areas, such as users experience in the area of complex physical phenomena analysis or multi-sensory area. The discussed in this work aspects of heterogeneous objects analysis task, theoretical and practical solutions allow considering the application, further development and enhancement of the results in multidisciplinary areas of GPU accelerated High-performance visualisation pipelines design and multi-sensory analysis