Konstruksi Bounding Volume Hierarchy dengan Metode Agglomerative Clustering untuk Meningkatkan Performa Ray Tracing

Ray Tracing sebagai algoritma rendering yang menghasilkan citra realistis memiliki beberapa kekurangan. Salah satu di antaranya adalah perhitungan persilangan ray-object pada tiap pixel yang memakan 75% waktu dari keseluruhan proses rendering. Penelitian ini menerapkan metode yang diharapkan dapat mempersingkat proses perhitungan persilangan ray-object dengan membangun struktur data berupa binary tree. Tree yang dibangun sering juga disebut sebagai Bounding Volume Hierarchy (BVH) di mana masing-masing node-nya adalah sebuah container. Struktur data tersebut akan dibangun dengan metode Approximate Agglomerative Clustering (AAC) yang merupakan metode bottom-up clustering dengan top-down preprocessing. Metode AAC dengan parameter yang baik dapat meningkatkan performa Ray Tracing. Metode-metode yang diterapkan sangat mudah diparalelkan sehingga performa algoritma meningkat jika dijalankan pada lingkungan paralel. Hasil uji coba menunjukkan peningkatan kecepatan hingga 3 kali lipat dibandingkan tanpa menerapkan paralelisme. Pada hasil uji coba, juga didapatkan dua jenis parameter yang masing-masing memiliki karakteristik tersendiri (6= cepat, 12= kualitas baik)

Entwicklung und Evaluation einer auf der Hauptkomponentenanalyse basierenden Bounding Volume Hierarchy

Die vorliegende Arbeit beschäftigt sich im übergeordneten Kontext mit den Bounding Volume Hierarchies zur Veinfachung des Intersection Testings beim Raytracing. Die derzeitige Problematik besteht vor allem in der immer noch zu optimierenden Laufzeit. Dementsprechend wird trotz der bereits bestehenden Beschleunigungsdatenstrukturen wie unter anderem der Bounding Volume Hierarchy versucht, effizientere Strukturen oder Erstellungsprozeduren zu entwickeln. Für die Bounding Volume Hierarchy bedeutet dies, dass vor allem hinsichtlich verschiedener Splitting-Methoden und Möglichkeiten für die Baumoptimierung geforscht wird. Explizit wird daher innerhalb dieser Arbeit untersucht, wie die Bounding Volume Hierarchy durch die Verwendung der Hauptkomponentenanalyse bei der Erstellung optimiert werden kann und wie effizient der daraus resultierende Ansatz gegenüber der klassischen Bounding Volume Hierarchy sowie deren Splitting-Methoden ist. Eine Evaluation anhand 12 verschiedener Szenen zeigte, dass der vorliegende Ansatz unter Verwendung der SAH-Methode wie auch mit der Middle-Methode 17.70% respektive 13.14% geringere Renderlaufzeiten als der distanzbasierte Ansatz aufweist. Des Weiteren konnte mittels der kombinierten Verwendung aus klassischer SAH-Methode und PCA-basierter SAH-Methode eine weitere Verbesserung um 6.65% gegenüber der SAH-Methode der PCA-BVH erreicht werden

Efficient Ray Tracing of CSG Models

Tato práce zkoumá metody sledování paprsku v kombinaci s konstruktivní geometrií těles (CSG). Dále navrhuje způsob využití Embree, vysoce optimalizované knihovny používající hierarchii obálek pro sledování paprsků v trojúhelníkových sitích, pro zobrazení CSG v kombinaci s trojúhelníkovými sítěmi.This work explores ray tracing of constructive solid geometry (CSG) and its acceleration in combination with ray tracing triangles. It proposes a way how to exploit Embree, a highly optimized library using bounding volume hierarchy for ray tracing triangle meshes, for rendering CSG with triangle meshes

On R-trees with low query complexity

The R-tree is a well-known bounding-volume hierarchy that is suitable for storing geometric data on secondary memory. Unfortu- nately, no good analysis of its query time exists. We describe a new algo- rithm to construct an R-tree for a set of planar objects that has provably good query complexity for point location queries and range queries with ranges of small width. For certain important special cases, our bounds are optimal. We also show how to update the structure dynamically, and we generalize our results to higher-dimensional spaces

최대 접촉 토러스 패치를 이용한 효율적인 기하학적 알고리즘

학위논문(석사) -- 서울대학교대학원 : 공과대학 컴퓨터공학부, 2021.8. 손상현.We present efficient geometric algorithms that are based upon toroidal patches. To begin with, we present to use osculating toroidal patches to approximate a regular surface and propose a reparametrization method for the approximating toroidal patches. Then, we show that the toroidal patches can approximate special kinds of freeform parametric surfaces that are built upon planar profil e curves much more effectively than general surfaces. Thanks to these precise toroidal patches, we can construct a very compact bounding volume hierarchy for a parametric surface. With the bounding volume hierarchy, we can perform fast and precise point projection, i.e., minimum distance computation from a point to the surface. Also, we can easily find binormal lines, i.e. lines that connect two geometric entities orthogonally, between toroidal patches and use them to find meaningful distance measures for parametric surfaces. We show that we can fi nd such binormal lines easily by fi nding binormal lines between circles in space. Using these fundamental toroidal geometric operations, we present an efficient minimum distance computation algorithm for solids of revolution. This algorithm accelerates the minimum distance computation 10-100 times faster than conventional method. Also, we propose an efficient Hausdorff Distance computation algorithm that is applicable to various kinds of parametric surfaces. We can fi nd the Hausdorff Distance, almost up to machine precision, without much cost increase. Even though these algorithms follow conventional frameworks in large, they exhibit much better precision and efficiency than previous methods because of the toroidal patches that we use in our hierarchy.본 논문에서는 토러스 패치를 이용한 효율적인 기하학적 알고리즘들을 소개한다. 먼저, 임의의 일반적인 정칙 곡면을 근사하기 위해 최대 접촉 토러스 패치를 사용할 것을 제안한다. 이를 위해 정칙 곡면의 변수를 토러스 패치의 변수로 변환하는 재매개화 공식을 제시한다. 이에 더해, 토러스 패치가 평면 곡선에 기반한 특수한 곡면들을 일반 곡면들보다 더 효과적으로 근사할 수 있음을 보인다. 이러한 토러스 패치의 정확성 덕분에, 임의의 곡면을 감싸는 굉장히 효율적인 bounding volume hierarchy를 얻을 수 있다. 이 자료 구조를 이용하여 공간 상의 한 점에서 해당 곡면으로의 점 투영 연산을 굉장히 빠르고 정확하게 할 수 있다. 또한, 곡면들 사이의 다양한 거리들을 찾기 위해 이 자료 구조에 저장된 토러스 패치들을 수직으로 연결하는 binormal 직선을 이용할 수 있다. 이러한 binormal 직선을 효율적으로 찾기 위해 공간 상의 원들을 이용할 수 있음을 보인다. 토러스 패치가 제공하는 위와 같은 기초적인 기하학적 연산들을 토대로, 효율적인 회전체 사이의 최단 거리 계산 알고리즘을 제시한다. 이 알고리즘은 기존의 알고리즘에 비해 10-100배 빠른 속도로 최단 거리를 계산한다. 또한, 효율적인 하우스도르프 거리 계산 알고리즘 역시 제안한다. 실험 결과, 이 알고리즘을 통해 거의 기계 정확도 내에서 정확한 하우스도르프 거리를 큰 비용 증가 없이 계산할 수 있었다. 이와 같은 성능 향상은 본 논문에서 사용한 토러스 패치의 정확성과 효율성에 기반하고 있다.Chapter 1 Introduction 1 1.1 Background 1 1.2 Research Objectives and Contributions 4 1.3 Thesis Organization 6 Chapter 2 Preliminaries 7 2.1 Freeform Parametric Surface 7 2.1.1 B ezier Surface 8 2.1.2 Surface of Revolution 9 2.1.3 Surface of Linear Extrusion 10 2.2 Torus 11 Chapter 3 Related Work 13 3.1 Bounding Volume Hierarchy 13 3.2 Minimum Distance Computation 15 3.3 Hausdor Distance Computation 15 Chapter 4 Bounding Volume Hierarchy 17 4.1 Construction 17 4.2 Toroidal Patch Approximation 19 4.2.1 Regular surface 19 4.2.2 Surface of Revolution 23 4.2.3 Surface of Linear Extrusion 24 4.3 Toroidal Operations 25 4.3.1 Point Projection 25 4.3.2 Binormal Computation 27 Chapter 5 Geometric Algorithms 30 5.1 Minimum distance computation for solids of revolution 30 5.1.1 General Framework 30 5.1.2 Algorithm 31 5.1.3 Experimental Results 33 5.2 Hausdor Distance computation 37 5.2.1 General Framework 37 5.2.2 Algorithm 39 5.2.3 Experimental Results 42 Chapter 6 Conculsion 50 Appendices 52 Chapter A Torus reparametrization 53 Bibliography 60 초록 67 Acknowledgments 68석

Interactive isosurface ray tracing of time-varying tetrahedral volumes

Journal ArticleAbstract- We describe a system for interactively rendering isosurfaces of tetrahedral finite-element scalar fields using coherent ray tracing techniques on the CPU. By employing state-of-the art methods in polygonal ray tracing, namely aggressive packet/frustum traversal of a bounding volume hierarchy, we can accomodate large and time-varying unstructured data. In conjunction with this efficiency structure, we introduce a novel technique for intersecting ray packets with tetrahedral primitives. Ray tracing is flexible, allowing for dynamic changes in isovalue and time step, visualization of multiple isosurfaces, shadows, and depth-peeling transparency effects. The resulting system offers the intuitive simplicity of isosurfacing, guaranteed-correct visual results, and ultimately a scalable, dynamic and consistently interactive solution for visualizing unstructured volumes

Generalized Neighbor Search using Commodity Hardware Acceleration

Tree-based Nearest Neighbor Search (NNS) is hard to parallelize on GPUs. However, newer Nvidia GPUs are equipped with Ray Tracing (RT) cores that can build a spatial tree called Bounding Volume Hierarchy (BVH) to accelerate graphics rendering. Recent work proposed using RT cores to implement NNS, but they all have a hardware-imposed constraint on the type of distance metric, which is the Euclidean distance. We propose and implement two approaches for generalized distance computations: filter-refine, and monotone transformation, each of which allows non-euclidean nearest neighbor queries to be performed in terms of Euclidean distances. We find that our reductions improve the time taken to perform distance computations during the search, thereby improving the overall performance of the NNS