Accelerating and simulating detected physical interations

The aim of this doctoral thesis is to present a body of work aimed at improving performance and developing new methods for animating physical interactions using simulation in virtual environments. To this end we develop a number of novel parallel collision detection and fracture simulation algorithms. Methods for traversing and constructing bounding volume hierarchies (BVH) on graphics processing units (GPU) have had a wide success. In particular, they have been adopted widely in simulators, libraries and benchmarks as they allow applications to reach new heights in terms of performance. Even with such a development however, a thorough adoption of techniques has not occurred in commercial and practical applications. Due to this, parallel collision detection on GPUs remains a relatively niche problem and a wide number of applications could benefit from a significant boost in proclaimed performance gains. In fracture simulations, explicit surface tracking methods have a good track record of success. In particular they have been adopted thoroughly in 3D modelling and animation software like Houdini [124] as they allow accurate simulation of intricate fracture patterns with complex interactions, which are generated using physical laws. Even so, existing methods can pose restrictions on the geometries of simulated objects. Further, they often have tight dependencies on implicit surfaces (e.g. level sets) for representing cracks and performing cutting to produce rigid-body fragments. Due to these restrictions, catering to various geometries can be a challenge and the memory cost of using implicit surfaces can be detrimental and without guarantee on the preservation of sharp features. We present our work in four main chapters. We first tackle the problem in the accelerating collision detection on the GPU via BVH traversal - one of the most demanding components during collision detection. Secondly, we show the construction of a new representation of the BVH called the ostensibly implicit tree - a layout of nodes in memory which is encoded using the bitwise representation of the number of enclosed objects in the tree (e.g. polygons). Thirdly, we shift paradigm to the task of simulating breaking objects after collision: we show how traditional finite elements can be extended as a way to prevent frequent re-meshing during fracture evolution problems. Finally, we show how the fracture surface–represented as an explicit (e.g. triangulated) surface mesh–is used to generate rigid body fragments using a novel approach to mesh cutting

Fast collision detection for deformable models using representativetriangles.

Abstract We present a new approach to accelerate collision detection for deformable models. Our formulation applies to all triangulated models and significantly reduces the number of elementary tests between features of the mesh, i.e., vertices, edges and faces. We introduce the notion of Representative-Triangles, standard geometric triangles augmented with mesh feature information and use this representation to achieve better collision query performance. The resulting approach can be combined with bounding volume hierarchies and works well for both inter-object and self-collision detection. We demonstrate the benefit of Representative-Triangles on continuous collision detection for cloth simulation and N-body collision scenarios. We observe up to a one-order of magnitude reduction in featurepair tests and up to a 5X improvement in query time

Interactive ray tracing of massive and deformable models

Ray tracing is a fundamental algorithm used for many applications such as computer graphics, geometric simulation, collision detection and line-of-sight computation. Even though the performance of ray tracing algorithms scales with the model complexity, the high memory requirements and the use of static hierarchical structures pose problems with massive models and dynamic data-sets. We present several approaches to address these problems based on new acceleration structures and traversal algorithms. We introduce a compact representation for storing the model and hierarchy while ray tracing triangle meshes that can reduce the memory footprint by up to 80%, while maintaining high performance. As a result, can ray trace massive models with hundreds of millions of triangles on workstations with a few gigabytes of memory. We also show how to use bounding volume hierarchies for ray tracing complex models with interactive performance. In order to handle dynamic scenes, we use refitting algorithms and also present highly-parallel GPU-based algorithms to reconstruct the hierarchies. In practice, our method can construct hierarchies for models with hundreds of thousands of triangles at interactive speeds. Finally, we demonstrate several applications that are enabled by these algorithms. Using deformable BVH and fast data parallel techniques, we introduce a geometric sound propagation algorithm that can run on complex deformable scenes interactively and orders of magnitude faster than comparable previous approaches. In addition, we also use these hierarchical algorithms for fast collision detection between deformable models and GPU rendering of shadows on massive models by employing our compact representations for hybrid ray tracing and rasterization

Hardware Accelerators for Animated Ray Tracing

Future graphics processors are likely to incorporate hardware accelerators for real-time ray tracing, in order to render increasingly complex lighting effects in interactive applications. However, ray tracing poses difficulties when drawing scenes with dynamic content, such as animated characters and objects. In dynamic scenes, the spatial datastructures used to accelerate ray tracing are invalidated on each animation frame, and need to be rapidly updated. Tree update is a complex subtask in its own right, and becomes highly expensive in complex scenes. Both ray tracing and tree update are highly memory-intensive tasks, and rendering systems are increasingly bandwidth-limited, so research on accelerator hardware has focused on architectural techniques to optimize away off-chip memory traffic. Dynamic scene support is further complicated by the recent introduction of compressed trees, which use low-precision numbers for storage and computation. Such compression reduces both the arithmetic and memory bandwidth cost of ray tracing, but adds to the complexity of tree update.This thesis proposes methods to cope with dynamic scenes in hardware-accelerated ray tracing, with focus on reducing traffic to external memory. Firstly, a hardware architecture is designed for linear bounding volume hierarchy construction, an algorithm which is a basic building block in most state-of-the-art software tree builders. The algorithm is rearranged into a streaming form which reduces traffic to one-third of software implementations of the same algorithm. Secondly, an algorithm is proposed for compressing bounding volume hierarchies in a streaming manner as they are output from a hardware builder, instead of performing compression as a postprocessing pass. As a result, with the proposed method, compression reduces the overall cost of tree update rather than increasing it. The last main contribution of this thesis is an evaluation of shallow bounding volume hierarchies, common in software ray tracing, for use in hardware pipelines. These are found to be more energy-efficient than binary hierarchies. The results in this thesis both confirm that dynamic scene support may become a bottleneck in real time ray tracing, and add to the state of the art on tree update in terms of energy-efficiency, as well as the complexity of scenes that can be handled in real time on resource-constrained platforms

New geometric algorithms and data structures for collision detection of dynamically deforming objects

Any virtual environment that supports interactions between virtual objects and/or a user and objects, needs a collision detection system to handle all interactions in a physically correct or plausible way. A collision detection system is needed to determine if objects are in contact or interpenetrates. These interpenetrations are resolved by a collision handling system. Because of the fact, that in nearly all simulations objects can interact with each other, collision detection is a fundamental technology, that is needed in all these simulations, like physically based simulation, robotic path and motion planning, virtual prototyping, and many more. Most virtual environments aim to represent the real-world as realistic as possible and therefore, virtual environments getting more and more complex. Furthermore, all models in a virtual environment should interact like real objects do, if forces are applied to the objects. Nearly all real-world objects will deform or break down in its individual parts if forces are acted upon the objects. Thus deformable objects are becoming more and more common in virtual environments, which want to be as realistic as possible and thus, will present new challenges to the collision detection system. The necessary collision detection computations can be very complex and this has the effect, that the collision detection process is the performance bottleneck in most simulations. Most rigid body collision detection approaches use a BVH as acceleration data structure. This technique is perfectly suitable if the object does not change its shape. For a soft body an update step is necessary to ensure that the underlying acceleration data structure is still valid after performing a simulation step. This update step can be very time consuming, is often hard to implement and in most cases will produce a degenerated BVH after some simulation steps, if the objects generally deform. Therefore, the here presented collision detection approach works entirely without an acceleration data structure and supports rigid and soft bodies. Furthermore, we can compute inter-object and intraobject collisions of rigid and deformable objects consisting of many tens of thousands of triangles in a few milliseconds. To realize this, a subdivision of the scene into parts using a fuzzy clustering approach is applied. Based on that all further steps for each cluster can be performed in parallel and if desired, distributed to different GPUs. Tests have been performed to judge the performance of our approach against other state-of-the-art collision detection algorithms. Additionally, we integrated our approach into Bullet, a commonly used physics engine, to evaluate our algorithm. In order to make a fair comparison of different rigid body collision detection algorithms, we propose a new collision detection Benchmarking Suite. Our Benchmarking Suite can evaluate both the performance as well as the quality of the collision response. Therefore, the Benchmarking Suite is subdivided into a Performance Benchmark and a Quality Benchmark. This approach needs to be extended to support soft body collision detection algorithms in the future.Jede virtuelle Umgebung, welche eine Interaktion zwischen den virtuellen Objekten in der Szene zulässt und/oder zwischen einem Benutzer und den Objekten, benötigt für eine korrekte Behandlung der Interaktionen eine Kollisionsdetektion. Nur dank der Kollisionsdetektion können Berührungen zwischen Objekten erkannt und mittels der Kollisionsbehandlung aufgelöst werden. Dies ist der Grund für die weite Verbreitung der Kollisionsdetektion in die verschiedensten Fachbereiche, wie der physikalisch basierten Simulation, der Pfadplanung in der Robotik, dem virtuellen Prototyping und vielen weiteren. Auf Grund des Bestrebens, die reale Umgebung in der virtuellen Welt so realistisch wie möglich nachzubilden, steigt die Komplexität der Szenen stetig. Fortwährend steigen die Anforderungen an die Objekte, sich realistisch zu verhalten, sollten Kräfte auf die einzelnen Objekte ausgeübt werden. Die meisten Objekte, die uns in unserer realen Welt umgeben, ändern ihre Form oder zerbrechen in ihre Einzelteile, wenn Kräfte auf sie einwirken. Daher kommen in realitätsnahen, virtuellen Umgebungen immer häufiger deformierbare Objekte zum Einsatz, was neue Herausforderungen an die Kollisionsdetektion stellt. Die hierfür Notwendigen, teils komplexen Berechnungen, führen dazu, dass die Kollisionsdetektion häufig der Performance-Bottleneck in der jeweiligen Simulation darstellt. Die meisten Kollisionsdetektionen für starre Körper benutzen eine Hüllkörperhierarchie als Beschleunigungsdatenstruktur. Diese Technik ist hervorragend geeignet, solange sich die Form des Objektes nicht verändert. Im Fall von deformierbaren Objekten ist eine Aktualisierung der Datenstruktur nach jedem Schritt der Simulation notwendig, damit diese weiterhin gültig ist. Dieser Aktualisierungsschritt kann, je nach Hierarchie, sehr zeitaufwendig sein, ist in den meisten Fällen schwer zu implementieren und generiert nach vielen Schritten der Simulation häufig eine entartete Hüllkörperhierarchie, sollte sich das Objekt sehr stark verformen. Um dies zu vermeiden, verzichtet unsere Kollisionsdetektion vollständig auf eine Beschleunigungsdatenstruktur und unterstützt sowohl rigide, wie auch deformierbare Körper. Zugleich können wir Selbstkollisionen und Kollisionen zwischen starren und/oder deformierbaren Objekten, bestehend aus vielen Zehntausenden Dreiecken, innerhalb von wenigen Millisekunden berechnen. Um dies zu realisieren, unterteilen wir die gesamte Szene in einzelne Bereiche mittels eines Fuzzy Clustering-Verfahrens. Dies ermöglicht es, dass alle Cluster unabhängig bearbeitet werden und falls gewünscht, die Berechnungen für die einzelnen Cluster auf verschiedene Grafikkarten verteilt werden können. Um die Leistungsfähigkeit unseres Ansatzes vergleichen zu können, haben wir diesen gegen aktuelle Verfahren für die Kollisionsdetektion antreten lassen. Weiterhin haben wir unser Verfahren in die Physik-Engine Bullet integriert, um das Verhalten in dynamischen Situationen zu evaluieren. Um unterschiedliche Kollisionsdetektionsalgorithmen für starre Körper korrekt und objektiv miteinander vergleichen zu können, haben wir eine Benchmarking-Suite entwickelt. Unsere Benchmarking- Suite kann sowohl die Geschwindigkeit, für die Bestimmung, ob zwei Objekte sich durchdringen, wie auch die Qualität der berechneten Kräfte miteinander vergleichen. Hierfür ist die Benchmarking-Suite in den Performance Benchmark und den Quality Benchmark unterteilt worden. In der Zukunft wird diese Benchmarking-Suite dahingehend erweitert, dass auch Kollisionsdetektionsalgorithmen für deformierbare Objekte unterstützt werden

Visualization and inspection of the geometry of particle packings

Gegenstand dieser Dissertation ist die Entwicklung von effizienten Verfahren zur Visualisierung und Inspektion der Geometrie von Partikelmischungen. Um das Verhalten der Simulation für die Partikelmischung besser zu verstehen und zu überwachen, sollten nicht nur die Partikel selbst, sondern auch spezielle von den Partikeln gebildete Bereiche, die den Simulationsfortschritt und die räumliche Verteilung von Hotspots anzeigen können, visualisiert werden können. Dies sollte auch bei großen Packungen mit Millionen von Partikeln zumindest mit einer interaktiven Darstellungsgeschwindigkeit möglich sein. . Da die Simulation auf der Grafikkarte (GPU) durchgeführt wird, sollten die Visualisierungstechniken die Daten des GPU-Speichers vollständig nutzen. Um die Qualität von trockenen Partikelmischungen wie Beton zu verbessern, wurde der Korngrößenverteilung große Aufmerksamkeit gewidmet, die die Raumfüllungsrate hauptsächlich beeinflusst und daher zwei der wichtigsten Eigenschaften des Betons bestimmt: die strukturelle Robustheit und die Haltbarkeit. Anhand der Korngrößenverteilung kann die Raumfüllungsrate durch Computersimulationen bestimmt werden, die analytischen Ansätzen in der Praxis wegen der breiten Größenverteilung der Partikel oft überlegen sind. Eine der weit verbreiteten Simulationsmethoden ist das Collective Rearrangement, bei dem die Partikel zunächst an zufälligen Positionen innerhalb eines Behälters platziert werden. Später werden Überlappungen zwischen Partikeln aufgelöst, indem überlappende Partikel voneinander weggedrückt werden. Durch geschickte Anpassung der Behältergröße während der Simulation, kann die Collective Rearrangement-Methode am Ende eine ziemlich dichte Partikelpackung generieren. Es ist jedoch sehr schwierig, den gesamten Simulationsprozess ohne ein interaktives Visualisierungstool zu optimieren oder dort Fehler zu finden. Ausgehend von der etablierten rasterisierungsbasierten Methode zum Darstellen einer großen Menge von Kugeln, bietet diese Dissertation zunächst schnelle und pixelgenaue Methoden zur neuartigen Visualisierung der Überlappungen und Freiräume zwischen kugelförmigen Partikeln innerhalb eines Behälters.. Die auf Rasterisierung basierenden Verfahren funktionieren gut für kleinere Partikelpackungen bis ca. eine Million Kugeln. Bei größeren Packungen entstehen Probleme durch die lineare Laufzeit und den Speicherverbrauch. Zur Lösung dieses Problems werden neue Methoden mit Hilfe von Raytracing zusammen mit zwei neuen Arten von Bounding-Volume-Hierarchien (BVHs) bereitgestellt. Diese können den Raytracing-Prozess deutlich beschleunigen --- die erste kann die vorhandene Datenstruktur für die Simulation wiederverwenden und die zweite ist speichereffizienter. Beide BVHs nutzen die Idee des Loose Octree und sind die ersten ihrer Art, die die Größe von Primitiven für interaktives Raytracing mit häufig aktualisierten Beschleunigungsdatenstrukturen berücksichtigen. Darüber hinaus können die Visualisierungstechniken in dieser Dissertation auch angepasst werden, um Eigenschaften wie das Volumen bestimmter Bereiche zu berechnen. All diese Visualisierungstechniken werden dann auf den Fall nicht-sphärischer Partikel erweitert, bei denen ein nicht-sphärisches Partikel durch ein starres System von Kugeln angenähert wird, um die vorhandene kugelbasierte Simulation wiederverwenden zu können. Dazu wird auch eine neue GPU-basierte Methode zum effizienten Füllen eines nicht-kugelförmigen Partikels mit polydispersen überlappenden Kugeln vorgestellt, so dass ein Partikel mit weniger Kugeln gefüllt werden kann, ohne die Raumfüllungsrate zu beeinträchtigen. Dies erleichtert sowohl die Simulation als auch die Visualisierung. Basierend auf den Arbeiten in dieser Dissertation können ausgefeiltere Algorithmen entwickelt werden, um großskalige nicht-sphärische Partikelmischungen effizienter zu visualisieren. Weiterhin kann in Zukunft Hardware-Raytracing neuerer Grafikkarten anstelle des in dieser Dissertation eingesetzten Software-Raytracing verwendet werden. Die neuen Techniken können auch als Grundlage für die interaktive Visualisierung anderer partikelbasierter Simulationen verwendet werden, bei denen spezielle Bereiche wie Freiräume oder Überlappungen zwischen Partikeln relevant sind.The aim of this dissertation is to find efficient techniques for visualizing and inspecting the geometry of particle packings. Simulations of such packings are used e.g. in material sciences to predict properties of granular materials. To better understand and supervise the behavior of these simulations, not only the particles themselves but also special areas formed by the particles that can show the progress of the simulation and spatial distribution of hot spots, should be visualized. This should be possible with a frame rate that allows interaction even for large scale packings with millions of particles. Moreover, given the simulation is conducted in the GPU, the visualization techniques should take full use of the data in the GPU memory. To improve the performance of granular materials like concrete, considerable attention has been paid to the particle size distribution, which is the main determinant for the space filling rate and therefore affects two of the most important properties of the concrete: the structural robustness and the durability. Given the particle size distribution, the space filling rate can be determined by computer simulations, which are often superior to analytical approaches due to irregularities of particles and the wide range of size distribution in practice. One of the widely adopted simulation methods is the collective rearrangement, for which particles are first placed at random positions inside a container, later overlaps between particles will be resolved by letting overlapped particles push away from each other to fill empty space in the container. By cleverly adjusting the size of the container according to the process of the simulation, the collective rearrangement method could get a pretty dense particle packing in the end. However, it is very hard to fine-tune or debug the whole simulation process without an interactive visualization tool. Starting from the well-established rasterization-based method to render spheres, this dissertation first provides new fast and pixel-accurate methods to visualize the overlaps and free spaces between spherical particles inside a container. The rasterization-based techniques perform well for small scale particle packings but deteriorate for large scale packings due to the large memory requirements that are hard to be approximated correctly in advance. To address this problem, new methods based on ray tracing are provided along with two new kinds of bounding volume hierarchies (BVHs) to accelerate the ray tracing process --- the first one can reuse the existing data structure for simulation and the second one is more memory efficient. Both BVHs utilize the idea of loose octree and are the first of their kind to consider the size of primitives for interactive ray tracing with frequently updated acceleration structures. Moreover, the visualization techniques provided in this dissertation can also be adjusted to calculate properties such as volumes of the specific areas. All these visualization techniques are then extended to non-spherical particles, where a non-spherical particle is approximated by a rigid system of spheres to reuse the existing simulation. To this end a new GPU-based method is presented to fill a non-spherical particle with polydisperse possibly overlapping spheres efficiently, so that a particle can be filled with fewer spheres without sacrificing the space filling rate. This eases both simulation and visualization. Based on approaches presented in this dissertation, more sophisticated algorithms can be developed to visualize large scale non-spherical particle mixtures more efficiently. Besides, one can try to exploit the hardware ray tracing of more recent graphic cards instead of maintaining the software ray tracing as in this dissertation. The new techniques can also become the basis for interactively visualizing other particle-based simulations, where special areas such as free space or overlaps between particles are of interest

Model Simplification for Efficient Collision Detection in Robotics

Motion planning for industrial robots is a computationally intensive task due to the massive number of potential motions between any two configurations. Calculating all possibilities is generally not feasible. Instead, many motion planners sample a sub-set of the available space until a viable solution is found. Simplifying models to improve collision detection performance, a significant component of motion planning, results in faster and more capable motion planners. Several approaches for simplifying models to improve collision detection performance have been presented in the literature. However, many of them are sub-optimal for an industrial robotics application due to input model limitations, accuracy sacrifices, or the probability of increasing false negatives during collision queries. This thesis focuses on the development of model simplification approaches optimised for industrial robotics applications. Firstly, a new simplification approach, the Bounding Sphere Simplification (BSS), is presented that converts triangle-mesh inputs to a collection of spheres for efficient collision and distance queries. Additionally, BSS removes small features and generates an output model less prone to false negatives

Virtual Assembly and Disassembly Analysis: An Exploration into Virtual Object Interactions and Haptic Feedback

In recent years, researchers have developed virtual environments, which allow more realistic human-computer interactions and have become increasingly popular for engineering applications such as computer-aided design and process evaluation. For instance, the demand for product service, remanufacture, and recycling has forced companies to consider ease of assembly and disassembly during the design phase of their products. Evaluating these processes in a virtual environment during the early stages of design not only increases the impact of design modifications on the final product, but also eliminates the time, cost, and material associated with the construction of physical prototypes. Although numerous virtual environments for assembly analysis exist or are under development, many provide only visual feedback. A real-time haptic simulation test bed for the analysis of assembly and disassembly operations has been developed, providing the designer with force and tactile feedback in addition to traditional visual feedback. The development such a simulation requires the modeling of collisions between virtual objects, which is a computationally expensive process. Also, the demands of a real-time simulation incorporating haptic feedback introduce additional complications for reliable collision detection. Therefore, the first objective of this work was to discover ways in which current collision detection libraries can be improved or supplemented to create more robust interaction between virtual objects. Using the simulation as a test bed, studies were then conducted to determine the potential usefulness of haptic feedback for analysis of assembly and disassembly operations. The following significant contributions were accomplished: (1) a simulation combining the strengths of an impulse-based simulation with a supplemental constraint maintenance scheme for modeling object interactions, (2) a toolkit of supplemental techniques to support object interactions in situations where collision detection algorithms commonly fail, (3) a haptic assembly and disassembly simulation useful for experimentation, and (4) results from a series of five experimental user studies with the focus of determining the effectiveness of haptic feedback in such a simulation. Additional contributions include knowledge of the usability and functionality of current collision detection libraries, the limitations of haptic feedback devices, and feedback from experimental subjects regarding their comfort and overall satisfaction with the simulation.Ph.D.Committee Chair: Bras, Bert; Committee Member: Baker, Nelson; Committee Member: Griffin, Paul; Committee Member: Paredis, Chris; Committee Member: Rosen, Davi

의상 시뮬레이션을 위한 수렴 보장 풀림 방법

학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2022.2. 고형석.수십 년 동안 그래픽스 필드에선 의상 시뮬레이션 중에 발생하는 자가 충돌 처리 실패(엉킴)를 해결하기 위한 여러가지 방법이 제안되었다. 그러나 제안된 방법들은 간단한 의상(티셔츠, 바지)에 대해서만 동작하고, 실제 가상 피팅이나 에니메이션 제작에 등장하는 복잡한 의상에선 대다수가 엉킴 해결에 실패하였다. 본 논문에서는 엉킴을 두 그룹으로 나누고, 각각에 대한 새로운 이산 충돌 처리 방법을 제안하며, 엉킴이 있는 복잡한 의상에 적용하는 실험을 통해 제안된 방법의 효용성을 입증한다. 첫번째 그룹, BLI를 제외한 6가지 엉킴에 대해서는 ESEF(변-압축 / 입실론-압출)를 제안하였다. 6가지 엉킴은 잘못된 영역이 확정적으로 정의됨을 이용하며, 가장 바깥부분부터 서서히 해결하는 아웃투인 방식으로 엉킴을 점진적으로 해결하였다. 이를 위해 매 타임 스텝마다 의상 메쉬의 엉킴 분석을 수행하고, 그 결과를 정점, 변, 삼각형을 채색하는 형태로 저장하였다. 이후 채색을 참조하여 메쉬의 필요한 영역에 두가지 기법 삼각형-수축과 정점-당기기를 가하였고, 최종적으로 모든 엉킴이 없어질때까지 이를 반복적으로 적용하였다. 삼각형-수축과 정점-당기기는 연속 충돌 처리에서 통상적으론 반올림 오류를 보정하기 위해 사용되어 왔던 입실론 값의 의미를 재해석하였다. 입실론의 효용을 반올림 오류 방어로 한정하지 않고, 더 나아가서 이산 충돌 처리에 응용하여 특정 조건에서 유한한 타임 스텝안에 엉킴 해결을 보장할 수 있게 되었다. 두번째 그룹, BLI에 대해서는 BLI-Resolver를 제안하였다. 먼저 BLI의 특징과 어떤 상황에서 발생하는지 분석하고, 이를 통해 원하는 엉킴 해결의 형태(스타일)가 의상의 분류 또는 특정 영역에 따라 달라져야 함을 보였다. 따라서 각각의 스타일에 대응하기 위해 BLI를 해결할 세 가지 알고리즘, 메쉬-찢기, 영역-교차, 접힘-교차를 제안하였다. 메쉬-찢기는 의상 메쉬를 필요에 따라 임시로 몇몇 삼각형들을 누락 후 재구성하여 엉킴 해결에 유리한 메쉬로 변경하였다. 영역-교차, 접힘-교차는 BLI를 직접적으로 해결하지 않고, 다른 6가지 엉킴으로 변환하여, ESEF가 해결할 수 있게 해주었다. 제안된 두가지 방법(ESEF, BLI-Resolver)을 통합하여 엉킴의 스펙트럼을 모두 다룰 수 있게 되어, 의상 시뮬레이션 속의 이산충돌처리의 마침표를 찍게 되었다. 이 방법들은 기존의 연속 충돌 처리가 구현되어 있는 시뮬레이터에 쉽게 통합이 가능하며, 시뮬레이터의 종류에 영향을 받지 않는 특징이 있다. 또한 의상의 복잡도나 종류에 구애받지 않고 유한한 타임스텝 내로 엉킴이 풀림을 보장할 수 있으며, 의상의 디자인에 대한 정보가 제공된 경우 엉킴이 디자인에 적합한 방향으로 해결된다. 최종적으로 실험을 통해 이전의 방법으로 해결할 수 없었던 다양하고 실용적인 의복에서의 엉킴이 해결됨을 보였다.For decades, methods have been proposed to solve the failure of self-collision (intersection) that occurs during clothing simulation. But when applied in reality, they report failure in various cases. In this paper, we divide these intersections into two groups and propose a new discrete collision handling (DCH) method for each to solve them properly in real situations. The first method, Edge-Shortening / Epsilon-Finessing (ESEF), is a method that guarantees convergence of six among seven intersection classifications except for BLI. It performs intersection analysis of the clothing mesh at every time step, and stores the result in the form of coloring the vertices, edges, and triangles. Referring to the coloring, the method resolves the tanglements in an out-to-in manner by applying the proposed operations, triangle shrinkage and vertex pull. The operations reinterpret the traditional use of tolerance value in continuous collision handling (CCH) methods, which were normally used for defending round-off errors. It gives a second thought to that tolerance value, and proposes a new DCH method that uses the tolerance value for the resolution purpose. Under certain conditions, ESEF turns out to guarantee the resolution of the tanglements in a finite number of time steps. The second method, BLI-Resolver, specifically targets BLI only. We analyze how BLIs occur, and realize that the desired form of resolution (i.e., resolution style) can vary depending on the type or particular region of the garment. Therefore, we identify the need for three resolution algorithms for BLI, namely, Mesh-Tearing, Regional-Flip, Crease-Flip, in order to cover the resolution styles. BLI-Resolver is the first to (1) identify the need for the resolution styles for the case of BLI, (2) propose the actual algorithms to cover each resolution style, and (3) demonstrate that the proposed resolution styles and algorithms work stably for BLIs. With the two methods, we can now cover the full spectrum of intersections. Intersections are guaranteed to resolve, in a design-appropriate direction when sufficient information of the clothing is given. Experiments report success in various and practical clothing where previous methods failed to resolve.1 Introduction 1 2 Related Works 5 2.1 Cloth Untangling: General 5 2.2 Cloth Untangling: Multi-Garment 7 2.3 Summary and Limitations 8 2.4 Contribution of Proposed Work 12 3 Preliminary 17 3.1 Edge-Shortening / Epsilon-finessing 17 3.2 Boundary-Loop-Interior Resolver 20 3.2.1 Repulsive-ICM on BLI 20 3.2.2 New Approach for BLI 23 4 Edge Shortening / Epsilon Finessing 25 4.1 Overview 25 4.2 Modifications to Conventional Simulator 28 4.2.1 UV-Space Mesh Update 28 4.2.2 CCH vs. m-CCH 33 4.2.3 Resolution of Elementary Tanglements over Simulation Loop 35 4.2.4 Working of ε_CCD-Finesses in a Cloth Mesh 36 4.2.5 Possible Scenario of Edge Shortening Hindrance 39 4.3 Scheduling the Operations 40 4.3.1 Possible Scenarios when No Fan is TIT-Passable 44 4.4 Soundness in Intrinsically Planar Cases 44 4.5 Extensions to Process Clothing 48 5 Boundary-Loop-Interior Resolver 51 5.1 Overview 51 5.2 Modifications to Conventional Simulator 52 5.3 Mesh-Tearing 52 5.3.1 L-to-B Propagation 55 5.3.2 Revived Triangles 56 5.4 Regional-Flip 59 5.4.1 Crease-Flip 60 5.5 Selecting Resolution Style/Algorithm 62 6 Experiment Results 65 6.1 Overview 65 6.2 Rudimentary Cases 69 6.3 Exploded Handkerchief 69 6.4 Clothes 73 6.5 Round Folds 78 6.6 Sharp Folds 78 6.7 User Interactions 78 6.8 Exploded Handkerchief 80 7 Conclusion 85 A Edge Shortening When Intersection Path Exists Across Multiple Panels 89 B Edge Shortening When Intersection Path Exists Across the Dart Opening 95 C Convexification 97 D Discussion on the Values of ε_RG and γ 99 E Details of BLI Coupling for Regional-Flip 103 Bibliography 105 초록 119박