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

A numerical method for fluid-structure interactions of slender rods in turbulent flow

This thesis presents a numerical method for the simulation of fluid-structure interaction (FSI) problems on high-performance computers. The proposed method is specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic structures, the latter being modeled as Cosserat rods. From a numerical point of view, such kind of FSI requires special techniques to reach numerical stability. When using a partitioned fluid-structure coupling approach this is usually achieved by an iterative procedure, which drastically increases the computational effort. In the present work, an alternative coupling approach is developed based on an immersed boundary method (IBM). It is unconditionally stable and exempt from any global iteration between the fluid part and the structure part. The proposed FSI solver is employed to simulate the flow over a dense layer of vegetation elements, usually designated as canopy flow. The abstracted canopy model used in the simulation consists of 800 strip-shaped blades, which is the largest canopy-resolving simulation of this type done so far. To gain a deeper understanding of the physics of aquatic canopy flows the simulation data obtained are analyzed, e.g., concerning the existence and shape of coherent structures

Large Growth Deformations of Thin Tissue using Solid-Shells

Simulating large scale expansion of thin structures, such as in growing leaves, is challenging. Sold-shells have a number of potential advantages over conventional thin-shell methods, but have thus far only been investigated for small plastic deformation cases. In response, we present a new general-purpose FEM growth framework for simulating large plastic deformations using a new solid-shell growth approach while supporting morphogen diffusion and collision handling. Large plastic deformations are handled by augmenting solid-shell elements with \textit{plastic embedding} and strain-aware adaptive remeshing. Plastic embedding is an approach to model large plastic deformations by modifying the rest configuration in response to displacement strain. We exploit the solid-shell's ability of describing both stretching and bending in terms of displacement strain to implement both plastic stretching and bending using the same plasticity model. The large deformations are adaptively remeshed using a strain-aware criteria to anticipate buckling and eliminate low-quality elements. We perform qualitative investigations on the capabilities of the new solid-shell growth approach in reproducing buckling, rippling, rolling, and collision deformations, relevant towards animating growing leaves, flowers, and other thin structures. The qualitative experiments demonstrates that solid-shells are a viable alternative to thin-shells for simulating large and intricate growth deformations

Compaction Algorithms for Non-Convex Polygons and Their Applications

Given a two-dimensional, non-overlapping layout of convex and non-convex polygons, compaction refers to a simultaneous motion of the polygons that generates a more densely packed layout. In industrial two-dimensional packing applications, compaction can improve the material utilization of already tightly packed layouts. Efficient algorithms for compacting a layout of non-convex polygons are not previously known. This dissertation offers the first systematic study of compaction of non-convex polygons. We start by formalizing the compaction problem as that of planning a motion that minimizes some linear objective function of the positions. Based on this formalization, we study the complexity of compaction and show it to be PSPACE-hard. The major contribution of this dissertation is a position-based optimization model that allows us to calculate directly new polygon positions that constitute a locally optimum solution of the objective via linear programming. This model yields the first practically efficient algorithm for translational compaction-compaction in which the polygons can only translate. This compaction algorithm runs in almost real time and improves the material utilization of production quality human-generated layouts from the apparel industry. Several algorithms are derived directly from the position-based optimization model to solve related problems arising from manual or automatic layout generation. In particular, the model yields an algorithm for separating overlapping polygons using a minimal amount of motion. This separation algorithm together with a database of human-generated markers can automatically generate markers that approach human performance. Additionally, we provide several extensions to the position-based optimization model. These extensions enables the model to handle small rotations, to offer the flexible control of the distances between polygons and to find optimal solution to two-dimensional packing of non-convex polygons. This dissertation also includes a compaction algorithm based on existing physical simulation approaches. Although our experimental results showed that it is not practical for compacting tightly packed layouts, this algorithm is of interest because it shows that the simulation can speed up significantly if we use geometrical constraints to replace physical constraints. It also reveals the inherent limitations of physical simulation algorithms in compacting tightly packed layouts. Most of the algorithms presented in this dissertation have been implemented on a SUN SparcStationTM and have been included in a software package licensed to a CAD company.Engineering and Applied Science

Simulating Humans: Computer Graphics, Animation, and Control

People are all around us. They inhabit our home, workplace, entertainment, and environment. Their presence and actions are noted or ignored, enjoyed or disdained, analyzed or prescribed. The very ubiquitousness of other people in our lives poses a tantalizing challenge to the computational modeler: people are at once the most common object of interest and yet the most structurally complex. Their everyday movements are amazingly uid yet demanding to reproduce, with actions driven not just mechanically by muscles and bones but also cognitively by beliefs and intentions. Our motor systems manage to learn how to make us move without leaving us the burden or pleasure of knowing how we did it. Likewise we learn how to describe the actions and behaviors of others without consciously struggling with the processes of perception, recognition, and language

Numerical investigation of fracture of polycrystalline ice under dynamic loading

Cohesive zone model is a promising technique for simulating fracture processes in brittle ice. In this work it is applied to investigate the fracture behavior of polycrystalline cylindrical samples under uniaxial loading conditions, four-point beam bending, and L-shaped beam bending. In each case, the simulation results are compared with the corresponding experimental data that was collected by other researchers. The model is based on the implicit finite element method combined with Park-Paulino-Roesler formulation for cohesive potential and includes an adaptive time stepping scheme, which takes into account the rate of damage and failure of cohesive zones. The benefit of the implicit scheme is that it allows larger time steps than explicit integration. Material properties and model parameters are calibrated using available experimental data for freshwater ice and sea ice samples. For polycrystalline ice, granular geometry is generated and cohesive zones are inserted between grains. Simulations are performed for samples with different grain sizes, and the resulting stress–strain and damage accumulation curves are recorded. Investigation of the dependency between the grain size and fracture strength shows a strengthening effect that is consistent with experimental results. The proposed framework is also applied to simulate the dynamic fracture processes in Lshaped beams of sea ice, in which case the cohesive zones are inserted between the elements of the mesh. Evolution of the stress distribution on the surface of the beam is modeled for the duration of the loading process, showing how it changes with progressive accumulation of damage in the material, as well as the development of cracks. An analytical formula is derived for estimating the breaking force based on the dimensions of the beam and the ice strength. Experimental data obtained from the 2014-2016 tests are re-evaluated with the aid of this new analysis. The computation is implemented efficiently with GPU acceleration, allowing to handle geometries with higher resolution than would be possible otherwise. Several technical contributions are described in detail including GPU-accelerated FEM implementation, an efficient way of creation of sparse matrix structure, and comparison of different unloading/reloading relations when using an implicit integration scheme. A mechanism for collision response allows modeling the interaction of fragmented material. To evaluate the collision forces, an algorithm for computing first and second point-triangle distance derivatives was developed. The source code is made available as open-source

Multiscale methods for fabrication design

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 135-146).Modern manufacturing technologies such as 3D printing enable the fabrication of objects with extraordinary complexity. Arranging materials to form functional structures can achieve a much wider range of physical properties than in the constituent materials. Many applications have been demonstrated in the fields of mechanics, acoustics, optics, and electromagnetics. Unfortunately, it is difficult to design objects manually in the large combinatorial space of possible designs. Computational design algorithms have been developed to automatically design objects with specified physical properties. However, many types of physical properties are still very challenging to optimize because predictive and efficient simulations are not available for problems such as high-resolution non-linear elasticity or dynamics with friction and impact. For simpler problems such as linear elasticity, where accurate simulation is available, the simulation resolution handled by desktop workstations is still orders of magnitudes below available printing resolutions. We propose to speed up simulation and inverse design process of fabricable objects by using multiscale methods. Our method computes coarse-scale simulation meshes with data-drive material models. It improves the simulation efficiency while preserving the characteristic deformation and motion of elastic objects. The first step in our method is to construct a library of microstructures with their material properties such as Young's modulus and Poisson's ratio. The range of achievable material properties is called the material property gamut. We developed efficient sampling method to compute the gamut by focusing on finding samples near and outside the currently sampled gamut. Next, with a pre-computed gamut, functional objects can be simulated and designed using microstructures instead of the base materials. This allows us to simulate and optimize complex objects at a much coarser scale to improve simulation efficiency. The speed improvement leads to designs with as many as a trillion voxels to match printer resolutions. It also enables computational design of dynamic properties that can be faithfully reproduced in reality. In addition to efficient design optimization, the gamut representation of the microstructure envelope provides a way to discover templates of microstructures with extremal physical properties. In contrast to work where such templates are constructed by hand, our work enables the first computational method to automatically discovery microstructure templates that arise from voxel representations.by Desai Chen.Ph. D

Understanding Acoustics

This open access textbook, like Rayleigh’s classic Theory of Sound, focuses on experiments and on approximation techniques rather than mathematical rigor. The second edition has benefited from comments and corrections provided by many acousticians, in particular those who have used the first edition in undergraduate and graduate courses. For example, phasor notation has been added to clearly distinguish complex variables, and there is a new section on radiation from an unbaffled piston. Drawing on over 40 years of teaching experience at UCLA, the Naval Postgraduate School, and Penn State, the author presents a uniform methodology, based on hydrodynamic fundamentals for analysis of lumped-element systems and wave propagation that can accommodate dissipative mechanisms and geometrically-complex media. Five chapters on vibration and elastic waves highlight modern applications, including viscoelasticity and resonance techniques for measurement of elastic moduli, while introducing analytical techniques and approximation strategies that are revisited in nine subsequent chapters describing all aspects of generation, transmission, scattering, and reception of waves in fluids. Problems integrate multiple concepts, and several include experimental data to provide experience in choosing optimal strategies for extraction of experimental results and their uncertainties. Fundamental physical principles that do not ordinarily appear in other acoustics textbooks, like adiabatic invariance, similitude, the Kramers-Kronig relations, and the equipartition theorem, are shown to provide independent tests of results obtained from numerical solutions, commercial software, and simulations. Thanks to the Veneklasen Research Foundation, this popular textbook is now open access, making the e-book available for free download worldwide. Provides graduate-level treatment of acoustics and vibration suitable for use in courses, for self-study, and as a reference Highlights fundamental physical principles that can provide independent tests of the validity of numerical solutions, commercial software, and computer simulations Demonstrates approximation techniques that greatly simplify the mathematics without a substantial decrease in accuracy Incorporates a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation Emphasizes actual applications as examples of topics explained in the text Includes realistic end-of-chapter problems, some including experimental data, as well as a Solutions Manual for instructors. Features “Talk Like an Acoustician“ boxes to highlight key terms introduced in the text