Real-time simulation and visualisation of cloth using edge-based adaptive meshes

Real-time rendering and the animation of realistic virtual environments and characters has progressed at a great pace, following advances in computer graphics hardware in the last decade. The role of cloth simulation is becoming ever more important in the quest to improve the realism of virtual environments. The real-time simulation of cloth and clothing is important for many applications such as virtual reality, crowd simulation, games and software for online clothes shopping. A large number of polygons are necessary to depict the highly exible nature of cloth with wrinkling and frequent changes in its curvature. In combination with the physical calculations which model the deformations, the effort required to simulate cloth in detail is very computationally expensive resulting in much diffculty for its realistic simulation at interactive frame rates. Real-time cloth simulations can lack quality and realism compared to their offline counterparts, since coarse meshes must often be employed for performance reasons. The focus of this thesis is to develop techniques to allow the real-time simulation of realistic cloth and clothing. Adaptive meshes have previously been developed to act as a bridge between low and high polygon meshes, aiming to adaptively exploit variations in the shape of the cloth. The mesh complexity is dynamically increased or refined to balance quality against computational cost during a simulation. A limitation of many approaches is they do not often consider the decimation or coarsening of previously refined areas, or otherwise are not fast enough for real-time applications. A novel edge-based adaptive mesh is developed for the fast incremental refinement and coarsening of a triangular mesh. A mass-spring network is integrated into the mesh permitting the real-time adaptive simulation of cloth, and techniques are developed for the simulation of clothing on an animated character

실시간 의복 시뮬레이션을 위한 선형 모델 연구

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2013. 8. 고형석.옷에서 일어나는 변형은 크게 평면 내 변형과 평면 외 변형으로 나눌 수 있다. 인장과 전단이 평면 내 변형, 굽힘이 평면 외 변형에 속한다. 의류 시뮬레이션은 위 세 가지 변형을 모두 포함한다. 본 논문에서는 옷의 변형에 대한 새로운 물리 모델을 제시한다. 본 논문에서 제시하는 모델의 의의는 그것의 수치적 시뮬레이션이 실시간에 이루어질 수 있다는 점과 기존의 실시간 모델에 존재했던 몇가지 결함을 해결함으로써 시뮬레이션 결과에서 보였던 문제점들을 해결했다는 점에 있다. 본 논문이 새로운 물리 모델을 개발함에 있어 주요한 아이디어는 에너지 함수에 존재하는 (x-C)^2 항을 x^* 라는 상수 벡터를 도입하여x-x^*^2 라는 항으로 바꾼 데 있다. 이렇게 함으로써 힘 자코비안 행렬을 상수로 만들고 그에 따라 시스템 행렬 역시 상수로 만든다. 그 결과 시스템 행렬의 역행렬을 시뮬레이션 시작 전 사전 계산 시간에 미리 구할 수 있고, 내연적 시뮬레이션 진행 과정에서 시스템 행렬을 매번 새로 구성하고 해를 구해야 했던 과정을 단순한 행렬과 벡터의 곱셈으로 대체할 수 있다. 본 논문은 이러한 선형 물리 모델을 선분 기반 시스템과 삼각형 기반 시스템에 대해 제시한다. 추가적으로 행렬과 벡터 곱셈 과정의 속도를 향상하기 위해 최신의 희소 촐레스키 분해 방법을 살펴보고 의상 시뮬레이션에 효과적인 적용 방법을 소개한다.Deformations occurring in cloth can be decomposed into two components: the in-plane and the out-of-plane deformations. Stretch and shear are in-plane deformation, and bending is out-of-plane deformation. Clothing simulation involves all the above types of deformations. This paper proposes a new physical model for deformations of clothes. The significance of the proposed models is that (1) their numerical simulation can be done in real-time, and (2) the models fix some flaws that existed in previous real-time models, leading to conspicuous reduction of artifacts. The essential idea in inventing the new models is to replace (-C)^2 in the energy function with^2 for some constant vector x^*. Then, the force jacobian becomes a constant, and so does the system matrix. As a result, its inverse matrix can be pre-computed only once in off-line, so that the on-line semi-implicit integration can be replaced with (the constant) matrix-vector multiplications. This paper develops such simplified physical models for both edge-based and triangle-based systems. In addition, to speed up the process of matrix-vector multiplications, this work reviews the current state-of-the-art in the Sparse Cholesky factorization methods and introduces an effective method for the current purpose.Abstract i Contents iii List of Figures v List of Tables vii 1 Introduction 1 1.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Edge-Based Formulation of Stretch Energy and Force . . . . . 4 1.3 Explicit Formulation . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Implicit Formulation . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Related Work 9 3 Edge-Based Linear Stretch Model 13 3.1 Conventional Stretch Model . . . . . . . . . . . . . . . . . . . . 14 3.2 Our Stretch Model . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Representation of Shear Deformations . . . . . . . . . . . . . . 20 3.4 A Killer Application of This Model . . . . . . . . . . . . . . . 21 4 Triangle-Based Linear Stretch/Shear Model 22 4.1 Material Space to 3D Space Mapping S . . . . . . . . . . . . . 23 4.2 Conventional Stretch and Shear Model . . . . . . . . . . . . . . 24 4.3 Our Stretch and Shear Model . . . . . . . . . . . . . . . . . . . 24 5 Linear Bending Model 28 5.1 Calculating Bending Vector . . . . . . . . . . . . . . . . . . . . 28 5.2 Applying Bending Force . . . . . . . . . . . . . . . . . . . . . . 30 5.3 Jacobian of the Bending Force . . . . . . . . . . . . . . . . . . 31 6 Sparse Cholesky Factorization 32 6.1 Cholesky Factorization . . . . . . . . . . . . . . . . . . . . . . . 32 6.2 Reordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 7 Experimental Results 48 8 Conclusion 65 Bibliography 67 초록 71Docto