Parachute simulation: integration methods

Mass-spring models are frequently employed in parachute simulations due to their simplicity and efficiency. A series of integration methods can be used to solve the dynamic system, however their use presents some difficulties often associated with the stability, accuracy and the computational resources consumption. We compared some of these methods in four different situations: simple pendulum, spring pendulum and two parachute models, and for each system the behavior of the integration methods was different. In the parachute simulations, which are the main objective of this thesis, the Improved Explicit Euler presented the best performance in the first model, although the simulation ended up diverging. For the second model, all of the tested schemes worked.Trabalho de Conclusão de Curso (Graduação)Modelos massa-mola são frequentemente empregados em simulações de paraquedas devido à sua simplicidade e eficiência. Diversos métodos de integração podem ser utilizados para a resolução desses sistemas, entretanto, sua utilização pode acarretar em dificuldades associadas à estabilidade, acurácia e ao consumo de recursos computacionais. Comparamos alguns desses métodos em quatro diferentes situações: um pendulo simples, um pêndulo com mola e dois modelos de paraquedas. E para cada modelo, o comportamento dos métodos de integração mostrou-se diferente. Nas simulações de paraquedas, o principal objetivo deste trabalho, o Método Melhorado de Euler Explícito apresentou a melhor performance no primeiro modelo, apesar de a simulação acabar divergindo. Para o segundo modelo de paraquedas, todos os métodos testados funcionaram

Simulation of the Beating Heart Based on Physically Modeling aDeformable Balloon

The motion of the beating heart is complex and createsartifacts in SPECT and x-ray CT images. Phantoms such as the JaszczakDynamic Cardiac Phantom are used to simulate cardiac motion forevaluationof acquisition and data processing protocols used for cardiacimaging. Two concentric elastic membranes filled with water are connectedto tubing and pump apparatus for creating fluid flow in and out of theinner volume to simulate motion of the heart. In the present report, themovement of two concentric balloons is solved numerically in order tocreate a computer simulation of the motion of the moving membranes in theJaszczak Dynamic Cardiac Phantom. A system of differential equations,based on the physical properties, determine the motion. Two methods aretested for solving the system of differential equations. The results ofboth methods are similar providing a final shape that does not convergeto a trivial circular profile. Finally,a tomographic imaging simulationis performed by acquiring static projections of the moving shape andreconstructing the result to observe motion artifacts. Two cases aretaken into account: in one case each projection angle is sampled for ashort time interval and the other case is sampled for a longer timeinterval. The longer sampling acquisition shows a clear improvement indecreasing the tomographic streaking artifacts

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

Efficient techniques for soft tissue modeling and simulation

Performing realistic deformation simulations in real time is a challenging problem in computer graphics. Among numerous proposed methods including Finite Element Modeling and ChainMail, we have implemented a mass spring system because of its acceptable accuracy and speed. Mass spring systems have, however, some drawbacks such as, the determination of simulation coefficients with their iterative nature. Given the correct parameters, mass spring systems can accurately simulate tissue deformations but choosing parameters that capture nonlinear deformation behavior is extremely difficult. Since most of the applications require a large number of elements i. e. points and springs in the modeling process it is extremely difficult to reach realtime performance with an iterative method. We have developed a new parameter identification method based on neural networks. The structure of the mass spring system is modified and neural networks are integrated into this structure. The input space consists of changes in spring lengths and velocities while a "teacher" signal is chosen as the total spring force, which is expressed in terms of positional changes and applied external forces. Neural networks are trained to learn nonlinear tissue characteristics represented by spring stiffness and damping in the mass spring algorithm. The learning algorithm is further enhanced by an adaptive learning rate, developed particularly for mass spring systems. In order to avoid the iterative approach in deformation simulations we have developed a new deformation algorithm. This algorithm defines the relationships between points and springs and specifies a set of rules on spring movements and deformations. These rules result in a deformation surface, which is called the search space. The deformation algorithm then finds the deformed points and springs in the search space with the help of the defined rules. The algorithm also sets rules on each element i. e. triangle or tetrahedron so that they do not pass through each other. The new algorithm is considerably faster than the original mass spring systems algorithm and provides an opportunity for various deformation applications. We have used mass spring systems and the developed method in the simulation of craniofacial surgery. For this purpose, a patient-specific head model was generated from MRI medical data by applying medical image processing tools such as, filtering, the segmentation and polygonal representation of such model is obtained using a surface generation algorithm. Prism volume elements are generated between the skin and bone surfaces so that different tissue layers are included to the head model. Both methods produce plausible results verified by surgeons

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented