We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.

We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.

We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.

We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.

Understanding and synthesizing locomotion of humans and animals will have far-reaching impacts in computer animation, robotic and biomechanics. However, due to the complexity of the neuromuscular control and physical interactions with the environment, computationally modeling these seemingly effortless locomotion imposes a grand challenge for scientists, engineers and artists. The focus of this thesis is to present a set of computational tools, which can simulate the physical environment and optimize the control strategy, to automatically synthesize locomotion for humans and animals. We first present computational tools to study swimming motions for a wide variety of aquatic animals. This method first builds a simulation of two-way interaction between fluid and an articulated rigid body system. It then searches for the most energy efficient way to swim for a given body shape in the simulated hydrodynamic environment. Next, we present an algorithm that can synthesize locomotion of soft body animals that do not have skeleton support. We combine a finite element simulation with a muscle model that is inspired by muscular hydrostat in nature. We then formulate a quadratic program with complementarity condition (QPCC) to optimize the muscle contraction and contact forces that can lead to meaningful locomotion. We develop an efficient QPCC solver that solves a challenging optimization problem at the presence of discontinuous contact events. We also present algorithms to model human locomotion with a passive mechanical device: riding a bicycle in this case. We apply a powerful reinforcement learning algorithm, which can search for both the parametrization and the parameters of a control policy, to enable a virtual human character to perform bicycle stunts in a physically simulated environment. Finally, we explore the possibility to use the computational tools that are developed for computer animation to control a real robot. We develop a simulation calibration technique which reduces the discrepancy between the simulated results and the performance of the robot in the real environments. For certain motion planning tasks, this method can transfer the controllers optimized for a virtual character in a simulation to a robot that operates in a real environment.

Realism in animation sequences requires movements to be adapted to changing environments within the virtual world. To enhance visual experiences from animated characters, research is being focused on recreating realistic character movement adapted to surrounding environment within the character's world. Existing methods as applied to the problem of controlling character animations are often poorly suited to the problem as they focus on modifying and adapting static sequences, favoring responsiveness and reaching the motion objective rather than realism in characters movements.   Algorithms for synthesizing motion sequences can then bridge the gap between motion quality and responsiveness, and recent methods have shown to open the possibility to recreate specific motions and movement patterns. Effectiveness of proposed methods to synthesize motion can however be questioned, particularly due to the sparsity and quality of evaluations between methods. An issue which is further complicated by variations in learning tasks and motion data used to train models.   Rather than directly propose a new synthesis method, focus is put on refuting existing methods by applying them to the task of synthesizing objective-oriented motion involving the action of throwing a ball. To achieve this goal, two experiments are designed. The first experiment evaluates if a phase-functioned neural network (PFNN) model based on absolute joint configurations can generate objective oriented motion.   To achieve this objective, a separate approach utilizing a hierarchy of phase-function networks is designed and implemented. By comparing application of the two methods on the learning task, the proposed hierarchy model showed significant improvement regarding the ability to fit generated motion to intended end effector trajectories.   To be able to refute the idea of using dense feed-forward neural networks, a second experiment is performed comparing PFNN and feed-forward based network hierarchies. Outcome from the experiment show significant differences in favor for the hierarchy model utilizing phase-function networks.   To facilitate experimentation, objective oriented motion data for training network models are obtained by researching and implementing methods for processing optical motion capture data over repeated practices of over-arm ball throws. Contribution is then threefold: creation of a dataset containing motion sequences of ball throwing actions, evaluation of PFNN on the task of learning sequences of objective oriented motion, and definition of a hierarchy based neural network model applicable to the motion synthesis task.

Interactive 3D animation of human figures is very common in video games, animation studios and virtual environments. However, it is difficult to produce full body animation that looks realistic enough to be comparable to studio quality human motion data. The commercial motion capture systems are expensive and not suitable for capture in everyday environments. Real-time requirements tend to reduce quality of animation. We present a motion graph based framework to produce high quality motion sequences in real-time using a set of inertial sensor based controllers. The user's action generates signals from the controllers that provide constraints to select appropriate sequence of motions from a structured database of human motions, namely \emph{motion graph}. Our local search algorithm utilizes noise prone and rapidly varying input sensor signals for querying a large database in real-time. The ability to waive the controllers for producing high quality animation provides a simple 3D user interface that is intuitive to use. The proposed framework is low cost and easy to setup. / Master of Science

A challenging goal for both the game industry and the research community of computer graphics is the generation of 3D virtual avatars that automatically perform realistic human motions with high speed at low monetary cost. So far, full body motion estimation of human complexity remains an important open problem. We propose a realistic motion estimation framework to control the animation of 3D avatars. Instead of relying on a motion capture device as the control signal, we use low-cost and ubiquitously available 3D accelerometer sensors. The framework is developed in a data-driven fashion, which includes two phases: model learning from an existing high quality motion database, and motion synthesis from the control signal. In the phase of model learning, we built a high quality motion model of less complexity that learned from a large motion capture database. Then, by taking the 3D accelerometer sensor signal as input, we were able to synthesize high-quality motion from the motion model we learned. In this thesis, we present two different techniques for model learning and motion synthesis, respectively. Linear and nonlinear reduction techniques for data dimensionality are applied to search for the proper low dimensional representation of motion data. Two motion synthesis methods, interpolation and optimization, are compared using the 3D acceleration signals with high noise. We evaluate the result visually compared to the real video and quantitatively compared to the ground truth motion. The system performs well, which makes it available to a wide range of interactive applications, such as character control in 3D virtual environments and occupational training. / Master of Science

For a general J wheeled mobile platform capable of up to 3-Degrees-Of-Freedom (DOF) planar motion, there are up to 2J independent input parameters yet the output of the planar platform is specified with only three independent parameters. Currently, the motion synthesis for such platforms is done with a Jacobian based “pseudo” inverse that uses a rectangular matrix for Jacobian. However, a mobile platform is a parallel mechanism and has a more direct solution to the inverse kinematics problem. To this effect, we propose a physical methodology for kinematic modeling of multi-wheeled mobile platforms using Instant Centers (IC) to describe the kinematic state of all system points up to the kth order using a generalized algebraic formulation. This is achieved by using a series of ICs (velocity, acceleration, jerk, etc.) where each point in the system has a time state with its magnitude proportional to the radial distance of the point from the associated IC and at a constant angle relative to that radius. The use of IC’s for mobile platform kinematics is not new, however we present a completely generalized and extensive formulation that also treats the higher order kinematics. To the best of our knowledge, this is the first time the third and higher order ICs have been presented in the literature. The components of this research effort are: (i) extension of the theory of instantaneous invariants to the higher order motion by generalizing the theory to any order, (ii) studying some special case 1-DOF, 2-DOF motions to understand the physical nature of the higher order ICs, (iii) applying the results of (i) and (ii) to the motion synthesis of planar, wheeled mobile platforms by first categorizing them into four distinct categories, and (iv) studying the dynamic model of a representative mobile platform to emphasize the importance of wheel dynamics and traction parameters on the performance of the mobile platform. The IC based formulation presents a concise expression for a general order time state of a general point on the rigid body with the magnitude and direction separated and identified. We showed that the method based on instant centers provides a straightforward and yet physically intuitive way to synthesize a general kth order planar motion of mobile platforms. The study of special case 1-DOF/2-DOF motions emphasized the geometric nature of the higher order ICs and also helped understand the influence of instantaneous kinematic states (such as angular velocity _, angular acceleration, _, etc.) on the various ICs. The application of this theory to planar mobile platform allowed us to categorize the platforms based on their dexterity and to generalize the motion synthesis to some extent. The study of the dynamic model of a representative mobile platform showed us that the redundant inputs (2J inputs versus 3 outputs) in this case may be employed to sustain and manage the uncertainties and nonlinearities in the wheel ground interaction. / text

A long-standing goal in computer graphics is to create and control realistic motion for virtual human characters. Despite the progress made over the last decade, it remains challenging to design a system that allows a random user to intuitively create and control life-like human motions. This dissertation focuses on exploring theory, algorithms and applications that enable novice users to quickly and easily create and control natural-looking motions, including both full-body movement and hand articulations, for human characters. More specifically, the goals of this research are: (1) to investigate generative statistical models and physics-based dynamic models to precisely predict how humans move and (2) to demonstrate the utility of our motion models in a wide range of applications including motion analysis, synthesis, editing and acquisition. We have developed two novel generative statistical models from prerecorded motion data and show their promising applications in real time motion editing, online motion control, offline animation design, and motion data processing. In addition, we have explored how to model subtle contact phenomena for dexterous hand grasping and manipulation using physics-based dynamic models. We show for the first time how to capture physically realistic hand manipulation data from ambiguous image data obtained by video cameras.