A consistent bending model for cloth simulation with corotational subdivision finite elements

Modelling bending energy in a consistent way is decisive for the realistic simulation of cloth. With existing approaches characteristic behaviour like folding and buckling cannot be reproduced in a physically convincing way. We present a new method based on a corotational formulation of subdivision finite elements. Due to the non-local nature of the employed subdivision basis functions a C1-continuous displacement field can be defined. It is thus possible to use the governing equations of thin shell analysis leading to a physically accurate bending behaviour. Using a corotated strain tensor allows the large displacement analysis of cloth while retaining a linear system of equations. Hence, known convergence properties and computational efficiency are preserved

Construcción de matriz espacial de cascarilla cónica plegable de una capa

The paper covers the visualization of a volume-space form of the flexible inextensible one-layer shell that is represented in the stress and strain state appearing during fastening the shell on the upper edge and its free location below the fastening border in the field of gravitational and elastic forces of the material. With no account taken of the gravitational forces, the shell is a right circular flattened cone. A developed program module can be used in designing and calculating the thin-wall shell structures during their non-linear deformation and their visualization. Visualization of the space form of the shell structure can be used for simulating various products, for instance, the cone antennae or the textile products, flexible elastic shells in the hydraulic engineering, etc.Aquí se considera la visualización de una matriz volumétrica espacial de la cascarilla cónica plegable de una sola capa. Se representa la cascarilla en el estado de estrés y tensión registrado, cuando se fija la cascarilla en el borde superior y en su localización bajo del borde de anclaje en la campo de fuerzas elásticas y de gravedad del material. Sin tener en cuenta las fuerzas de gravedad, se define la cascarilla como un cono recto circular truncado. Se puede usar el módulo de programa desarrollado para diseñar y calcular estructuras de cascos con paredes delgadas expuestas a deformación no lineal así como durante su visualización. Se puede usar la visualización de la matriz espacial de la estructura de casco para simular diversos productos, por ejemplo, antenas cónicas o productos textiles, cascarillas plegables para ingeniería hidráulica, etc

Construcción de matriz espacial de cascarilla cónica plegable de una capa

Aquí se considera la visualización de una matriz volumétrica espacial de la cascarilla cónica plegable de una sola capa. Se representa la cascarilla en el estado de estrés y tensión registrado, cuando se fija la cascarilla en el borde superior y en su localización bajo del borde de anclaje en la campo de fuerzas elásticas y de gravedad del material. Sin tener en cuenta las fuerzas de gravedad, se define la cascarilla como un cono recto circular truncado. Se puede usar el módulo de programa desarrollado para diseñar y calcular estructuras de cascos con paredes delgadas expuestas a deformación no lineal así como durante su visualización. Se puede usar la visualización de la matriz espacial de la estructura de casco para simular diversos productos, por ejemplo, antenas cónicas o productos textiles, cascarillas plegables para ingeniería hidráulica, et

Subdivision Directional Fields

We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the finite-element representation with discrete exterior calculus. By commuting with differential operators, our subdivision is structure-preserving: it reproduces curl-free fields precisely, and reproduces divergence-free fields in the weak sense. Moreover, our subdivision scheme directly extends to directional fields with several vectors per face by working on the branched covering space. Finally, we demonstrate how our scheme can be applied to directional-field design, advection, and robust earth mover's distance computation, for efficient and robust computation

Modeling and grasping of thin deformable objects

Deformable modeling of thin shell-like and other objects have potential application in robot grasping, medical robotics, home robots, and so on. The ability to manipulate electrical and optical cables, rubber toys, plastic bottles, ropes, biological tissues, and organs is an important feature of robot intelligence. However, grasping of deformable objects has remained an underdeveloped research area. When a robot hand applies force to grasp a soft object, deformation will result in the enlarging of the finger contact regions and the rotation of the contact normals, which in turn will result in a changing wrench space. The varying geometry can be determined by either solving a high order differential equation or minimizing potential energy. Efficient and accurate modeling of deformations is crucial for grasp analysis. It helps us predict whether a grasp will be successful from its finger placement and exerted force, and subsequently helps us design a grasping strategy. The first part of this thesis extends the linear and nonlinear shell theories to describe extensional, shearing, and bending strains in terms of geometric invariants including the principal curvatures and vectors, and the related directional and covariant derivatives. To our knowledge, this is the first non-parametric formulation of thin shell strains. A computational procedure for the strain energy is then offered for general parametric shells. In practice, a shell deformation is conveniently represented by a subdivision surface. We compare the results via potential energy minimization over a couple of benchmark problems with their analytical solutions and the results generated by two commercial softwares ABAQUS and ANSYS. Our method achieves a convergence rate an order of magnitude higher. Experimental validation involves regular and freeform shell-like objects (of various materials) grasped by a robot hand, with the results compared against scanned 3-D data (accuracy 0.127mm). Grasped objects often undergo sizable shape changes, for which a much higher modeling accuracy can be achieved using the nonlinear elasticity theory than its linear counterpart. The second part numerically studies two-finger grasping of deformable curve-like objects under frictional contacts. The action is like squeezing. Deformation is modeled by a degenerate version of the thin shell theory. Several differences from rigid body grasping are shown. First, under a squeeze, the friction cone at each finger contact rotates in a direction that depends on the deformable object\u27s global geometry, which implies that modeling is necessary for grasp prediction. Second, the magnitude of the grasping force has to be above certain threshold to achieve equilibrium. Third, the set of feasible finger placements may increase significantly compared to that for a rigid object of the same shape. Finally, the ability to resist disturbance is bounded in the sense that increasing the magnitude of an external force may result in the breaking of the grasp

A Consistent Bending Model for Cloth Simulation with Corotational Subdivision Finite Elements

Wrinkles and folds play an important role in the appearance of real textiles. The way in which they form depends mainly on the bending properties of the specific material type. Existing approaches fail to reliably reproduce characteristic behaviour like folding and buckling for different material types or resolutions. It is therefore crucial for the realistic simulation of cloth to model bending energy in a physically accurate and consistent way. In this paper we present a new method based on a corotational formulation of subdivision finite elements. Due to the non-local nature of the employed subdivision basis functions a C -continuous displacement field can be defined

W.: A consistent bending model for cloth simulation with corotational subdivision finite elements

Modelling bending energy in a consistent way is decisive for the realistic simulation of cloth. With existing approaches characteristic behaviour like folding and buckling cannot be reproduced in a physically convincing way. We present a new method based on a corotational formulation of subdivision finite elements. Due to the non-local nature of the employed subdivision basis functions a C 1-continuous displacement field can be defined. It is thus possible to use the governing equations of thin shell analysis leading to a physically accurate bending behaviour. Using a corotated strain tensor allows the large displacement analysis of cloth while retaining a linear system of equations. Hence, known convergence properties and computational efficiency are preserved.

The Material Point Method for Solid and Fluid Simulation

The Material Point Method (MPM) has shown its high potential for physics-based simulation in the area of computer graphics. In this dissertation, we introduce a couple of improvements to the traditional MPM for different applications and demonstrate the advantages of our methods over the previous methods.First, we present a generalized transfer scheme for the hybrid Eulerian/Lagrangian method: the Polynomial Particle-In-Cell Method (PolyPIC). PolyPIC improves kinetic energy conservation during transfers, which leads to better vorticity resolution in fluid simulations and less numerical damping in elastoplasticity simulations. Our transfers are designed to select particle-wise polynomial approximations to the grid velocity that are optimal in the local mass-weighted L2 norm. Indeed our notion of transfers reproduces the original Particle-In-Cell Method (PIC) and recent Affine Particle-In-Cell Method (APIC). Furthermore, we derive a polynomial basis that is mass orthogonal to facilitate the rapid solution of the optimality condition. Our method applies to both of the collocated and staggered grid.As the second contribution, we present a novel method for the simulation of thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high-resolution examples. Furthermore, we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.In the third part, we present a new hybrid Lagrangian Material Point Method for simulating volumetric objects with frictional contact. The resolution of frictional contact in the thin shell simulation cannot be generalized to the case of volumetric materials directly. Also, even though MPM allows for the natural simulation of hyperelastic materials represented with Lagrangian meshes, it usually coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts, e.g., numerical cohesion. We demonstrate that our hybrid method can efficiently resolve these issues. We show the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

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

Numerical Methods in Shape Spaces and Optimal Branching Patterns

The contribution of this thesis is twofold. The main part deals with numerical methods in the context of shape space analysis, where the shape space at hand is considered as a Riemannian manifold. In detail, we apply and extend the time-discrete geodesic calculus (established by Rumpf and Wirth [WBRS11, RW15]) to the space of discrete shells, i.e. triangular meshes with fixed connectivity. The essential building block is a variational time-discretization of geodesic curves, which is based on a local approximation of the squared Riemannian distance on the manifold. On physical shape spaces this approximation can be derived e.g. from a dissimilarity measure. The dissimilarity measure between two shell surfaces can naturally be defined as an elastic deformation energy capturing both membrane and bending distortions. Combined with a non-conforming discretization of a physically sound thin shell model the time-discrete geodesic calculus applied to the space of discrete shells is shown to be suitable to solve important problems in computer graphics and animation. To extend the existing calculus, we introduce a generalized spline functional based on the covariant derivative along a curve in shape space whose minimizers can be considered as Riemannian splines. We establish a corresponding time-discrete functional that fits perfectly into the framework of Rumpf and Wirth, and prove this discretization to be consistent. Several numerical simulations reveal that the optimization of the spline functional—subject to appropriate constraints—can be used to solve the multiple interpolation problem in shape space, e.g. to realize keyframe animation. Based on the spline functional, we further develop a simple regression model which generalizes linear regression to nonlinear shape spaces. Numerical examples based on real data from anatomy and botany show the capability of the model. Finally, we apply the statistical analysis of elastic shape spaces presented by Rumpf and Wirth [RW09, RW11] to the space of discrete shells. To this end, we compute a Fréchet mean within a class of shapes bearing highly nonlinear variations and perform a principal component analysis with respect to the metric induced by the Hessian of an elastic shell energy. The last part of this thesis deals with the optimization of microstructures arising e.g. at austenite-martensite interfaces in shape memory alloys. For a corresponding scalar problem, Kohn and Müller [KM92, KM94] proved existence of a minimizer and provided a lower and an upper bound for the optimal energy. To establish the upper bound, they studied a particular branching pattern generated by mixing two different martensite phases. We perform a finite element simulation based on subdivision surfaces that suggests a topologically different class of branching patterns to represent an optimal microstructure. Based on these observations we derive a novel, low dimensional family of patterns and show—numerically and analytically—that our new branching pattern results in a significantly better upper energy bound