Computer graphics techniques for modeling page turning

Turning the page is a mechanical part of the cognitive act of reading that we do literally unthinkingly. Interest in realistic book models for digital libraries and other online documents is growing. Yet actually producing a computer graphics implementation for modeling page turning is a challenging undertaking. There are many possible foundations: two-dimensional models that use reflection and rotation; geometrical models using cylinders or cones; mass-spring models that simulate the mechanical properties of paper at varying degrees of fidelity; finite-element models that directly compute the actual forces within a piece of paper. Even the simplest methods are not trivial, and the more sophisticated ones involve detailed physical and mathematical models. The variety, intricacy and complexity of possible ways of simulating this fundamental act of reading is virtually unknown. This paper surveys computer graphics models for page turning. It combines a tutorial introduction that covers the range of possibilities and complexities with a mathematical synopsis of each model in sufficient detail to serve as a basis for implementation. Illustrations are included that are generated by our implementations of each model. The techniques presented include geometric methods (both two- and three-dimensional), mass-spring models with varying degrees of accuracy and complexity, and finite-element models. We include a detailed comparison of experimentally-determined computation time and subjective visual fidelity for all methods discussed. The simpler techniques support convincing real-time implementations on ordinary workstations

Discrete Differential Geometry of Thin Materials for Computational Mechanics

Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation

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

Non-smooth developable geometry for interactively animating paper crumpling

International audienceWe present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations

Projective Dynamics: Fusing Constraint Projections for Fast Simulation

We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuumbased potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation