Interactive multiresolution animation of deformable models (original) (raw)
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Simulating deformable objects for computer animation: a numerical perspective
ArXiv, 2021
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control and fabrication. The goals and merits of suitable numerical algorithms for these applications are different from those of typical numerical analysis research in dynamical systems. Here the mathematical model is not fixed a priori but must be adjusted as necessary to capture the desired behaviour, with an emphasis on effectively producing lively animations of objects with complex geometries. Results are often judged by how realistic they appear to observers (by the “eye-norm”) as well as by the efficacy of the numerical procedures employed. And yet, we show that with an adjusted view numerical analysis and applied mathematics can contribute significantly to the development of appropriate methods and their analysis in a variety of areas including fin...
A multiresolution framework for dynamic deformations
2002
We present a novel framework for dynamic simulation of elastically deformable solids. Our approach combines classical finite element methodology with subdivision wavelets to meet the needs of computer graphics applications. We represent deformations using a wavelet basis constructed from volumetric Catmull-Clark subdivision. Catmull-Clark subdivision solids allow the domain of deformation to be taylored to objects of arbitrary topology. The domain of deformation can correspond to the interior of a subdivision surface or can enclose an arbitrary surface mesh. Within the wavelet framework we develop the equations of motion for elastic deformations in the presence of external forces and constraints. We solve the resulting differential equations using an implicit method, which lends stability. Our framework allows trade-off between speed and accuracy. For interactive applications, we accelerate the simulation by adaptively refining the wavelet basis while avoiding visual "popping" artifacts. Off-line simulations can employ a fine basis for higher accuracy at the cost of more computation time. By exploiting the properties of smooth subdivision we can compute less expensive solutions using a trilinear basis yet produce a smooth result that meets the constraints.
ACM SIGGRAPH Computer Graphics, 1987
The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.
Time-critical animation of deformable solids
Computer Animation and Virtual Worlds, 2005
This article presents a model for handling multi-resolution animation of complex deformable models. An octree-based animation and algorithmic tools are introduced to provide real-time interaction on complex objects. Some efficient collision detection scheme is also described for deformable models. A method is also presented for time-guaranteed mechanical simulation: It allows an automatic tuning of the octree resolution to match some external performance constraints, such as a pre-defined CPU consumption limit.
Dynamic Animation of N-Dimensional Deformable Objects
This paper presents a new, accurate, efficient and unified method for dynamic animation of one, two or three-dimensional deformable objects. The objects are modelled as d-dimensional juxtapositions of ddimensional patches defined as parametric blending of a common d-dimensional mesh of 3D control points. Animation of the object is achieved by dynamic animation of its control points. This ensures that at each time step the object shape conforms to its patches definitions, and, thus, that every property implied by the nature of the blending functions is verified. Dynamic animation of these continuous models implies no "matter discretising" as the control points are not considered as material points but moreover as the degrees of freedom of the continuous object. A generic (both for blending functions nature and object intrinsic dimension d) mechanical model reflecting this idea is proposed. Then, according to this modelling idea, a convenient generic dynamic animation engine is built from Lagrangian Equations. This engine relies upon an accurate and very efficient linear system. Forces and constraints handling as well as numerical resolution process are then briefly discussed in this scheme.
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '02, 2002
The linear strain measures that are commonly used in real-time animations of deformable objects yield fast and stable simulations. However, they are not suitable for large deformations. Recently, more realistic results have been achieved in computer graphics by using Green's non-linear strain tensor, but the non-linearity makes the simulation more costly and introduces numerical problems.
Real-time deformable models for surgery simulation: a survey
Computer Methods and Programs in Biomedicine, 2005
Simulating the behaviour of elastic objects in real time is one of the current objectives of computer graphics. One of its fields of application lies in virtual reality, mainly in surgery simulation systems. In computer graphics, the models used for the construction of objects with deformable behaviour are known as deformable models. These have two conflicting characteristics: interactivity and motion realism. The different deformable models developed to date have promoted only one of these (usually interactivity) to the detriment of the other (biomechanical realism). In this paper, we present a classification of the different deformable models that have been developed. We present the advantages and disadvantages of each one. Finally, we make a comparison of deformable models and perform an evaluation of the state of the art and the future of deformable models.
Real-time simulation of deformable objects: Tools and application
Computer …, 2001
This paper presents algorithms for animating deformable objects in real-time. It focuses on computing the deformation of an object subject to external forces and detecting collisions among deformable and rigid objects. The targeted application domain is surgical training. This application relies more on visual realism than exact, patientspecific deformation, but requires that computations be performed in real-time. This is in contrast with pre-operative surgical planning, where computations may be done offline, but must provide accurate results. To achieve realtime performance, the proposed algorithms take advantage of the facts that most deformations are local, human-body tissues are well damped, and motions of surgical instruments are relatively slow. They have been integrated into a virtual-reality system for simulating the suturing of small blood vessels (microsurgery).