5140837
Modeling hair using level-of-detail representations
We present a novel approach for modeling hair using level-of-detail representations. The set of representations include individual strands, hair clusters, and hair strips. They are represented using subdivision curves or surfaces, and have the same underlying base skeleton to maintain consistent high-level physical behavior when a transition between different levels-of detail occurs. This framework supports automatic simplification of dynamic simulation, collision detection, and graphical rendering of animated hair. It also offers flexibility to balance between the overall performance and visual quality, and can be used to model and render different hairstyles. We have used these level-of-detail representations to animate various hairstyles and obtained noticeable performance improvement, with little loss in visual quality.
7169150
A versatile interactive 3D brush model
We present a flexible modeling approach capable of realistically simulating many varieties of brushes commonly used in painting. Our geometric model of brush heads is a combination of subdivision surfaces and hundreds of individual bristles represented by thin polygonal strips. We exploit bristle-to-bristle coherence, simulating only a fraction of the bristles and using interpolation for the remainder. Our dynamic model incorporates realistic physically-based deformation, including anisotropic friction, brush plasticity, and tip spreading. We use an energy minimization framework with a novel geometric representation of the brush head to generate a wider variety of brushes. Finally, we have developed an improved haptic model that provides realistic force feedback, directly related to the results of the brush dynamic simulation. Using this model, we are able to simulate a wide range of brush styles and create an excellent variety of strokes such as the crisp, curvy strokes of Western decorative painting, or rough scratchy strokes like certain Oriental calligraphy. We have also developed an exporter for a popular free 3D modeling package that makes it easier for non-programmers to create any desired style of brush, real or fanciful.
9041268
Modeling ice dynamics as a thin-film Stefan problem
Large, 3D ice formations such as icicles exhibit a high degree of geometric and optical complexity. Modeling these features by hand can be a daunting task, so we present a novel physically-based algorithm for simulating this phenomenon. Solidification is usually posed as a so-called 'Stefan problem', but the problem in its classic form is inappropriate for simulating the ice typically found in a winter scene. We instead use the 'thin-film' variant of the Stefan problem to derive velocity equations for a level set simulation. However, due to the scales involved in the problem, even an adaptive grid level set solver is still insufficient to track the tip of an icicle. Therefore, we derive an analytical solution for the icicle tip and use it to correct the level set simulation. The results appear to be in agreement with experimental data. We also present a physically-based technique for modeling ripples along the ice surface that alleviates the need to explicitly track small-scale geometry. To our knowledge, our approach is the most complete model available, and produces complex visual phenomena that no previous method has been able to capture.
7639620
Stable and responsive six-degree-of-freedom haptic manipulation using implicit integration
In this paper we present a novel approach for simulating the rigid body dynamics of a haptically manipulated object using implicit integration. Our formulation requires the linearization of contact and manipulation forces, and it provides higher stability and responsiveness than previous methods. The linearization of contact forces, coupled with fast, perceptually based collision detection algorithms, enables us to perform highly stable and responsive 6-degree-of-freedom haptic rendering of complex polygonal models.
206451107
Sensation-Preserving Haptic Rendering
Most human-computer interactive systems focus primarily on the graphical rendering of visual information and, to a lesser extent, on the display of auditory information. Haptic interfaces have the potential to increase the quality of human-computer interaction by accommodating the sense of touch. They provide an attractive augmentation to visual display and enhance the level of understanding of complex data sets. A haptic rendering system generates contact or restoring forces to prevent penetration into the virtual objects and create a sense of touch. The system computes contact forces by first detecting if a collision or penetration has occurred. Then, the system determines the (projected) contact points on the model surface. Finally, it computes restoring forces based on the amount of penetration. Researchers have recently investigated the problem of rendering the contact forces and torques between 3D virtual objects. This problem is known as six-degrees-of-freedom (6-DOF) haptic rendering, as the computed output includes both 3-DOF forces and 3-DOF torques. This article presents an overview of our work in this area. We suggest different approximation methods based on the principle of preserving the dominant perceptual factors in haptic exploration.
6243696
Geometry-driven physical interaction between avatars and virtual environments
We present an interactive technique on virtual contact handling for avatars in virtual environments using geometry-driven physics. If a contact has occurred between an articulated avatar and a virtual environment, the global penetration depth and contact points are estimated based on a fast local penetration depth computation for decomposed convex pieces. The penetration depth and contact information are then used to resolve overlap between the avatar and the virtual environment. If applicable, joint angles for an articulated body are computed using an inverse kinematics approach based on cyclic coordinate descent. Resulting dynamic response with friction is modeled with impulse-based dynamics under the Coulomb friction law. We demonstrate the algorithm on a modestly complex virtual environment. The resulting system is able to maintain an interactive frame rate of 30–60 Hz. Copyright © 2004 John Wiley & Sons, Ltd.
890758
On Balanced Graphs
Berge defined a hypergraph to be balanced if its incidence matrix is balanced. We consider this concept applied to graphs, and call a graph to be balanced when its clique matrix is balanced. Characterizations of balanced graphs by forbidden subgraphs and by clique subgraphs are proved in this work. Using properties of domination we define four subclasses of balanced graphs. Two of them are characterized by 0–1 matrices and can be recognized in polynomial time. Furthermore, we propose polynomial time combinatorial algorithms for the problems of stable set, clique-independent set and clique-transversal for one of these subclasses of balanced graphs. Finally, we analyse the behavior of balanced graphs and these four subclasses under the clique graph operator.
30294156
Cycle embedding in faulty wrapped butterfly graphs
In this paper, we study the maximal length of cycle embedding in a faulty wrapped butterfly graph BFn with at most two faults in vertices and/or edges. When there is one vertex fault and one edge fault, we prove that the maximum cycle length is n2n − 2 if n is even and n2n − 1 if n is odd. When there are two faulty vertices, the maximum cycle length is n2n − 2 for odd n. All these results are optimal because the wrapped butterfly graph is bipartite if and only if n is even. © 2003 Wiley Periodicals, Inc.
2903221
Algorithms for clique-independent sets on subclasses of circular-arc graphs
A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a 3K2-free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n2). These algorithms suppose that an HCA model of the graph is given.
5909240
The Computational Complexity of the Reliability Problem on Distributed Systems
Abstract The reliability of a distributed program in a distributed computing system is the probability that a program which runs on multiple processing elements and needs to communicate with other processing elements for remote data files will be executed successfully. This reliability varies according to 1. (1) the topology of the distributed computing system 2. (2) the reliability of the communication links 3. (3) the data files and program distribution among processing elements and 4. (4) the data files required to execute a program. This paper shows that solving this reliability problem is NP-hard even when the distributed computing system is restricted to a series-parallel, a 2-tree, a tree, or a star structure.
9086045
The distributed program reliability analysis on star topologies
We show that computing distributed program reliability on the star distributed computing system is NP-hard. We develop a polynomially solvable case to compute distributed program reliability when some additional file distribution is restricted on the star topology. We also propose a polynomial time algorithm for computing distributed program reliability with an approximate solution when the star topology is not satisfied with the additional file distribution.