15734500
Fast Animation of Lightning Using an Adaptive Mesh
We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model" is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick," but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky" factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering
6288895
A Survey on Hair Modeling: Styling, Simulation, and Rendering
Realistic hair modeling is a fundamental part of creating virtual humans in computer graphics. This paper surveys the state of the art in the major topics of hair modeling: hairstyling, hair simulation, and hair rendering. Because of the difficult, often unsolved problems that arise in alt these areas, a broad diversity of approaches is used, each with strengths that make it appropriate for particular applications. We discuss each of these major topics in turn, presenting the unique challenges facing each area and describing solutions that have been presented over the years to handle these complex issues. Finally, we outline some of the remaining computational challenges in hair modeling
30756082
Sensation preserving simplification for haptic rendering
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.
919090
Fast penetration depth estimation using rasterization hardware and hierarchical refinement
We present a novel and fast algorithm to estimate penetration depth (PD) between two polyhedral models. Given two overlapping polyhedra, it computes the minimal translational distance to separate them using a combination of discretized computations and hierarchical refinement. The algorithm computes pair-wise Minkowski sums of decomposed convex pieces, performs closest point query using rasterization hardware, and refines the estimated PD by incremental walking. It uses bounding volume hierarchies, model simplification, and culling algorithms to further accelerate the computation and refines the estimated PD in a hierarchical manner. We highlight its performance on complex models.
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.
14636806
Channel density reduction by routing over the cells
We propose a new approach for reducing the density of a channel by routing some nets (or subnets) over the cells (i.e., outside the channel). Previous research assumed that the more nets being routed over the cells the greater the reduction in the channel density. We show that only the removal of critical nets contributes to the re- duction in the channel density. We divide channel into zones where each zone has a zone density and the removal of any net from a zone will reduce its density by one. In order to reduce the channel density, only certain critical zones need to have their nets routed over the cells. A bipartite graph is used to represent the relationship between nets and zones. The problem is transformed into a constrained covering problem and formulated as an integer linear programming problem. In comparison with previous research, our approach reduces more channel densities while using fewer tracks over the cells. For Deutsch's difficult khannel, a previous aiiproach needs 15 tracks over the cells to reduce the channel density by 3 while we need only 5 tracks to achieve the same result . Index Terms-Over-the-cell routing, channel density reduction, stan- dard-cell layout, VLSI routing, integer linear programming.
16198203
On Semantics of Reactive Rule-Based Systems
In this paper we address special issues which arise when the rule-based programming paradigm is emlployed in development of reactive real-time systems. We begin by presenting a rule-based language which has emerged while developing intelligent cruise control systems. We describe a naive operational semantics based on an an implemented inference engine, and explain why the semantics is not appropriate in safety-critical real-time contexts. We then deene a number of correct-ness criteria ensuring termination, consistency and determinism, based on a formal declarative semantics. However, the declarative semantics is non-constructive. In order to be able to build an implementation satisfying the correctness criteria, two alternative approaches are proposed. Both approaches build upon static checks of a rule-based program. In the rst approach some correctness criteria are met by accepting only stratiied programs after the static checks. In the second approach we accept programs which are correct with respect to a constructive semantics. For both approaches we present the analysis methods and soundness results with respect to the desired declarative semantics. Abstract In this paper we address special issues which arise when the rule-based programming paradigm is emlployed in development of reactive real-time systems. We begin by presenting a rule-based language which has emerged while developing intelligent cruise control systems. We describe a naive operational semantics based on an an implemented inference engine, and explain why the semantics is not appropriate in safety-critical real-time contexts. We then deene a number of correct-ness criteria ensuring termination, consistency and determinism, based on a formal declarative semantics. However, the declarative semantics is non-constructive. In order to be able to build an implementation satisfying the correctness criteria, two alternative approaches are proposed. Both approaches build upon static checks of a rule-based program. In the rst approach some correctness criteria are met by accepting only stratiied programs after the static checks. In the second approach we accept programs which are correct with respect to a constructive semantics. For both approaches we present the analysis methods and soundness results with respect to the desired declarative semantics.
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.
33339608
Almost Optimal Solutions for Bin Coloring Problems
In this paper we study two interesting bin coloring problems: Minimum Bin Coloring Problem (MinBC) and Online Maximum Bin Coloring Problem (OMaxBC), motivated from several applications in networking. For the MinBC problem, we first show that it is NP-complete, and then present two near linear time approximation algorithms to achieve almost optimal solutions, i.e., no more than OPT+2 and OPT+1 respectively, where OPT is the optimal solution. For the OMaxBC problem, we first introduce a deterministic 2-competitive greedy algorithm, and then give lower bounds for any deterministic and randomized (against adaptive offline adversary) online algorithms. The lower bounds show that our deterministic algorithm achieves the best possible competitive ratio.
5692452
k-server optimal task scheduling problem with convex cost function
We consider a class of k-server optimal task scheduling problems partitioning and scheduling N tasks with various real-time constrains and work loads on k servers with convex task processing cost function so as to minimize the total task processing cost while still guaranteeing satisfaction of all time constraints. This class has broad expressing power for practical scheduling problems in several areas such as real-time multimedia wireless transmission , CPU energy conservation, and warehouse order processing management, et. al. Our formulation is quite general such that most previous works can be readily reduced to a special case of the presented k-server optimal task scheduling problem. We show that, when k = 1, optimal solution can be obtained in computational complexity of O(N) and the corresponding optimal scheduling problem is equivalent to finding the shortest 2D Euclidean distance between two vertices inside a well-defined 2D polygon. However, when k 2, the optimal scheduling problem can be demonstrated to be NP-hard by reducing it to a well-known NP-complete bin-packing problem. Therefore, we conclude no polynomial time algorithm exists for a general k-server optimal task scheduling problem. We then construct approximation algorithms to solve the presented k-server problem in a practical way and illustrate its performance by simulation results and analysis.