This paper presents a theoretical analysis of the relationship between incoming radiance and irradiance. Radiance and irradiance are basic optical quantities, and their relationship is of fundamental interest to many fields, including computer vision, radiative transfer, and computer graphics. Physically, we are interested in analyzing the properties of the light field generated when a homogeneous convex curved Lambertian surface of known geometry reflects a distant illumination field. A Lambertian surface reflects light proportional to the incoming irradiance, so analysis of this physical system is equivalent to a mathematical analysis of the relationship between incoming radiance and irradiance

In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in three-dimensional (3-D) geometries. We present extensive experimental comparisons with the capacitance extraction code FASTCAP [1] and demonstrate that, for a wide variety of geometries commonly encountered in integrated circuit packaging, on-chip interconnect and micro-electro-mechanical systems, the new "precorrectedFFT " algorithm is superior to the fast multipole algorithm used in FASTCAP in terms of execution time and memory use. At engineering accuracies, in terms of a speed-memory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.

Abstract. We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allows us to address the various interactions between forms and vector fields (such as Lie derivatives) which are important in applications. Previous attempts at discrete exterior calculus have addressed only differential forms. We also introduce the notion of a circumcentric dual of a simplicial complex. The importance of dual complexes in this field has been well understood, but previous researchers have used barycentric subdivision or barycentric duals. We show that the use of circumcentric duals is crucial in arriving at a theory of discrete

The Theremin was one of the first electronic musical instruments, yet it provides a degree of expressive real-time control that remains lacking in most modern electronic music interfaces. Underlying the deceptively simple capacitance measurement used by it and its descendants are a number of surprisingly interesting current transport mechanisms that can be used to inexpensively, unobtrusively, robustly, and remotely detect the position of people and objects. We review the relevant physics, describe appropriate measurement instrumentation, and discuss applications that began with capturing virtuosic performance gesture on traditional stringed instruments and evolved into the design of new musical interfaces. 1)

The present work describes an alternative to the classical partial differential equations-based approach to the discretization of physical field problems. This alternative is based on a preliminary reformulation of the mathematical model in a partially discrete form, which preserves as much as possible the physical and geometrical content of the original problem, and is made possible by the existence and properties of a common mathematical structure of physical field theories. The goal is to maintain the focus, both in the modeling and in the discretizati on step, on the physics of the problem, thinking in terms of numerical methods for physical field problems, and not for a particular mathematical form (for example, a partial differential equation) into which the original physical problem happens to be translated.

this paper, we describe the construction of parametric surface skins using real spherical polar basis functions. As the use of such functions for protein shape representation is novel, a brief summary of their properties is also provided. We then give a description of the algebraic manipulations necessary to develop an efficient search for docking orienta- tions by incrementally rotating and translating the parametric representations. We also show that this spherical polar approach provides a natural way to model macromolecular electrostatic complementarity

In Ill, a boundary-element based algorithm is presented for computing the capacitance of three-dimensional m-conductor structures whose computational complexity grows nearly as mn, where n is the number of elements used to discretize the conductor surfaces. In that algorithm, a generalized conjugate residual iterative technique is used to solve the n x n linear system arising from the discretization, and a multipole algorithm is used to compute the iterates. In this paper, several improvements to that algorithm are described which make the approach in [1] applicable and computationally efficient for almost any geometry of conductors in a homogeneous dielectric. In particular, a new adaptive multipole algorithm is described, along with a strategy for accelerating the iterative algorithm by exploiting electrostatic screening. Results using these techniques in a program which computes the capacitance of general three-dimensional structures are presented to demonstrate that the new algorithm is nearly as accurate as the more standard direct factorization approach, and is more than two orders of magnitude faster for large examples.

We present a routing paradigm called PB-routing that utilizes steepest gradient search methods to route data packets. More specifically, the PB-routing paradigm assigns scalar potentials to network elements and forwards packets in the direction of maximum positive force. We show that the family of PB-routing schemes are loop free and that the standard shortest path routing algorithms are a special case of the PB-routing paradigm. We then show how to design a potential function that accounts for traffic conditions at a node. The resulting routing algorithm routes around congested areas while preserving the key desirable properties of IP routing mechanisms including hop-byhop routing, local route computations and statistical multiplexing. Our simulations using the ns simulator indicate that the traffic aware routing algorithm shows significant improvements in end-to-end delay and jitter when compared to standard shortest path routing algorithms. The simulations also indicate that our algorithm does not incur too much control overheads and is fairly stable even when traffic conditions are dynamic.

A novel approach to 3D part segmentation is presented It is a well-known physical fact that electrical charge on the surface of a conductor tends to accumulate at a sharp convexity and vanish at a sharp concavity. Thus object part boundaries, which are usually denoted by a sharp surface concavity, can be detected by locating surface points exhibiting local charge density minima. Beginning with single- or multi-view range data of a 3D object, we simulate the charge density distribution over an object's surface which has been tessellated by a triangular mesh. We detect the deep surface concavities by tracing local charge density minima and then decompose the object into parts at these points. The charge density computation does not require an assumption on surface smoothness and uses weighted global data to produce robust local surface features for part segmentation.

In this series of lectures, we describe the analytic and computational foundations of fast multipole methods, as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the cost of computing all pairwise interactions in a system of N particles from O(N 2)toO(N)orO(N log N) operations. They are equally useful, however, in solving certain partial differential equations by first recasting them as integral equations. We will draw heavily from the existing literature, especially Greengard [23, 24, 25]; Greengard and Rokhlin [29, 32]; Greengard and Strain [34].