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On the relationship between radiance and irradiance: determining the illumination from images of a convex Lambertian object
, 2001
"... 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. Physi ..."
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Cited by 117 (10 self)
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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
Discrete Exterior Calculus
, 2003
"... 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 actin ..."
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Cited by 88 (7 self)
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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
A PrecorrectedFFT Method for Electrostatic Analysis of Complicated 3D Structures
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 1997
"... 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 threedimensio ..."
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Cited by 69 (26 self)
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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 threedimensional (3D) 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, onchip interconnect and microelectromechanical 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 speedmemory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.
Musical Applications of Electric Field Sensing
 Computer Music Journal
, 1997
"... The Theremin was one of the first electronic musical instruments, yet it provides a degree of expressive realtime 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 surpris ..."
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Cited by 57 (16 self)
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The Theremin was one of the first electronic musical instruments, yet it provides a degree of expressive realtime 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)
Protein Docking Using Spherical Polar Fourier Correlations
 Proteins
, 1999
"... 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 nec ..."
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Cited by 49 (16 self)
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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
The Finite Volume, Finite Element, and Finite Difference Methods as Numerical Methods for Physical Field Problems
 Journal of Computational Physics
, 2000
"... The present work describes an alternative to the classical partial differential equationsbased 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 possi ..."
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Cited by 47 (1 self)
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The present work describes an alternative to the classical partial differential equationsbased 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.
3D Part Segmentation Using Simulated Electrical Charge Distributions
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1996
"... A novel approach to 3D part segmentation is presented It is a wellknown 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, c ..."
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Cited by 37 (0 self)
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A novel approach to 3D part segmentation is presented It is a wellknown 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 multiview 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.
Capacitance Extraction of General ThreeDimensional Structures
 IEEE Trans. on Microwave Theory and Techniques
, 1992
"... In Ill, a boundaryelement based algorithm is presented for computing the capacitance of threedimensional mconductor 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 ..."
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Cited by 36 (13 self)
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In Ill, a boundaryelement based algorithm is presented for computing the capacitance of threedimensional mconductor 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 threedimensional 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.
A SignalProcessing Framework for Reflection
 ACM TRANSACTIONS ON GRAPHICS
, 2004
"... ... In this paper, we formalize these notions, showing that the reflected light field can be thought of in a precise quantitative way as obtained by convolving the lighting and BRDF, i.e. by filtering the incident illumination using the BRDF. Mathematically, we are able to express the frequencyspac ..."
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Cited by 35 (4 self)
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... In this paper, we formalize these notions, showing that the reflected light field can be thought of in a precise quantitative way as obtained by convolving the lighting and BRDF, i.e. by filtering the incident illumination using the BRDF. Mathematically, we are able to express the frequencyspace coe#cients of the reflected light field as a product of the spherical harmonic coe# cients of the illumination and the BRDF. These results are of practical importance in determining the wellposedness and conditioning of problems in inverse renderingestimation of BRDF and lighting parameters from real photographs. Furthermore, we are able to derive analytic formulae for the spherical harmonic coe#cients of many common BRDF and lighting models. From this formal analysis, we are able to determine precise conditions under which estimation of BRDFs and lighting distributions are well posed and wellconditioned. Our mathematical analysis also has implications for forward renderingespecially the e#cient rendering of objects under complex lighting conditions specified by environment maps. The results, especially the analytic formulae derived for Lambertian surfaces, are also relevant in computer vision in the areas of recognition, photometric stereo and structure from motion.
Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301
, 1998
"... In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground s ..."
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Cited by 35 (10 self)
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In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground state of the full theory. We discuss the lightcone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD boundstates of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The lightcone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of lightcone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavyquark contributions to structure functions. A general nonperturbative method for numerically solving quantum field theories, â€śdiscretized lightcone quantizationâ€ť, is outlined and applied to several gauge theories. This method is invariant under the