D. Wilton, S. Rao, A. Glisson, D. Schaubert, O. Al-- Bundak, C. Butler, Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains, IEEE Trans. Antennas and Propagation, AP--32, No. 3, pg. 276--281 (March 1984).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....loop, b, since some of the magnetic field passes through b. b ba dI = I a jSd Crossection of a of the loops and over their cross sections as well, if these are not negligible. For some simple structures, these integrals may be solved analytically (see for instance [3] [6] or [7] We will look at the special case of loops consisting of straight segments later in this paper. There are instances of ICs which include inductors as components of filter and oscillator circuits. But it is the inductors not deliberately designed into integrated circuits, namely the ....

....The interested reader is referred to Eq. 14) in [7] to see the exact expression for this situation. It is a correct formula, but not very robust and contains many numerical pitfalls. More analytic solutions for rectangular and triangular elements for practical implementations are provided in [6] and [7] If all attempts at finding an analytic solution to (9) fail, there is still the possibility to use numerical integration techniques, such as Gaussian quadrature [8] to solve the integrals. These methods tend to be more robust and flexible than most analytic solutions, but also much ....

D. Wilton, S. Rao, A. Glisson, D. Schaubert, O. Al-- Bundak, C. Butler, Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains, IEEE Trans. Antennas and Propagation, AP--32, No. 3, pg. 276--281 (March 1984).

....( JGs d S o . s d S o = 1 jwe o 4p ( n o T ( J. Gs d S o s d S o 30 and 0 is the null vector. The singularities in evaluating the integrals in equation (18) are handled analytically by using the closed form expressions given in [8]. Using Maxwell s equation , the surface integral on the right hand side of the equation (3) can be written as (19) where H inp is the magnetic field over the input plane obtained from matching the modal expansion of waveguide fields with the unknowns fields at the input plane[9] By equivalence ....

D.R.Wilton, S.M.Rao, D.H.Shaubert, O.M. Al-Bunduck and C.M.Butler, "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. on Antennas and Propagation, Vol.AP-32, pp.276-281, March 1984.

.... 21 A 22 : A 2N Gamma1 : AN1 AN2 : ANN Gamma1 S 1 S 2 : SN 0 1 C C C C C C C C C C C C C C C C C C C C C C A (14) where A ik = Z T k 1 jr i Gamma r 0 j dS 0 ; i; j = 1; 2; N: 15) 13 Since the integral in (15) can be evaluated analytically [52], the charge density distribution ae k and the constant V can be obtained by solving the set of linear equations given in (12) Since the potential on a particular triangle is actually contributed by the charge on all of the other triangles, the matrix A is dense. In the actual computation, the ....

D. Wilton, S. M. Rao, A. W. Glisson, et al. Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains. IEEE Transactions on Antennas and Propagation, AP-32(3):276--281, 1984.

....Let Q be the total charge on the conductor and S k be the area of T k . Then we have Q = N X k=1 ae k S k (9) Assuming Q is known, and using (8) and (9) we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (8) can be evaluated analytically [24], the charge density distribution ae k and the constant V can be obtained by solving a set of linear equations. The data for the above analysis were obtained using a laser rangefinder to scan objects from multiple views. Transformations between successive views were computed by employing a view ....

D. Wilton, S. M. Rao, A. W. Glisson, et al. Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains. IEEE Transactions on Antennas and Propagation, AP-32(3):276-- 281, 1984.

....object surface and S k be the 15 area of T k . Then we have Q = Z S ae(r)dS 0 N X k=1 ae k S k (12) Assuming Q is known, and given (11) and (12) we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (11) can be evaluated analytically [53], the charge density distribution ae k and the constant V can be obtained by solving the set of linear equations. Because the potential on a particular triangle is actually contributed by the charge on all of the triangles, the matrix A is dense. In the actual computation, the observation point r ....

D. Wilton, S. M. Rao, A. W. Glisson, et al. Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains. IEEE Transactions on Antennas and Propagation, AP-32(3):276--281, 1984.

....GDS II layout SPACE directly produces a SPICEnetlist ready for simulation. ambient dielectric are present, however, the Green function takes the form of an infinite sum over image charges. For the Coulomb potential and polygonal boundary elements, one of the integrations can be done analytically [6]. Due to transcendental functions in the analytic formulas, however, on RISC machines numerical integration may actually be faster than the use of these formulas. No analytic formulas are known for the second integral. There is a vast literature on fast numerical integration formulas for ....

D.R. Wilton, S.M. Rao, A.W. Glisson, D.H. Schaubert, O.M. Al-Bundak, and C.M. Butler, Potential Integrals for Uniform and Linear SourceDistributions on Polygonal and Polyhedral Domains, IEEE Transactions on Antennas and Propagation, AP-32, No. 3, March 1984, pp. 276-281.

....of a continuous contour (dashed line) b) The basis functions. C k . Then we have Q = N X k=1 ae k l k (9) Assuming Q is known and taking (8) and (9) we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (8) can be evaluated analytically (Wilton et al. 1984), the charge density distribution ae k and the constant V can be obtained by solving the set of linear equations. Readers are referred to (Wilton et al. 1984) for the details of the integral evaluation in (8) 2.3 Implementation Since a contour in an image is composed of a sequence of pixel ....

....we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (8) can be evaluated analytically (Wilton et al. 1984) the charge density distribution ae k and the constant V can be obtained by solving the set of linear equations. Readers are referred to (Wilton et al. 1984) for the details of the integral evaluation in (8) 2.3 Implementation Since a contour in an image is composed of a sequence of pixel points, a polygonal approximation can be formed automatically by linking all consecutive pixels on the contour by line segments. The middle point on each segment ....

[Article contains additional citation context not shown here]

Wilton D., S.M. Rao, A.W. Glisson, D.H. Schaubert, O.M. Al-Bundak and C.M. Butler, (1984). "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Transactions on Antennas and Propagation, vol. AP-32, no. 3, pp. 276--281.

.... B B B B B B A 11 A 12 : A 1N Gamma1 A 21 A 22 : A 2N Gamma1 : AN1 AN2 : ANN Gamma1 S 1 S 2 : SN 0 1 C C C C C C C C C C C C C C C C A (14) where A ik = Z T k 1 jr i Gamma r 0 j dS 0 ; i; j = 1; 2; N: 15) Since the integral in (15) can be evaluated analytically [51], the charge density distribution ae k and the constant V can be obtained by solving the set of linear equations given in (12) Since the potential on a particular triangle is actually contributed by the charge on all of the other triangles, the matrix A is dense. In the actual computation, the ....

D. Wilton, S. M. Rao, A. W. Glisson, et al., "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Transactions on Antennas and Propagation, vol. AP-32, no. 3, pp. 276--281, 1984.

....Let Q be the total charge on the conductor and S k be the area of T k . Then we have Q = N X k=1 ae k S k (9) Assuming Q is known, and using (8) and (9) we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (8) can be evaluated analytically [34], the charge density distribution ae k and the constant V can be obtained by solving a set of linear equations. 2.3 Implementation Our data are obtained using a laser rangefinder to scan objects from multiple views. Transformations between successive views are computed by a view registration ....

D. Wilton, S. M. Rao, A. W. Glisson, et al. Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains. IEEE Transactions on Antennas and Propagation, AP-32(3):276--281, 1984.

....Let Q be the total charge on the conductor and S k be the area of T k . Then we have Q = N X k=1 ae k S k (7) Assuming Q is known, and using (6) and (7) we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (6) can be evaluated analytically [17], the charge density distribution ae k and the constant V can be obtained by solving a set of linear equations. This is accomplished using a conjugate gradient squared method [1] a) b) Figure 3: Single view range data of an object. a) Frontal view. b) Side view. Due to self occlusion, ....

D. Wilton, S. M. Rao, A. W. Glisson, et al. Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains. IEEE Transactions on Antennas and Propagation, AP-32(3):276-- 281, 1984.

....Let Q be the total charge on the contour and l k be the length of C k . Then we have Q = N X k=1 ae k l k (9) Assuming Q is known and taking (8) and (9) we obtain a set of linear equations with N 1 unknowns, ae 1 ; ae N and V . Since the integral in (8) can be evaluated analytically [19], the charge density distribution ae k and the constant V can be obtained by solving the set of linear equations. 2.3. Implementation. Since a contour in an image is composed of a sequence of discrete data points, a polygonal approximation can be formed simply by linking consecutive data points ....

....algorithm to compute the charge density distribution over the surface of a 3D object. The results will be presented in a separate paper. Acknowledgements We wish to thank Professor Jonathan Webb for his kind help with electrostatic problems, Professor Allen W. Glisson for pointing out his paper [19], and Professor Gregory Dudek for making valuable comments on the manuscript. MDL would like to thank the Canadian Institute for Advanced Research and PRECARN for its support. This work was partially supported by a Natural Sciences and Engineering Research Council of Canada Strategic Grant and an ....

D. Wilton, S. M. Rao, A. W. Glisson, et al., "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Transactions on Antennas and Propagation, vol. AP-32, no. 3, pp. 276--281, 1984.

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Wilton, D.R. et al. 'Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains', IEEE Trans. on Antennas and Propagation, Vol. AP-32, No 3, pp. 276-281, March 1984.

No context found.

Wilton, Donald R.; Rao, S. M.; Glisson, Allen W.; Schaubert, Daniel H.; Al-Bundak, O. M.; and Butler, Chalmers M.: Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains. IEEE Trans. Antennas & Propag., vol. AP-32, no. 3, Mar. 1984, pp. 276--281.

No context found.

Wilton, Donald R.; Rao, S. M.; Glisson, Allen W.; Schaubert, Daniel H.; Al-Bundak, O. M.; and Butler, Chalmers M.: Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains. IEEE Trans. Antennas & Propag., vol. AP-32, no. 3, Mar. 1984, pp. 276--281.

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