Results 1 
3 of
3
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
Abstract

Cited by 623 (0 self)
 Add to MetaCart
(Show Context)
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
A Framework for Analysis of High Order SigmaDelta Modulators
"... In this paper a framework for the analysis of a family of high order interpolative sigmadelta modulators is introduced. It is shown that a large number of high order architectures can be reduced to a diagonal form which facilitates the stability analysis of the system. In addition, the diagonal fo ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper a framework for the analysis of a family of high order interpolative sigmadelta modulators is introduced. It is shown that a large number of high order architectures can be reduced to a diagonal form which facilitates the stability analysis of the system. In addition, the diagonal form is a canonical form which illustrates the equivalence of a variety of sigmadelta architectures. Architectural differences are manifested as differences in parameter values in the diagonal form, providing a convenient method of comparison between systems. It is also shown how transformation to the diagonal form may result in a reduction in order of a system. Finally, there is a brief discussion on the importance of diagonal systems as opposed to nondiagonal systems. Introduction SigmaDelta modulation systems are clocked, nonlinear systems which sample an input at signal rates much higher than the Nyquist frequency and feed back a low resolution approximation of this input. This allows ...
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS–I: FUNDAMENTAL THEORY AND APPLICATION 1 Stable highorder deltasigma DACs
"... Abstract — Stability analysis of highorder deltasigma loops is a challenge. In this brief, a sufficient design criterion is presented for highorder multibit errorfeedback DACs which are especially suitable for highspeed operation. This analytical criterion might be too conservative, but it allow ..."
Abstract
 Add to MetaCart
Abstract — Stability analysis of highorder deltasigma loops is a challenge. In this brief, a sufficient design criterion is presented for highorder multibit errorfeedback DACs which are especially suitable for highspeed operation. This analytical criterion might be too conservative, but it allows the design of stable, robust, and highresolution deltasigma DACs. Both analytical and numerical analysis are performed for verification. Also, experimental results of a discretecomponent multiplierfree prototype demonstrate 10bit operation at a very low oversampling ratio of 4. Index Terms — data conversion, DAC, delta sigma, sigma delta, stable, stability, error feedback, high order, high speed.