10936183
Direct manipulation of FFD: efficient explicit solutions and decomposible multiple point constraints
8093870
Reconstruction of curved solids from engineering drawings
This paper presents a new approach for reconstructing solids with planar, quadric and toroidal surfaces from three-view engineering drawings. By applying geometric theory to 3-D reconstruction, our method is able to remove restrictions placed on the axes of curved surfaces by existing methods. The main feature of our algorithm is that it combines the geometric properties of conics with affine properties to recover a wider range of 3-D edges. First, the algorithm determines the type of each 3-D candidate conic edge based on its projections in three orthographic views, and then generates that candidate edge using the conjugate diameter method. This step produces a wire-frame model that contains all candidate vertices and candidate edges. Next, a maximum turning angle method is developed to find all the candidate faces in the wire-frame model. Finally, a general and efficient searching technique is proposed for finding valid solids from the candidate faces; the technique greatly reduces the searching space and the backtracking incidents. Several examples are given to demonstrate the efficiency and capability of the proposed algorithm.
16456196
Degree reduction of B-spline curves
This work deals with the problem of degree reducing a B-spline curve without intermediate conversion to Bezier form. Degree elevation for B-spline curves may easily be described in blossom form. We also use blossoms for the degree reduction problem, and set up least squares problems for finding the B-spline coefficients directly. We also give an application to curve fairing.
16610043
Generalized Subdivision of Bézier Surfaces
In this paper, subdivision methods for rectangular Bezier surfaces are generalized to subdivide a rectangular Bezier surface patch of degreen×minto two rectangular Bezier surface patches of degreen× (m+n), while the parameter domain of the Bezier surface is decomposed into two trapezoids. As an application, a conversion from rectangular Bezier surfaces to triangular Bezier surfaces is presented.
42415947
An extension algorithm for B-splines by curve unclamping
This paper presents an algorithm for extending B-spline curves and surfaces. Based on the unclamping algorithm for B-spline curves, we propose a new algorithm for extending B-spline curves that extrapolates using the recurrence property of the de Boor algorithm. This algorithm provides a nice extension, with maximum continuity, to the original curve segment. Moreover, it can be applied to the extension of B-spline surfaces. Extension to both single and multiple target points/curves are considered in this paper.
204983160
Properties of two types of generalized ball curves
Ball basis was introduced for cubic polynomials by Ball, and was generalized for polynomials of higher degree by Wang and Said. In this paper, we investigate degree elevation and reduction, recursive algorithm, enveloping theorem, and Bezier representation of these two generalized Ball curves. Furthermore, the efficiency of de Casteljau algorithm for Bezier curves and recursive algorithms for two generalized Ball curves is compared.
17009072
Steiner network construction for timing critical nets
Conventionally, signal net routing is almost always implemented as Steiner trees. However, non-tree topology is often superior on timing performance as well as tolerance to open faults and variations. These advantages are particularly appealing for timing critical net routings in nano-scale VLSI designs where interconnect delay is a performance bottleneck and variation effects are increasingly remarkable. We propose Steiner network construction heuristics which can generate either tree or non-tree with different slack-wirelength tradeoff, and handle both long path and short path constraints. Incremental non-tree delay update techniques are developed to facilitate fast Steiner network evaluations. Extensive experiments in different scenarios show that our heuristics usually improve timing slack by hundreds of pico seconds compared to traditional tree approaches
41551155
A new RLC buffer insertion algorithm
9344765
An Efficient Algorithm for RLC Buffer Insertion
Traditional buffer insertion algorithms neglect the impact of inductance effect, which often introduces large error in circuit optimization. On the other hand, ultra-fast buffering techniques are always desirable as buffering is such a widely used technique in industry. It is a challenge to design an RLC buffering algorithm which excels in both runtime and solution quality. In this paper, such an algorithm is proposed. The new algorithm works under the dynamic programming framework and runs in provably linear time for multiple buffer types due to two novel techniques: restrictive cost bucketing and efficient delay update. Experiment results on industrial netlists demonstrate that the new algorithm consistently outperforms van Ginneken/Lillis algorithm (van Ginneken, 1990) and (Lillis, 1996) for RC buffering and all known RLC buffering algorithms. Without buffer cost minimization, the new algorithm saves up to 8.5% buffer area and provides up to 4times speedup over Ismail's algorithm (Ismail, 2001), When buffer cost minimization is handled, the new algorithm uses 33.4% fewer buffers than van Ginnenken-Lillis's algorithm, and saves up to 5.3% buffer area and gives up to 5times speedup compared to the algorithm in (Jiang et al., 2006)
5131804
Scalable peer-to-peer networked virtual environment
We propose a fully-distributed peer-to-peer architecture to solve the scalability problem of Networked Virtual Environment in a simple and efficient manner. Our method exploits locality of user interest inherent to such systems and is based on the mathematical construct Voronoi diagram. Scalable, responsive, fault-tolerant NVE can thus be constructed and deployed in an affordable way.
96005
Fast algorithms for slew constrained minimum cost buffering
As a prevalent constraint, sharp slew rate is often required in circuit design which causes a huge demand for buffering resources. This problem requires ultra-fast buffering techniques to handle large volume of nets, while also minimizing buffering cost. This problem is intensively studied in this paper. First, a highly efficient algorithm based on dynamic programming is proposed to optimally solve slew buffering with discrete buffer locations. Second, a new algorithm is developed to handle the difficult cases in which no assumption is made on buffer input slew. Third, an adaptive buffer selection approach is proposed to efficiently handle slew buffering with continuous buffer locations. Experiments on industrial netlists demonstrate that our algorithms are very effective and highly efficient: we achieve > 100times speed up and save up to 40% buffer area over the commonly-used van Ginneken style buffering