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.
13139757
Approximate merging of a pair of Bézier curves
This paper deals with the merging problem, i.e. to approximate two adjacent Bezier curves by a single Bezier curve. A novel approach for approximate merging is introduced in the paper by using the constrained optimization method. The basic idea of this method is to find conditions for the precise merging of Bezier curves first, and then compute the constrained optimization solution by moving the control points. “Discrete” coefficient norm in L2 sense and “squared difference integral” norm are used in our method. Continuity at the endpoints of curves are considered in the merging process, and approximate merging with points constraints are also discussed. Further, it is shown that the degree elevation of original Bezier curves will reduce the merging error.
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.
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.
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