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
41551155
A new RLC buffer insertion algorithm
86426
Gate Sizing for Cell-Library-Based Designs
With increasing time-to-market pressure and shortening semiconductor product cycles, more and more chips are being designed with library-based methodologies. In spite of this shift, the problem of discrete gate sizing has received significantly less attention than its continuous counterpart. On the other hand, cell sizes of many realistic libraries are sparse, for example, geometrically spaced, which makes the nearest rounding approach inapplicable as large timing violations may be introduced. Therefore, it is highly desirable to design an effective algorithm to handle this discrete gate-sizing problem. Such an algorithm is proposed in this paper. The algorithm is a continuous-solution-guided dynamic-programming-like approach. A set of novel techniques, such as locality-sensitive-hashing-based solution pruning, is also proposed to accelerate the algorithm. Our experimental results demonstrate that 1) the nearest rounding approach often leads to large timing violations and 2) compared to the well-known Coudert's approach, the new algorithm saves up to 21% in area cost while still satisfying the timing constraint.
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
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.
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.
14440830
A constructive approach to solving 3-D geometric constraint systems using dependence analysis
Solving geometric constraint systems in 3-D is much more complicated than that in 2-D because the number of variables is larger and some of the results valid in 2-D cannot be extended for 3-D. In this paper, we propose a new DOF-based graph constructive method to geometric constraint systems solving that can efficiently handle well-, over- and under-constrained systems based on the dependence analysis. The basic idea is that the solutions of some geometric elements depend on some others because of the constraints between them. If some geometric elements depend on each other, they must be solved together. In our approach, we first identify all structurally redundant constraints, then we add some constraints to well constrain the system. And we prove that the order of a constraint system after processing under-constrained cases is not more than that of the original system multiplied by 5. After that, we apply a recursive searching process to identify all the clusters, which is shown to be capable of getting the minimum order-reduction result of a well-constrained system. We also briefly describe the constraint evaluation phase and show the implementation results of our method.
11930854
Conversion between triangular and rectangular Bézier patches
This paper presents an explicit formula that converts a triangular Bezier patch of degree n to a degenerate rectangular Bezier patch of degree n × n by reparametrization. Based on this formula, we develop a method for approximating a degenerate rectangular Bezier patch by three nondegenerate Bezier patches; more patches can be introduced by subdivision to meet a user-specified error tolerance.  2001 Elsevier Science B.V. All rights reserved.
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.