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.
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.
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.
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.
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.
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)
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.