32819804
A note on approximation of discrete data by G1 arc splines
Meek and Walton discussed the approximation of discrete data by G1 arc splines in 1992. For a biarc from the start point A to the end point B, they assumed that the sum of two counterclockwise angles of the two arcs was equal to the sum of the counterclockwise angle from the start tangent vector to the vector B–A and that from the vector B–A to the terminal tangent vector. In this note, we show that the relation can be relaxed by the addition or subtraction of 2π.
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.
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.
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.
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.
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.
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
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
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.
9549886
A case for 3D streaming on peer-to-peer networks
One of the most serious issues holding back the widespread of 3D contents on Internet has been their inaccessibility due to large data volume. Many compression and progressive transmission techniques, as well as format standards, have been proposed in recent years to make 3D streaming increasingly viable for the efficient and accessible delivery of 3D contents. However, existing proposals have yet to seriously address one of the most important issues in practical adoption - a system's scalability in terms of the number of concurrent users. We argue that due to 3D contents' large data volume and interactive nature, client-server architecture, with its inherently fixed resource availability and high cost, will not be suitable to support popular Internet-scale 3D streaming. On the other hand, peer-to-peer (P2P) architectures hold the promise of both scalability and affordability. In this position paper, we describe the potential promises and challenges in adapting 3D streaming to P2P networks, using multi-user networked virtual environment (NVE) as an example. We also propose Flowing LoD (FLoD), a scalable, distributed and fault-tolerant P2P 3D streaming mechanism, that is based on Voronoi-based Overlay Network (VON), a P2P overlay specifically designed for NVE applications.