46118922
Modifying the shape of NURBS surfaces with geometric constraints
NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modification of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modified surface satisfies the given constraints. Comparison results and practical examples are also given.
10936183
Direct manipulation of FFD: efficient explicit solutions and decomposible multiple point constraints
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.
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.
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.
41551155
A new RLC buffer insertion algorithm
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