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.
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.
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.
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.
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.
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.
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
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.
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.