Smooth multiple B-spline surface fitting with Catmull%ndash;Clark subdivision surfaces for extraordinary corner patches

This paper presents an algorithm for simultaneously fitting smoothly connected multiple surfaces from unorganized measured data. A hybrid mathematical model of B-spline surfaces and Catmull–Clark subdivision surfaces is introduced to represent objects with general quadrilateral topology. The interconnected multiple surfaces are G ² continuous across all surface boundaries except at a finite number of extraordinary corner points where G ¹ continuity is obtained. The algorithm is purely a linear least-squares fitting procedure without any constraint for maintaining the required geometric continuity. In case of general uniform knots for all surfaces, the final fitted multiple surfaces can also be exported as a set of Catmull–Clark subdivision surfaces with global C ² continuity and local C ¹ continuity at extraordinary corner points. Published online: 14 May 2002 Correspondence to: W. Ma     

A system subdivision approach for large radiosity computation

O (n) for n subsystems. Moreover, the data necessary for each subsystem computation is completely localized, which allows the database to be stored on disk. The algorithm can easily be implemented with a slight modification of the hierarchical radiosity algorithm. Experiments demonstrate the efficiency of the algorithm.     

Surface intersection by switching from recursive subdivision to iterative refinement

This paper discusses an attempt to devise an efficient (involving minimal computations), accurate (numerically high precision), exhaustive (detecting all possible solutions), and robust (working without failures) method for detecting intersection of two parametric surfaces. The method starts with subdivision to ensure that all solutions are detected. Later it switches over to numerical iterative refinement for efficient and accurate evaluation of the intersection curve. The switching takes place only when the convergence of the refinement method is guaranteed. The necessary theory to arrive at a computable condition leading to this guarantee has been developed using fixed-point and contractionmapping theorems from topology and mathematical analysis. The implementation is discussed elaborating the data structures and the algorithms used for (1) detecting segments of the intersection curve, (2) generating points on these segments using refinement, and (3) tracing a continuous curve by identifying neighboring segments and joining them in order.     

Evaluation of piecewise smooth subdivision surfaces

Published online: 23 July 2002     

Polygonal mesh regularization for subdivision surfaces interpolating meshes of curves

Published online: 14 February 2003     

Implicit modeling using subdivision curves

C ¹ continuity everywhere. Moreover, they can be used to generate representations at different levels of detail, enabling the interactive display of at least a coarse version of the objects, whatever the performance of the workstation. We also present a practical solution to the unwanted-blending problem, used to avoid blending between parts of the surface that do not correspond to neighboring skeletal elements. Published online: 22 May 2003     

Surface skinning revisited

Published online: 15 March 2002     

Algorithms for rendering realistic terrain image sequences and their parellel implementation

We present algorithms for rendering realistic images of large terrains and their implementation on a parallel computer for rapid production of terrain-animation sequences. “Large” means datasets too large for RAM. A hybrid ray-casting and projection technique incorporates quadtree subdivision techniques and filtering using precomputed bit masks. Hilbert space-filling curves determine the imagepixel rendering order. A parallel version of the algorithm is based on a Meiko parallel computer architecture, designed to relieve dataflow bottlenecks and exploit temporal image coherence. Our parallel system, incorporating 26 processors, can generate a full color-terrain image at video resolution (without noticable aliasing artifacts) every 2 s, including I/O and communication overheads.     

Lower bounds for the broadcast problem in mobile radio networks

Summary.  In this paper, we prove a lower bound on the number of rounds required by a deterministic distributed protocol for broadcasting a message in radio networks whose processors do not know the identities of their neighbors. Such an assumption captures the main characteristic of mobile and wireless environments [3], i.e., the instability of the network topology. For any distributed broadcast protocol Π, for any n and for any D≦n/2, we exhibit a network G with n nodes and diameter D such that the number of rounds needed by Π for broadcasting a message in G is Ω(D log n). The result still holds even if the processors in the network use a different program and know n and D. We also consider the version of the broadcast problem in which an arbitrary number of processors issue at the same time an identical message that has to be delivered to the other processors. In such a case we prove that, even assuming that the processors know the network topology, Ω(n) rounds are required for solving the problem on a complete network (D=1) with n processors. Received: August 1994 / Accepted: August 1996     

Ray tracing: A quantitative analysis and a new practical algorithm

We present a new method to accelerate the process of finding nearest ray-object intersections in ray tracing. The algorithm consumes an amount of memory more or less linear in the number of objects. The basic ideas can be characterized with a modified BSP tree and plane traversal. Plane traversal is a fast linear time algorithm to find the closest intersection point in a list of bounding volumes hit by a ray. We use plane traversal at every node of the high outdegree BSP tree. Our implementation is competitive to fast ray-tracing programs. We present a benchmark suite that allows for an extensive comparison of ray-tracing algorithms.     

A self-stabilizing algorithm for the maximum flow problem

Summary.  The maximum flow problem is a fundamental problem in graph theory and combinatorial optimization with a variety of important applications. Known distributed algorithms for this problem do not tolerate faults or adjust to dynamic changes in network topology. This paper presents a distributed self-stabilizing algorithm for the maximum flow problem. Starting from an arbitrary state, the algorithm computes the maximum flow in an acyclic network in finitely many steps. Since the algorithm is self-stabilizing, it is inherently tolerant to transient faults. It can automatically adjust to topology changes and to changes in other parameters of the problem. The paper presents results obtained by extensively experimenting with the algorithm. Two main observations based on these results are (1) the algorithm requires fewer than n ² moves for almost all test cases and (2) the algorithm consistently performs at least as well as a distributed implementation of the well-known Goldberg-Tarjan algorithm for almost all test cases. The paper ends with the conjecture that the algorithm correctly computes a maximum flow even in networks that contain cycles. Received: October 1995 / Accepted: February 1997