Analyzing midpoint subdivision

Midpoint subdivision generalizes the Lane–Riesenfeld algorithm for uniform tensor product splines and can also be applied to non-regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo–Sabin algorithm and midpoint subdivision of degree 3 is a specific Catmull–Clark algorithm. In 2001, Zorin and Schröder were able to prove C¹-continuity for midpoint subdivision surfaces analytically up to degree 9. Here, we develop general analysis tools to show that the limiting surfaces under midpoint subdivision of any degree ?2 are C¹-continuous at their extraordinary points.     

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     

Biorthogonal wavelet construction for hybrid quad/triangle meshes

Ever since its introduction by Stam and Loop, the quad/triangle subdivision scheme, which is a generalization of the well-known Catmull–Clark subdivision and Loop subdivision, has attracted a great deal of interest due to its flexibility of allowing both quads and triangles in the same model. In this paper, we present a novel biorthogonal wavelet—constructed through the lifting scheme—that accommodates the quad/triangle subdivision. The introduced wavelet smoothly unifies the Catmull–Clark subdivision wavelet (for quadrilateral meshes) and the Loop subdivision wavelet (for triangular meshes) in a single framework. It can be used to flexibly and efficiently process any complicated semi-regular hybrid meshes containing both quadrilateral and triangular regions. Because the analysis and synthesis algorithms of the wavelet are composed of only local lifting operations allowing fully in-place calculations, they can be performed in linear time. The experiments demonstrate sufficient stability and fine fitting quality of the presented wavelet, which are similar to those of the Catmull–Clark subdivision wavelet and the Loop subdivision wavelet. The wavelet analysis can be used in various applications, such as shape approximation, progressive transmission, data compression and multiresolution edit of complex models.

Non-uniform recursive Doo–Sabin surfaces

This paper presents a generalization of Catmull–Clark-variant Doo–Sabin surfaces and non-uniform biquadratic B-spline surfaces called Non-Uniform Recursive Doo–Sabin Surfaces (NURDSes). One step of NURDS refinement can be factored into one non-uniform linear subdivision step plus one dual step. Compared to the prior non-uniform Doo–Sabin surfaces (i.e., quadratic NURSSes), NURDSes are convergent for arbitrary n-sided faces. Closed form limit point rules, which are important for applications in adaptive rendering and NC machining, are given as well.     

A simple method for interpolating meshes of arbitrary topology by Catmull–Clark surfaces

Interpolating an arbitrary topology mesh by a smooth surface plays important role in geometric modeling and computer graphics. In this paper we present an efficient new algorithm for constructing Catmull–Clark surface that interpolates a given mesh. The control mesh of the interpolating surface is obtained by one Catmull–Clark subdivision of the given mesh with modified geometric rule. Two methods—push-back operation based method and normal-based method—are presented for the new geometric rule. The interpolation method has the following features: (1) Efficiency: we obtain a generalized cubic B-spline surface to interpolate any given mesh in a robust and simple manner. (2) Simplicity: we use only simple geometric rule to construct control mesh for the interpolating subdivision surface. (3) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (4) Freedom: for each edge and face, there is one degree of freedom to adjust the shape of the limit surface. These features make interpolation using Catmull–Clark surfaces very simple and thus make the method itself suitable for interactive free-form shape design.     

Improved error estimate for extraordinary Catmull–Clark subdivision surface patches

Based on an optimal estimate of the convergence rate of the second order norm, an improved error estimate for extraordinary Catmull–Clark subdivision surface (CCSS) patches is proposed. If the valence of the extraordinary vertex of an extraordinary CCSS patch is even, a tighter error bound and, consequently, a more precise subdivision depth for a given error tolerance, can be obtained. Furthermore, examples of adaptive subdivision illustrate the practicability of the error estimation approach.     

Filling N-Sided Regions by Quad Meshes for Subdivision Surfaces

Given an n-sided region bounded by a loop of n polylines, we present a general algorithm to fill such a region by a quad mesh suitable for a subdivision scheme. Typically, the approach consists of two phases: the topological phase and the geometrical phase. In the first part, the connectivity of the mesh is based on determining a partitioning of the region into rectangular subregions across which regular grid could be constructed. The geometrical phase generalizes discrete Coon's patches to position the vertices in the 3D space. The generated mesh could be taken as input to any quad-based subdivision scheme, such as that of Catmull–Clark or Doo–Sabin to generate the corresponding limit surface. The goal of the algorithm is to generate smooth meshes with minimum number and less valence of extraordinary vertices deemed undesirable in such subdivision schemes.     

Extension of the Nicholls-Lee-Nichols algorithm to three dimensions

A new algorithm for clipping a line segment against a pyramid in E ³ is presented. This algorithm avoids computation of intersection points that are not end points of the output line segment. It also solves all cases more effectively. The performance of this algorithm is shown to be consistently better than that of existing algorithms, including the Cohen–Sutherland, Liang–Barsky, and Cyrus–Beck algorithms.     

Quad/Triangle Subdivision

In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad‐only meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known Catmull‐Clark and Loop subdivision algorithms. We show that our surfaces are C ¹ everywhere and provide a proof that it is impossible to construct such a C ² scheme at the quad/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples. ACM CSS: I.3.5 Computer Graphics—Curve, surface, solid, and object representations     

Efficient admission control algorithms for multimedia servers

In this paper, we have proposed efficient admission control algorithms for multimedia storage servers that are providers of variable-bit-rate media streams. The proposed schemes are based on a slicing technique and use aggressive methods for admission control. We have developed two types of admission control schemes: Future-Max (FM) and Interval Estimation (IE). The FM algorithm uses the maximum bandwidth requirement of the future to estimate the bandwidth requirement. The IE algorithm defines a class of admission control schemes that use a combination of the maximum and average bandwidths within each interval to estimate the bandwidth requirement of the interval. The performance evaluations done through simulations show that the server utilization is improved by using the FM and IE algorithms. Furthermore, the quality of service is also improved by using the FM and IE algorithms. Several results depicting the trade-off between the implementation complexity, the desired accuracy, the number of accepted requests, and the quality of service are presented.     

Parallel smoothing of quad meshes

For use in real-time applications, we present a fast algorithm for converting a quad mesh to a smooth, piecewise polynomial surface on the Graphics Processing Unit (GPU). The surface has well-defined normals everywhere and closely mimics the shape of Catmull–Clark subdivision surfaces. It consists of bicubic splines wherever possible, and a new class of patches—c-patches—where a vertex has a valence different from 4. The algorithm fits well into parallel streams so that meshes with 12,000 input quads, of which 60% have one or more non-4-valent vertices, are converted, evaluated and rendered with 9×9 resolution per quad at 50 frames per second. The GPU computations are ordered so that evaluation avoids pixel dropout.

Subdivision Schemes for Quadrilateral Meshes with the Least Polar Artifact in Extraordinary Regions

This paper presents subdivision schemes with subdivision stencils near an extraordinary vertex that are free from or with substantially reduced polar artifact in extraordinary regions while maintaining the best possible bounded curvature at extraordinary positions. The subdivision stencils are firstly constructed to meet tangent plane continuity with bounded curvature at extraordinary positions. They are further optimized towards curvature continuity at an extraordinary position with additional measures for removing or for minimizing the polar artifact in extraordinary regions. The polar artifact for subdivision stencils of lower valences is removed by applying an additional constraint to the subdominant eigenvalue to be the same as that of subdivision at regular vertices, while the polar artifact for subdivision stencils of higher valances is substantially reduced by introducing an additional thin‐plate energy function and a penalty function for maintaining the uniformity and regularity of the characteristic map. A new tuned subdivision scheme is introduced by replacing subdivision stencils of Catmull‐Clark subdivision with that from this paper for extraordinary vertices of valences up to nine. We also compare the refined meshes and limit surface quality of the resulting subdivision scheme with that of Catmull‐Clark subdivision and other tuned subdivision schemes. The results show that subdivision stencils from our method produce well behaved subdivision meshes with the least polar artifact while maintaining satisfactory limit surface quality.     

General triangular midpoint subdivision

In this paper, we introduce triangular subdivision operators which are composed of a refinement operator and several averaging operators, where the refinement operator splits each triangle uniformly into four congruent triangles and in each averaging operation, every vertex will be replaced by a convex combination of itself and its neighboring vertices. These operators form an infinite class of triangular subdivision schemes including Loop's algorithm with a restricted parameter range and the midpoint schemes for triangular meshes. We analyze the smoothness of the resulting subdivision surfaces at their regular and extraordinary points by generalizing an established technique for analyzing midpoint subdivision on quadrilateral meshes. General triangular midpoint subdivision surfaces are smooth at all regular points and they are also smooth at extraordinary points under certain conditions. We show some general triangular subdivision surfaces and compare them with Loop subdivision surfaces.     

Deadlock detection in distributed database systems: a new algorithm and a comparative performance analysis

This paper attempts a comprehensive study of deadlock detection in distributed database systems. First, the two predominant deadlock models in these systems and the four different distributed deadlock detection approaches are discussed. Afterwards, a new deadlock detection algorithm is presented. The algorithm is based on dynamically creating deadlock detection agents (DDAs), each being responsible for detecting deadlocks in one connected component of the global wait-for-graph (WFG). The DDA scheme is a “self-tuning” system: after an initial warm-up phase, dedicated DDAs will be formed for “centers of locality”, i.e., parts of the system where many conflicts occur. A dynamic shift in locality of the distributed system will be responded to by automatically creating new DDAs while the obsolete ones terminate. In this paper, we also compare the most competitive representative of each class of algorithms suitable for distributed database systems based on a simulation model, and point out their relative strengths and weaknesses. The extensive experiments we carried out indicate that our newly proposed deadlock detection algorithm outperforms the other algorithms in the vast majority of configurations and workloads and, in contrast to all other algorithms, is very robust with respect to differing load and access profiles. Received December 4, 1997 / Accepted February 2, 1999     

面向移动终端的三角网格逆细分压缩算法

针对移动用户的实时显示需求,提出一种基于逆细分的三角网格压缩算法.通过改进逆Butterfly简化算法,采用逆改版Loop模式,将细密的三角网格简化生成由稀疏的基网格和一系列偏移量组成的渐进网格;然后,通过设计偏移量小波树,将渐进网格进行嵌入式零树编码压缩.实验结果表明:该算法与以往方法相比,在获得较高压缩比的同时,运行速度较快.适用于几何模型的网络渐进传输和在移动终端上的3D图形实时渲染.     

Packet audio playout delay adjustment: performance bounds and algorithms

In packet audio applications, packets are buffered at a receiving site and their playout delayed in order to compensate for variable network delays. In this paper, we consider the problem of adaptively adjusting the playout delay in order to keep this delay as small as possible, while at the same time avoiding excessive “loss” due to the arrival of packets at the receiver after their playout time has already passed. The contributions of this paper are twofold. First, given a trace of packet audio receptions at a receiver, we present efficient algorithms for computing a bound on the achievable performance of any playout delay adjustment algorithm. More precisely, we compute upper and lower bounds (which are shown to be tight for the range of loss and delay values of interest) on the optimum (minimum) average playout delay for a given number of packet losses (due to late arrivals) at the receiver for that trace. Second, we present a new adaptive delay adjustment algorithm that tracks the network delay of recently received packets and efficiently maintains delay percentile information. This information, together with a “delay spike” detection algorithm based on (but extending) our earlier work, is used to dynamically adjust talkspurt playout delay. We show that this algorithm outperforms existing delay adjustment algorithms over a number of measured audio delay traces and performs close to the theoretical optimum over a range of parameter values of interest.     

Progressive Lossless Mesh Compression Via Incremental Parametric Refinement

In this paper, we propose a novel progressive lossless mesh compression algorithm based on Incremental Parametric Refinement, where the connectivity is uncontrolled in a first step, yielding visually pleasing meshes at each resolution level while saving connectivity information compared to previous approaches. The algorithm starts with a coarse version of the original mesh, which is further refined by means of a novel refinement scheme. The mesh refinement is driven by a geometric criterion, in spirit with surface reconstruction algorithms, aiming at generating uniform meshes. The vertices coordinates are also quantized and transmitted in a progressive way, following a geometric criterion, efficiently allocating the bit budget. With this assumption, the generated intermediate meshes tend to exhibit a uniform sampling. The potential discrepancy between the resulting connectivity and the original one is corrected at the end of the algorithm. We provide a proof-of-concept implementation, yielding very competitive results compared to previous works in terms of rate/distortion trade-off.     

Rendering optimal solar shadows with plural sunlight depth buffers

We propose a novel method, based on the two-pass Z-buffer algorithm, to calculate shadows with sufficient precision and efficiency for rendering a daytime landscape with solar penumbrae. The special feature of the proposed method is that the shadows can be preserved with a precision superior to that of any visible surface. We use the optimal number of plural shadow buffers to do this; it gives a fairly satisfying trade–off between computation time and quality of shadows.     

Wavelet-based progressive compression scheme for triangle meshes: wavemesh

We propose a new lossy to lossless progressive compression scheme for triangular meshes, based on a wavelet multiresolution theory for irregular 3D meshes. Although remeshing techniques obtain better compression ratios for geometric compression, this approach can be very effective when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. The simplification is based on the solving of an inverse problem. Optimization of both the connectivity and geometry of the processed mesh improves the approximation quality and the compression ratio of the scheme at each resolution level. We show why this algorithm provides an efficient means of compression for both connectivity and geometry of 3D meshes and it is illustrated by experimental results on various sets of reference meshes, where our algorithm performs better than previously published approaches for both lossless and progressive compression.     

Analyzing a generalized Loop subdivision scheme

In this paper a class of subdivision schemes generalizing the algorithm of Loop is presented. The stencils have the same support as those from the algorithm of Loop, but allow a variety of weights. By varying the weights a class of C ¹ regular subdivision schemes is obtained. This class includes the algorithm of Loop and the midpoint schemes of order one and two for triangular nets. The proof of C ¹ regularity of the limit surface for arbitrary triangular nets is provided for any choice of feasible weights. The purpose of this generalization of the subdivision algorithm of Loop is to demonstrate the capabilities of the applied analysis technique. Since this class includes schemes that do not generalize box spline subdivision, the analysis of the characteristic map is done with a technique that does not need an explicit piecewise polynomial representation. This technique is computationally simple and can be used to analyze classes of subdivision schemes. It extends previously presented techniques based on geometric criteria.