Parametric G n blending of curves and surfaces

We introduce a simple blending method for parametric curves and surfaces that produces families of parametrically defined, G ⁿ –continuous blending curves and surfaces. The method depends essentially on the parameterizations of the curves/surfaces to be blended. Hence, the flexibility of the method relies on the existence of suitable parameter transformations of the given curves/surfaces. The feasibility of the blending method is shown by several examples. The shape of the blend curve/surface can be changed in a predictable way with the aid of two design parameters (thumb weight and balance).     

基于B样条模型的曲线特征点检测法

提出了一种基于B样条模型的曲线特征点检测法。该方法首先用B样条函数对原始曲线进行副近,得到原始曲线的分段解析表达式,然后利用曲线曲率分布来确定其特征点。B样条曲线分段解析的特点提出了曲率估计的精度,进而使特征点检测的准确度也得到提高,同时B样曲线拟合过程在一定程度上起到了对原始曲线的平滑作用,可抑制噪声对特征点检测的影响,并且这种平滑不具有常规高斯平滑的萎缩效应。实验结果证明了本文方法的有效性。     

基于最佳圆弧样条逼近的快速距离曲面计算

距离曲面是一种常用的隐式曲面,它在几何造型和计算机动画中具有重要的应用价值,但以往往在对距离曲面进行多边形化时速较慢,为了提高点到曲线最近距离计算的效率,提出了一种基于最佳圆弧样条逼近的快速线骨架距离曲面计算方法,该算法对于一条任意的二维NURBS曲线,在用户给定的误差范围内,先用最少量的圆弧样条来逼近给定的曲线,从而把点到NURBS曲线最近距离的计算问题转化为点到圆弧样条最近距离的计算问题,由于在对曲面进行多边形化时,需要大量的点到曲线最近距离的计算,而该处可以将点到圆弧样条最近距离很少的计算量来解析求得,故该算法效率很高,该实验表明,算法简单实用,具有很大的应用价值。     

二次Bézier曲线的双圆弧样条插值二分算法*

在数控加工领域,通常需要用尽量少段数的圆弧样条来对曲线进行拟合。采用二分查找算法,用G1连续的双圆弧样条对二次Bézier曲线进行拟合。该算法在给定误差范围内所需的圆弧段数较少。最后给出了具体的实例说明。     

An efficient animation of wrinkled cloth with approximate implicit integration

This paper presents an efficient method for creating the animation of flexible objects. The mass-spring model was used to represent flexible objects. The easiest approach to creating animation with the mass-spring model is the explicit Euler method, but the method has a serious weakness in that it suffers from an instability problem. The implicit integration method is a possible solution, but a critical flaw of the implicit method is that it involves a large linear system. This paper presents an approximate implicit method for the mass-spring model. The proposed technique updates with stability the state of n mass points in O(n) time when the number of total springs is O(n). In order to increase the efficiency of simulation or reduce the numerical errors of the proposed approximate implicit method, the number of mass points must be as small as possible. However, coarse discretization with a small number of mass points generates an unrealistic appearance for a cloth model. By introducing a wrinkled cubic spline curve, we propose a new technique that generates realistic details of the cloth model, even though a small number of mass points are used for simulation.     

Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G¹ arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.     

Analog computation for phase-based disparity estimation: continuous and discrete models

The analog implementation of a phase-based technique for disparity estimation is discussed. This technique is based on the convolution of images with Gabor filters. The article shows that by replacing the Gaussian envelope with other envelopes, the convolution operation is equivalent to the solution of a system of differential equations, whose order is related to the smoothness of the kernel. A detailed comparison between the disparity estimates obtained using these kernels and those obtained using the standard filter is presented. The discretization of the model leads to lattice networks in which the number of connections per node required to perform convolution is limited to the first few nearest neighbors. The short connection length makes these filter suitable for analog VLSI implementation, for which the number of connection per node is a crucial factor. Experimental measures on a prototype CMOS 17-node chip validated the approach. Received: 27 October 1997 / Accepted: 18 June 1998     

C2 Local convexity-preserving interpolation through the control point form method

C ² continuous convexity-preserving parametric curves in ℝ² is presented. The control point form method, which was developed in the field of numerical grid generation, is used here to construct interpolating curves. Good control over the shape of the curves is obtained thanks to the capability of the proposed approach to interpolate not only the data points, but also some directions suitably associated with them.     

有理多结点样条插值曲线及曲面

鉴于多结点样条曲线（MSIC）是一种点点通过的插值样条曲线,因此在多结点样条插值曲线研究的基础上,给出了有理多结点条插值曲线和有理多结点样条插值曲面的定义,并讨论了有理多结点样条的性质,对有理多结 样条曲线和有理多结点样条曲面的光滑拼接问题进行了讨论,此外,还对有理多结点样条在计算机辅助几何设计中的若干应用问题进行了说明。     

Algorithms on cone spline surfaces and spatial osculating arc splines

Developable surfaces are of considerable importance to many industrial applications, e.g., sheet metal forming processes. The objective of this paper is to provide algorithms on the approximation of developable surfaces with pieces of right circular cones. Special emphasis is devoted to practical choices of free parameters and to error estimation. Furthermore, a new algorithm for the approximation of spatial curves with a circular arc spline is presented which stands in close relation to above algorithms on developable surfaces. The proposed arc spline has contact of order 2 to the given curve in a series of curve points. The investigation includes a segmentation algorithm and error estimation.     

Creating and Rendering Convolution Surfaces

Implicit surfaces obtained by convolution of multi-dimensional primitives with some potential function, are a generalisation of popular implicit surface models: blobs, metaballs and soft objects. These models differ in their choice of potential function but agree upon the use of underlying modelling primitives, namely, points. In this paper a method is described for modelling and rendering implicit surfaces built upon an expanded set of skeletal primitives: points, line segments, polygons, arcs and planes. An analytical solution to the convolution is described. This solution offers a more accurate and robust representation of the resultant implicit surface than previous methods. An algorithm for ray-tracing the surfaces formed through convolution of any combination of these primitives is also outlined.     

Reparameterization of piecewise rational Bezier curves and its applications

degree . Although the curve segments are C ¹ continuous in three dimensions, they may be C ⁰ continuous in four dimensions. In this case, the multiplicity of each interior knot cannot be reduced and the B-spline basis function becomes C ⁰ continuous. Using a surface generation method, such as skinning these kinds of rational B-spline curves to construct an interpolatory surface, may generate surfaces with C ⁰ continuity. This paper presents a reparameterization method for reducing the multiplicity of each interior knot to make the curve segments C ¹ continuous in four dimensions. The reparameterized rational B-spline curve has the same shape and degree as before and also has a standard form. Some applications in skinned surface and ruled surface generation based on the reparameterized curves are shown. Published online: 19 July 2001     

Global methods for stroke segmentation

Two methods for stroke segmentation from a global point of view are presented and compared. One is based on thinning methods and the other is based on contour curve fitting. For both cases an input image is binarized. For the former, Hilditch's method is used, then crossing points are sought, around which a domain is constructed. Outside the domain, a set of line segments are identified. These lines are connected and approximated by cubic B-spline curves. Smoothly connected lines are selected as segmented curves. This method works well for a limited class of crossing lines, which are shown experimentally. In the latter, a contour line is approximated by cubic B-spline curve, along which curvature is measured. According to the extreme points of the curvature graph, the contour line is segmented, based on which the line segment is obtained. Experimental results are shown for some difficult cases. Received October 31, 1998 / Revised January 12, 1999     

The normalform of a space curve and its application to surface design

x )=0 with ∥▿h∥=1. The normalform function h is (unlike the latter cases) not differentiable at curve points. Despite of this disadvantage the normalform is a suitable tool for designing surfaces which can be treated as common implicit surfaces. Many examples (bisector surfaces, constant distance sum/product surfaces, metamorphoses, blending surfaces, smooth approximation surfaces) demonstrate applications of the normalform to surface design. Published online: 25 July 2001     

Approximate convolution with pairs of cubic Bézier LN curves

In this paper we present an approximation method for the convolution of two planar curves using pairs of compatible cubic Bézier curves with linear normals (LN). We characterize the necessary and sufficient conditions for two compatible cubic Bézier LN curves with the same linear normal map to exist. Using this characterization, we obtain the cubic spline approximation of the convolution curve. As illustration, we apply our method to the approximation of a font where the letters are constructed as the Minkowski sum of two planar curves. We also present numerical results using our approximation method for offset curves and compare our method to previous results.     

Extra-Ordinary Human–Machine Interaction: What can be Learned from People with Disabilities?

When specifying, designing and implementing technology for work, it is very important to consider the whole of the potential user group, and not to forget that this might include people with disabilities. Obvious reasons for this are demography, disabled people forming a significant and growing proportion of the workforce, and legal obligations caused by equal opportunities legislation. There are more subtle reasons, however, which link so-called ‘disabled people’ with the rest of the population. The paper notes that most people have some disabilities, sometimes temporarily due to accident, or permanently due to ageing and other processes. In addition it notes that even otherwise fully functioning people can be seriously handicapped by hostile environments, and a parallel is drawn between the human interface needs of disabled people operating in ordinary situations and able-bodied people operating in high workload and stress situations. The paper concludes by suggesting a research agenda for the field on the basis of these considerations.     

Bézier样条曲线改进的近似弧长参数化方法

提出了Bézier样条曲线利用分割技术近似弧长参数化的一种方法,并给出了相应的算法。通过求出曲线上所谓的‘最坏点’并在相应点处进行分割,可得到两条Bézier样条曲线。让这两条Bézier样条曲线具有与它们的近似弧长成比例的权,并对所得到的新的Bézier样条曲线进行同样的工作最终可得到一条由多条Bézier样条曲线所构成的新曲线。将这多条Bézier样条曲线合并成为一条Bézier样条曲线并通过节点插入技术将所得Bézier样条曲线转化为B-样条曲线的形式可得到全局参数域,其中各条Bézier曲线在全局参数域中所占子区间的长度与它们的权成比例,这样便得到了一条近似弧长参数化曲线。     

Volume-based three-dimensional metamorphosis using sphere-guided region correspondence

surface metamorphosis extends this paradigm by interpolating between discrete volume representations of the surfaces. The insensitivity of the established techniques to the surface topology enables morphing between completely different surfaces: however it can also lead to intermediate surfaces which have different topology from the originals. We present a method which improves on this situation by ensuring that no part of each surface remains disconnected during the morph. The morph is guided by region correspondence, derived automatically from a sphere representation of each surface: this can be combined with manual correspondence to retain user control over the morph. What emerges is a fast and flexible method for morphing surfaces, as demonstrated on several examples. Published online: 19 July 2001     

Database indexing for large DNA and protein sequence collections

Our aim is to develop new database technologies for the approximate matching of unstructured string data using indexes. We explore the potential of the suffix tree data structure in this context. We present a new method of building suffix trees, allowing us to build trees in excess of RAM size, which has hitherto not been possible. We show that this method performs in practice as well as the O(n) method of Ukkonen [70]. Using this method we build indexes for 200 Mb of protein and 300 Mbp of DNA, whose disk-image exceeds the available RAM. We show experimentally that suffix trees can be effectively used in approximate string matching with biological data. For a range of query lengths and error bounds the suffix tree reduces the size of the unoptimised O(mn) dynamic programming calculation required in the evaluation of string similarity, and the gain from indexing increases with index size. In the indexes we built this reduction is significant, and less than 0.3% of the expected matrix is evaluated. We detail the requirements for further database and algorithmic research to support efficient use of large suffix indexes in biological applications. Received: November 1, 2001 / Accepted: March 2, 2002 Published online: September 25, 2002