A surface-scanning algorithm for displaying generalized cylinders

Generalized cylinders are objects defined by sweeping an arbitrary 2D closed contour along an arbitrary 3D trajectory while simultaneously scaling the contour in two perpendicular directions. A display algorithm for generalized cylinders is presented that is based on generating successive points on contours positioned at successive points on the trajectory. This surface-scanning algorithm requires that the contours as well as the points on a contour are taken close enough to guarantee that no gaps occur in the projected surface of the generalized cylinder. On the other hand, for the sake of efficiency, care has to be taken to restrict the number of super-fluous points. The paper describes solutions for these problems and shows that a surface-scanning algorithm is an elegant and efficient display algorithm for parametrically defined generalized cylinders.     

Approximate General Sweep Boundary of a 2D Curved Object

This paper presents an algorithm to compute an approximation to the general sweep boundary of a 2D curved moving object which changes its shape dynamically while traversing a trajectory. In effect, we make polygonal approximations to the trajectory and to the object shape at every appropriate instance along the trajectory so that the approximated polygonal sweep boundary is within a given error bound ϵ > 0 from the exact sweep boundary. The algorithm interpolates intermediate polygonal shapes between any two consecutive instances, and constructs polygons which approximate the sweep boundary of the object. Previous algorithms on sweep boundary computation have been mainly concerned about moving objects with fixed shapes; nevertheless, they have involved a fair amount of symbolic and/or numerical computations that have limited their practical uses in graphics modeling systems as well as in many other applications which require fast sweep boundary computation. Although the algorithm presented here does not generate the exact sweep boundaries of objects, it does yield quite reasonable polygonal approximations to them, and our experimental results show that its computation is reasonably fast to be of a practical use.     

三维破碎物体多尺度拼接技术

在分析三维物体碎片轮廓曲线的特征和表示的基础上,研究多尺度小波轮廓描述符的计算,提出了一种多尺度下轮廓曲线特征提取及基于多尺度分析的三维物体碎片拼接方法.轮廓曲线经多尺度小波变换平滑后,提取曲率和挠率构成特征矢量;在选择了基于小波轮廓描述符的三维曲线匹配起点后,比较2条轮廓曲线的特征矢量以判断轮廓的相似性,并将轮廓匹配的2块相邻物体碎片拼接,实现破碎物体复原.最后通过实验验证了该方法的有效性.     

Smooth surface approximation to serial cross-sections

The reconstruction of the surface model of an object from 2D cross-sections plays an important role in many applications. In this paper, we present a method for surface approximation to a given set of 2D contours. The resulting surface is represented by a bicubic closed B-spline surface with C² continuity. The method performs the skinning of intermediate contour curves represented by cubic B-spline curves on a common knot vector, each of which is fitted to its contour points within a given accuracy. In order to acquire more compact representation for the surface, the method includes an algorithm for reducing the number of knots in the common knot vector. The proposed method provides a smooth and accurate surface model, yet realizes efficient data reduction. Some experimental results are given using synthetic and MRI data.     

Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.     

Performance of scanline algorithms for direct display of CSG

Direct display algorithms display a CSG model without first converting the model into a boundary representation. Three such algorithms are described. All three are based on the scanline display algorithm, and are able to handle both polygonal and quadratic faces.The first algorithm is based on Atherton's recursive subdivision scanline algorithm, the second is a combination of a scanline and a ray casting algorithm, and the third is a scanline version of the Trickle algorithm. A multiprocessor system in which these algorithms can be incorporated is also described.The performances of the algorithms are compared. It turns out that the algorithms efficiently display CSG models on general-purpose architectures. A comparison is also made between the performances for polygon-approximated models and exact models for objects bounded by quadratic faces, such as spherical, cylindrical and conical faces, to get an indication of how many polygons can at most be used to approximate quadratic faces and still have better performance.     

基于特征线的三维服装部件参数化造型

基于特征线的服装三维造型方法有诸多优点,但是现有服装模型并不能很好地支持服装参数化设计.为此将参数化造型方法引入三维服装部件造型中,以得到参数化的服装部件.基于光顺人体模型,依据服装部件特点设计服装特征线,将特征线分为截面环和轮廓线,依次通过截面环和轮廓线的生成与调整、特征线综合调整和特征线添加约束3个步骤,得到服装特征线框架;并对该框架利用曲面插值方法得到服装曲面模型.实例结果表明,文中方法功能强大、方便灵活.     

Computer aided design of ventilation tubes for customized hearing aid devices

This work describes a framework for the modeling of sweep solids on freeform surfaces, considering various geometric and functional constrains. The sweeping procedure begins with the definition of a trajectory on the surface. Besides smoothness and minimal length, other requirements may apply. Therefore, it is convenient to formulate the optimal trajectory tracing as a geodesic curve computation on the surface. The trajectory defined on the surface is offsetted inside in order to make the sweep solid tangent to the surface. The offset curve shape is iteratively optimized while preserving minimal distance from the surface. Then, a frame field is defined over the offset curve and the cross-section contour is swept according to this field. The major obstacle is how to construct the frame field such that the resulting sweep solid will be smooth and free of self-intersections. In order to resolve these issues a new minimal distortion frame is introduced. The key idea is to weaken the orthogonality constraint between the cross-section plane and the trajectory curve to avoid self-intersections of the resulting sweep solid.The proposed approach was employed for semi-automatic computer aided design of ventilation tubes for customized hearing aid devices. This approach was tested in a real production environment, where it was proved robust and efficient. Although the modeling pipeline described in the paper is optimized for the specific design task, the proposed techniques are general and can be utilized in many related applications where sweeping surface modeling and manipulation are involved.     

Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution

We concentrate here on decomposition of 2D objects into meaningfulparts of visual form, orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution. We obtain a novel rule for decomposition of 2D objects into visual parts, called the hierarchical convexity rule, which states that visual parts are enclosed by maximal convex (with respect to the object) boundary arcs at different stages of the contour evolution. This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of the evolution hierarchy induce a hierarchical structure of the visual parts. The more advanced the stage of contour evolution, the more significant is the shape contribution of the obtained visual parts.     

Stereo‐Consistent Contours in Object Space

Notebook scribbles, art or technical illustrations—line drawings are a simplistic method to visually communicate information. Automated line drawings often originate from virtual 3D models, but one cannot trivially experience their three‐dimensionality. This paper introduces a novel concept to produce stereo‐consistent line drawings of virtual 3D objects. Some contour lines do not only depend on an objects geometry, but also on the position of the observer. To accomplish consistency between multiple view positions, our approach exploits geometrical characteristics of 3D surfaces in object space. Established techniques for stereo‐consistent line drawings operate on rendered pixel images. In contrast, our pipeline operates in object space using vector geometry, which yields many advantages: The position of the final viewpoint(s) is flexible within a certain window even after the contour generation, e.g. a stereoscopic image pair is only one possible application. Such windows can be concatenated to simulate contours observed from an arbitrary camera path. Various types of popular contour generators can be handled equivalently, occlusions are natively supported and stylization based on geometry characteristics is also easily possible.     

Self-intersection avoidance and integral properties of generalized cylinders

A generalized cylinder is an object bounded by a surface generated by moving a 2D contour curve along a 3D spine curve, possibly scaling the contour along the spine, and two end planes. Several important properties of such objects are presented. In particular, conditions to avoid local and global self-intersection of generalized cylinders are given, and some of their integral properties, such as area and volume, are discussed.     

Using stereokinetic effect to convey depth: computationally efficient depth-from-motion displays.

Recent developments in microelectronics have encouraged the use of 3D data bases to create compelling volumetric renderings of graphical objects. However, even with the computational capabilities of current-generation graphical systems, real-time displays of such objects are difficult, particularly when dynamic spatial transformations are involved. In this paper we discuss a type of visual stimulus (the stereokinetic effect display) that is computationally far less complex than a true three-dimensional transformation but yields an equally compelling depth impression, often perceptually indiscriminable from the true spatial transformation. Several possible applications for this technique are discussed (e.g., animating contour maps and air traffic control displays so as to evoke accurate depth percepts).     

基于等高线的三维地形造型算法

提出了一个从等高线地形图转换成三维真实感地形显示的快速算法，给出用深度标记法求出各点地形高度的插值算法，并对三维造型的快速显示作了探讨。实验证明本文造型方法速度快、精度高。     

基于多尺度分析的三维曲线匹配技术研究

从提取三维物体碎片轮廓曲线出发,提出一种基于多尺度分析的三维曲线匹配技术。轮廓曲线经多尺度平滑后,计算曲线的特征矢量,通过比较特征矢量以判断轮廓曲线的相似性,实现三维曲线匹配。实验表明提出的算法具有准确性、鲁棒性和容错性。     

Interactive 3D garment design with constrained contour curves and style curves

This paper presents interactive techniques to design 3D garments conveniently and precisely with constrained contour curves and style curves. Contour curves, including silhouette curves and cross section curves, are used for garment surface modeling. Style curves, including seam lines, dart lines, notch lines and grain lines, are introduced for designing patterns on the triangular garment surfaces. Contour curves are extracted automatically from the boundaries of garment sub-meshes. The definitions and resolving rules of various constraints are introduced for editing the contour curves conveniently. Style curves are generated by projecting control points onto 3D garment triangular surfaces. In order to draw the style curves validly, some constraints are also introduced according to the craft requirements of pattern design. Furthermore, the effects of style curves in pattern flattening are analyzed, which can guide the designer to draw style curves more reasonably and enhance the pattern design quality. Finally, some examples are given to show that our methods can make the 3D garment design more flexible and friendly, and style curves can be applied into design patterns on 3D triangular surface for shoes, toys and so on.     

A 3D face matching framework for facial curves

Among the many 3D face matching techniques that have been developed, are variants of 3D facial curve matching, which reduce the amount of face data to one or a few 3D curves. The face’s central profile, for instance, proved to work well. However, the selection of the optimal set of 3D curves and the best way to match them has not been researched systematically. We propose a 3D face matching framework that allows profile and contour based face matching. Using this framework we evaluate profile and contour types including those described in the literature, and select subsets of facial curves for effective and efficient face matching. With a set of eight geodesic contours we achieve a mean average precision (MAP) of 0.70 and 92.5% recognition rate (RR) on the 3D face retrieval track of the Shape Retrieval Contest (SHREC’08), and a MAP of 0.96 and 97.6% RR on the University of Notre Dame (UND) test set. Face matching with these curves is time-efficient and performs better than other sets of facial curves and depth map comparison.     

A haptic-rendering technique based on hybrid surface representation

A novel haptic rendering technique using a hybrid surface representation addresses conventional limitations in haptic displays. A haptic interface lets the user touch, explore, paint, and manipulate virtual 3D models in a natural way using a haptic display device. A haptic rendering algorithm must generate a force field to simulate the presence of these virtual objects and their surface properties (such as friction and texture), or to guide the user along a specific trajectory. We can roughly classify haptic rendering algorithms according to the surface representation they use: geometric haptic algorithms for surface data, and volumetric haptic algorithms based on volumetric data including implicit surface representation. Our algorithm is based on a hybrid surface representation - a combination of geometric (B-rep) and implicit (V-rep) surface representations for a given 3D object, which takes advantage of both surface representations.