Metamorphosis of arbitrary triangular meshes

Three-dimensional metamorphosis (or morphing) establishes a smooth transition from a source object to a target object. The primary issue in 3D metamorphosis is to establish surface correspondence between the source and target objects, by which each point on the surface of the source object maps to a point on the surface of the target object. Having established this correspondence, we can generate a smooth transition by interpolating corresponding points from the source to the target positions. We handle 3D geometric metamorphosis between two objects represented as triangular meshes. To improve the quality of 3D morphing between two triangular meshes, we particularly consider the following two issues: 1) metamorphosis of arbitrary meshes; 2) metamorphosis with user control. We can address the first issue using our recently proposed method based on harmonic mapping (T. Kanai et al., 1998). In that earlier work, we developed each of the two meshes (topologically equivalent to a disk and having geometrically complicated shapes), into a 2D unit circle by harmonic mapping. Combining those two embeddings produces surface correspondence between the two meshes. However, this method doesn't consider the second issue: how to let the user control surface correspondence. The article develops an effective method for 3D morphing between two arbitrary meshes of the same topology. We extend our previously proposed method to achieve user control of surface correspondence     

Fast and intuitive generation of geometric shape transitions

We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed. However, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely, specifying the morphing process intuitively with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Suitable 3D interaction techniques offer a simple and intuitive control over the whole morphing process.     

An Eulerian approach for constructing a map between surfaces with different topologies

3D objects of the same kind often have different topologies, and finding correspondence between them is important for operations such as morphing, attribute transfer, and shape matching. This paper presents a novel method to find the surface correspondence between topologically different surfaces. The method is characterized by deforming the source polygonal mesh to match the target mesh by using the intermediate implicit surfaces, and by performing a topological surgery at the appropriate locations on the mesh. In particular, we propose a mathematically well‐defined way to detect the topology change of surface by finding the non‐degenerate saddle points of the velocity fields that tracks implicit surfaces. We show the effectiveness and possible applications of the proposed method through several experiments.     

Automatic high-resolution optoelectronic photogrammetric 3D surface geometry acquisition system

A fast, high-resolution, automatic, non-contact 3D surface geometry measuring system using a photogrammetric optoelectronic technique based on lateral-photoeffect diode detectors has been developed. Designed for the acquisition of surface geometries such as machined surfaces, biological surfaces, and deformed parts, the system can be used in design, manufacturing, inspection, and range finding. A laser beam is focused and scanned onto the surface of the object to be measured. Two cameras in stereo positions capture the reflected light from the surface at 10 kHz. Photogrammetric triangulation quickly transforms the pair of 2D signals created by the camera detectors into 3D coordinates of the light spot. Because only one small spot on the object is illuminated at a time, the stereo correspondence problem is solved in real time. The resolution is determined by a 12-bit A/D converter and can be improved up to 25 60025 600 by oversampling. The irregular 3D data can be regularized for use with image-based algorithms. Received: 8 October 1996 / Accepted: 3 February 1997     

Machine tool condition monitoring using workpiece surface texture analysis

Tool wear affects the surface roughness dramatically. There is a very close correspondence between the geometrical features imposed on the tool by wear and micro-fracture and the geometry imparted by the tool on to the workpiece surface. Since a machined surface is the negative replica of the shape of the cutting tool, and reflects the volumetric changes in cutting-edge shape, it is more suitable to analyze the machined surface than look at a certain portion of the cutting tool. This paper discusses our work that analyzes images of workpiece surfaces that have been subjected to machining operations and investigates the correlation between tool wear and quantities characterizing machined surfaces. Our results clearly indicate that tool condition monitoring (the distinction between a sharp, semi-dull, or a dull tool) can be successfully accomplished by analyzing surface image data. Received: 9 June 1998 / Accepted: 6 October 1999     

圆弧路径法，一种新的多边形变形方法

二维形状变形技术在二维角色动画、模式匹配、几何造型、虚拟现实、工业模拟、科学计算可视化等领域有着重要的应用。本文提出了一种顶点路径圆弧法的二维形状变形新方法。该算法通过控制关键帧多边形顶点按照一条特殊的圆弧曲线路径进行运动，实现二维形状变形。通过许多实例的测试表明，该算法效果良好：不仅可以保持首末关键帧形状的共同特征，而且中间插值形状变化自然平滑。同时，我们的方法易于用户交互控制；容易推广到高维情形；计算量较小、能达到系统实时的要求。     

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     

Robust and efficient surface reconstruction from contours

We propose a new approach for surface recovery from planar sectional contours. The surface is reconstructed based on the so-called “equal importance criterion,” which suggests that every point in the region contributes equally to the reconstruction process. The problem is then formulated in terms of a partial differential equation, and the solution is efficiently calculated from distance transformation. To make the algorithm valid for different application purposes, both the isosurface and the primitive representations of the object surface are derived. The isosurface is constructed by means of a partial differential equation, which can be solved iteratively. The traditional distance interpolating method, which was used by several researchers for surface reconstruction, is an approximate solution of the equation. The primitive representations are approximated by Voronoi diagram transformation of the surface space. Isosurfaces have the advantage that subsequent geometric analysis of the object can be easily carried out while primitive representation is easy to visualize. The proposed technique allows for surface recovery at any desired resolution, thus avoiding the inherent problems of correspondence, tiling, and branching.     

Mobile robot navigation and scene modeling using stereo fish-eye lens system

We present an autonomous mobile robot navigation system using stereo fish-eye lenses for navigation in an indoor structured environment and for generating a model of the imaged scene. The system estimates the three-dimensional (3D) position of significant features in the scene, and by estimating its relative position to the features, navigates through narrow passages and makes turns at corridor ends. Fish-eye lenses are used to provide a large field of view, which images objects close to the robot and helps in making smooth transitions in the direction of motion. Calibration is performed for the lens-camera setup and the distortion is corrected to obtain accurate quantitative measurements. A vision-based algorithm that uses the vanishing points of extracted segments from a scene in a few 3D orientations provides an accurate estimate of the robot orientation. This is used, in addition to 3D recovery via stereo correspondence, to maintain the robot motion in a purely translational path, as well as to remove the effects of any drifts from this path from each acquired image. Horizontal segments are used as a qualitative estimate of change in the motion direction and correspondence of vertical segment provides precise 3D information about objects close to the robot. Assuming detected linear edges in the scene as boundaries of planar surfaces, the 3D model of the scene is generated. The robot system is implemented and tested in a structured environment at our research center. Results from the robot navigation in real environments are presented and discussed. Received: 25 September 1996 / Accepted: 20 October 1996     

Model-based interpretation of stereo imagery of textured surfaces

We present a scheme for reliable and accurate surface reconstruction from stereoscopic images containing only fine texture and no stable high-level features. Partial shape information is used to improve surface computation: first by fitting an approximate, global, parametric model, and then by refining this model via local correspondence processes. This scheme eliminates the window size selection problem in existing area-based stereo correspondence schemes. These ideas are integrated in a practical vision system that is being used by environmental scientists to study wind erosion of bulk material such as coal ore being transported in open rail cars. Received: 14 August 1995 / Accepted: 27 May 1997     

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     

Convolution surfaces for arcs and quadratic curves with a varying kernel

A convolution surface is an isosurface in a scalar field defined by convolving a skeleton, comprising of points, curves, surfaces, or volumes, with a potential function. While convolution surfaces are attractive for modeling natural phenomena and objects of complex evolving topology, the analytical evaluation of integrals of convolution models still poses some open problems. This paper presents some novel analytical convolution solutions for arcs and quadratic spline curves with a varying kernel. In addition, we approximate planar higher-degree polynomial spline curves by optimal arc splines within a prescribed tolerance and sum the potential functions of all the arc primitives to approximate the field for the entire spline curve. Published online: November 20, 2002     

Deterministic broadcasting in ad hoc radio networks

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time . Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Received: January 2000 / Accepted: June 2001     

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).     

带不失真纹理映射的三维Morphing动画研究及实现

介绍了三维Morphing，编程实现了相同顶点数和拓扑结构的物体之间的Morphing，并采用一种带不失真纹理映射的船形曲面造型法，有效地消除了形变曲面的纹理映射的图像失真问题，最后给出了基于任意拓扑结构的物体间Morphing的方法。     

Building a color classification system for textured and hue homogeneous surfaces: system calibration and algorithm

We present a system for classifying the color aspect of textured surfaces having a nearly constant hue (such as wooden boards, textiles, wallpaper, etc.). The system is designed to compensate for small fluctuations (over time) of the light source and for inhomogeneous illumination conditions (shading correction). This is an important feature because even in industrial environments where the lighting conditions are controlled, a constant and homogeneous illumination cannot be guaranteed. Together with an appropriate camera calibration (which includes a periodic update), our approach offers a robust system which is able to “distinguish” (i.e., classify correctly) between surface classes which exhibit visually barely perceptible color variations. In particular, our approach is based on relative (not absolute) color measurements. In this paper, we outline the classification algorithm while focusing in detail on the camera calibration and a method for compensating for fluctuations of the light source. Received: 1 September 1998 / Accepted: 16 March 2000     

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     

Minimal area for surface reconstruction from cross sections

Surface reconstruction from cross-sectional data is important in a variety of applications. It is usually possible to generate a surface in many ways, but only reasonable ones are acceptable. A surface of minimal area has been considered as one of the most natural optimal criteria for the original tiling method of surface reconstruction from cross sections. In the paper, we consider minimal surfaces for continuous generalization of the tiling approach and in the general situation of reconstruction from cross sections. We show that in these cases the minimal area criterion leads to defective surfaces and is thus unacceptable. Published online: 23 July 2002 Correspondence to: D. Berzin     

THRED: a two-handed design system

This paper describes a computer-aided design system for sketching free-form polygonal surfaces such as terrains and other natural objects. The user manipulates two 3D position and orientation trackers with three buttons, one for each hand. Each hand has a distinct role to play, with the dominant hand being responsible for picking and manipulation, and the less dominant hand being responsible for context setting of various kinds. The less dominant hand holds the workpiece, sets which refinement level that can be picked by the dominant hand, sets the constraint mode and the reshape operator, and generally acts as a counterpoint to the dominant hand. In this paper, the architecture of the system is outlined, the interaction techniques are presented, and a simple surface is shown.     

Protocol synthesis and re-synthesis with optimal allocation of resources based on extended Petri nets

Protocol synthesis is used to derive a protocol specification, that is, the specification of a set of application components running in a distributed system of networked computers, from a specification of services (called the service specification) to be provided by the distributed application to its users. Protocol synthesis reduces design costs and errors by specifying the message exchanges between the application components, as defined by the protocol specification. In general, maintaining such a distributed application involves applying frequent minor modifications to the service specification due to changes in the user requirements. Deriving the protocol specification after each modification using the existing synthesis methods is considered expensive and time consuming. Moreover, we cannot identify what changes we should make to the protocol specification in correspondence to the changes in the service specification. In this paper, we present a new synthesis method to re-synthesize only those parts of the protocol specification that must be modified in order to satisfy the changes in the service specification. The method consists of a set of simple rules that are applied to the protocol specification written in an extended Petri net model. An application example is given along with some experimental results. Received: July 2001 / Accepted: July 2002 RID="*" ID="*" Supported by International Communications Foundation (ICF), Japan RID="**" ID="**" Supported by Communications and Information Technology Ontario (CITO) and Natural Sciences and Engineering Research Council (NSERC), Canada RID="*" ID="*" Supported by International Communications Foundation (ICF), Japan