3D Polygon Research Articles

The modelling of particle systems with real shapes.

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

Towards Comprehensive 3D Enabled Web-Based Learning

Traditional web-based learning techniques focus on extensive usage of multimedia data such as images, videos and audios. In this paper, we validate 3D model and 3D motion retrieval as an integrated part of e-learning architecture. New approaches, including a novel shape representation of arbitrary 3D polygon models, are proposed as preliminary solutions, with potential applications in digital library, interactive learning, etc.

Optimal Single Biarc Fitting and its Applications

AbstractThis paper proposes a new approach for fitting an optimized biarc to a given 2D polygon and its two end tangents. A biarc can be constructed which matches two end points and two end tangents, but an additional constraint is required to make the biarc unique. The conventional approach to biarc construction, which has been adopted in arc spline approximation, introduces additional constraints to uniquely determine the biarc. Instead of imposing such constraints, the proposed approach exploits the inherent freedom in the choice of the biarc to achieve a better fit minimizing the distance between the polygon and the biarc. The approach is simple in concept and acceptable in computation. When applied in arc spline approximation tasks, the approach can play an important role in reducing the number of segments in the resulting arc spline. Some experimental results demonstrate its usefulness and quality.

特徴量空間に基づく形と色の定量的独自性を用いた工業デザインの発想支援(S54-1 設計支援手法・CAD/CAE(1),S54 設計支援手法・CAD/CAE)

A computerized method of (a) calculating shape and color features of existing designs from their 3D polygon models, (b) analyzing the designs by representing them as vectors in a feature space, and (c) searching for a distinctive usage of shape and color as a vector furthermost from the existing vectors in the space, is proposed. In this method, a distinctiveness of a design from existing designs is mathematically defined and used for the search process. A searched solution should help a designer to think of a new design distinctive from existing ones to attract consumer attention. The proposed method is implemented as a software and applied to simplified models of nine personal computer designs and seven digital camera designs.

Shape similarity comparison of 3D polygon soup models

Shape similarity comparison of 3D polygon soup models

Reduction algorithm of 3D polygon data

Reduction algorithm of 3D polygon data

Evaluation of angular error between two lines

The error caused by the fitting of a set of data points to two lines having a specified angle is defined as the angular error. The evaluation of angular error needs to find two pairs of parallel lines that follow the angular constraint and bound the data points under the minimum zone criterion. The evaluation of angular error is difficult in mathematics, so it is usually simplified by treating one line as the datum and the form error of the other line calculated from the datum as the solution. The datum is assumed to be perfect that doesn’t tell the real properties of the actual line but gives incorrect solutions in general. To give an exact solution to the angular error problem based on the minimum zone criterion, a new mathematical model is proposed in this paper. The basic idea of this model is to rotate the data points of one line to the same direction as that of the other line so that the evaluation of angular error is simplified as solving a straightness problem. The angular error obtained from the proposed model is proved to be minimum. The proposed model offers a simple approach to solve the tough angular error problem, and it also provides a feasible tool to explore more complicated problems, like 3D angular error and polygon error.

On the Optimality of Valence‐based Connectivity Coding

Abstract We show that the average entropy of the distribution of valences in valence sequences for the class of manifold 3D triangle meshes and the class of manifold 3D polygon meshes is strictly less than the entropy of these classes themselves. This implies that, apart from a valence sequence, another essential piece of information is needed for valence‐based connectivity coding of manifold 3D meshes. Since there is no upper bound on the size of this extra piece of information, the result implies that the question of optimality of valence‐based connectivity coding is still open.

On intrinsic representations of 3D polygons for shape blending

An intrinsic representation of a geometric object comprises a set of parameters that are invariant under Euclidean transformations and determine the shape and size of the object uniquely. Unlike the case of a two-dimensional polygon which has essentially only one intrinsic representation, a three-dimensional (3D) polygon allows several variations. We study three different intrinsic representations of a 3D polygon, focusing on properties regarding their applications in shape blending. We show that only one of these representations, which is a natural extension to the intrinsic functions of a 3D differentiable curve, is suitable for shape blending, while the others lead to discontinuous shape transformation. Detailed discussions about the evaluation criteria, numerical sensitivity, and an inherent difficulty in shape blending of 3D polygons are also presented.

Feature-based light field morphing

We present a feature-based technique for morphing 3D objects represented by light fields. Our technique enables morphing of image-based objects whose geometry and surface properties are too difficult to model with traditional vision and graphics techniques. Light field morphing is not based on 3D reconstruction; instead it relies on ray correspondence, i.e., the correspondence between rays of the source and target light fields. We address two main issues in light field morphing: feature specification and visibility changes. For feature specification, we develop an intuitive and easy-to-use user interface (UI). The key to this UI is feature polygons, which are intuitively specified as 3D polygons and are used as a control mechanism for ray correspondence in the abstract 4D ray space. For handling visibility changes due to object shape changes, we introduce ray-space warping. Ray-space warping can fill arbitrarily large holes caused by object shape changes; these holes are usually too large to be properly handled by traditional image warping. Our method can deal with non-Lambertian surfaces, including specular surfaces (with dense light fields). We demonstrate that light field morphing is an effective and easy-to-use technqiue that can generate convincing 3D morphing effects.

Convexifying polygons with simple projections

It is known that not all polygons in 3D can be convexified when crossing edges are not permitted during any motion. In this paper we prove that if a 3D polygon admits a non-crossing orthogonal projection onto some plane, then the 3D polygon can be convexified. If an algorithm to convexify the planar projection exists and runs in time P, then our algorithm to convexify the 3D polygon runs in O( n+ P) time.

2317 形状とテクスチャの変化に対応した物体のポリゴン化

2317 形状とテクスチャの変化に対応した物体のポリゴン化

Parallel visualization for molecular dynamics simulations

A 3D polygon rendering system conforming to the specification of OpenGL is implemented on a PVM (parallel virtual machine). The system is targeted to a low speed network of low cost serial computers. In our parallel rendering algorithm, image space is decomposed to exactly the number of regions equal to the number of processors which reduces the volume of communication and the polygons needed to be rendered more than once on separate renderers. We also propose a transmission scheme that distributes the passing of data throughout the whole process of rendering. Taking advantage of frame-to-frame coherence, load balancing is achieved by decomposing the image space unequally so that the workloads in each space region are proportional to the processing power of the corresponding renders. Distribution of workload and processing power that is volatile during rendering are obtained with linear prediction from statistics of previous frames. The system is practical and scalable for moderate number of processors.

A company-office system “Valentine” providing informal communication and personal space based on 3D virtual space and avatars

In this paper we propose a virtual office environment that integrates natural communication and secure private space. The features of this system are the following. (1) This system has a virtual shared room based on the idea of “shared room metaphor” and 3D graphics on an SGI workstation is used for this system. It uses Ethernet media (i.e. real-time audio/video streams). (2) This system implements the field of view of a human by using our “around view” technique. This provides more natural communication between members. (3) “Sound effects” are used to help users feel the presence of other members. For instance, members hear the sound of a door opening when someone logs into our system and the sound of footsteps when someone is walking around our virtual room. (4) At times our system limits the flow of awareness information. A person concentrating on his/her work may not want to perceive excessive awareness of others. To support such situation, we define “awareness space” which restricts the field where other members' awareness is transmitted. Awareness space changes in size with the degree of concentration which is measured through two factors: the movement of a chair and the frequency of keyboard typing. (5) “Headphone metaphor”. A picture of a headphone is attached above a person's image and changes color depending on the degree of concentration. This enables other members to recognize his/her state and can be a criterion as to whether he/she is available to communicate or not. (6) In the virtual space, users are represented as avatars built of 3D polygons and still pictures. The avatars change shape automatically according to the users' action.

FreeWalk: a 3D virtual space for casual meetings

A meeting environment for casual communication in a networked community, FreeWalk provides a 3D common area where everyone can meet and talk freely. FreeWalk represents participants as 3D polygon pyramids, on which their live video is mapped. Voice volume remains proportional to the distance between sender and receiver. For evaluation, we compared communications in FreeWalk to a conventional desktop videoconferencing system and a face-to-face meeting.

Controlling Gameplay

Controlling Gameplay

Digital watermarking of MPEG-4 facial animation parameters

The enforcement of intellectual property rights is difficult for digital data. One possibility of supporting enforcement is the embedding of digital watermarks containing information about copyright owner and/or receiver of the data. Watermarking methods have already been presented for audio, images, video, and polygonal 3D models. In this paper, we present a method for digital watermarking of MPEG-4 facial animation parameter data sets. The watermarks are additively embedded into the parameter values and can be retrieved either from the watermarked parameters or from video sequences rendered using the watermarked animation parameters for head animation. For retrieval from rendered sequences, the facial animation parameters have to be estimated first. We use a model-based approach for the estimation of the facial parameters that combines a motion model of an explicit 3D textured wireframe with the optical flow constraint from the video data. This leads to a linear algorithm that is robustly solved in a hierarchical framework with low computational complexity. Experimental results confirm the applicability of the presented watermarking technique.

Efficient clipping of arbitrary polygons

Clipping 2D polygons is one of the basic routines in computer graphics. In rendering complex 3D images it has to be done several thousand times. Efficient algorithms are therefore very important. We present such an efficient algorithm for clipping arbitrary 2D-polygons. The algorithm can handle arbitrary closed polygons, specifically where the clip and subject polygons may self-intersect. The algoirthm is simple and faster that Vatti's (1992) algorithm, which was designed for the general case as well. Simple modifications allow determination of union and set-theoretic differences of two arbitrary polygons.

Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications

The clustering algorithm DBSCAN relies on a density-based notion of clusters and is designed to discover clusters of arbitrary shape as well as to distinguish noise. In this paper, we generalize this algorithm in two important directions. The generalized algorithm—called GDBSCAN—can cluster point objects as well as spatially extended objects according to both, their spatial and their nonspatial attributes. In addition, four applications using 2D points (astronomy), 3D points (biology), 5D points (earth science) and 2D polygons (geography) are presented, demonstrating the applicability of GDBSCAN to real-world problems.

Parallel implementing OpenGL on PVM

A 3D polygon rendering system conforming to the specification of OpenGL is implemented on a PVM (parallel virtual machine). The system is targeted to a low speed network of low cost serial computers. In our parallel rendering algorithm, image space is decomposed to exactly the number of regions equal to the number of processors which reduces the volume of communication and the polygons needed to be rendered more than once on separate renderers. We also propose a transmission scheme that distributes the passing of data throughout the whole process of rendering. Taking advantage of frame-to-frame coherence, load balancing is achieved by decomposing the image space unequally so that the workloads in each space region are proportional to the processing power of the corresponding renders. Distribution of workload and processing power that is volatile during rendering are obtained with linear prediction from statistics of previous frames. The system is practical and scalable for moderate number of processors.