Algebraic pruning: a fast technique for curve and surface intersection

Computing the intersection of parametric and algebraic curves and surfaces is a fundamental problem in computer graphics and geometric modeling. This problem has been extensively studied in the literature and different techniques based on subdivision, interval analysis and algebraic formulation are known. For low degree curves and surfaces algebraic methods are considered to be the fastest, whereas techniques based on subdivision and Bézier clipping perform better for higher degree intersections. In this paper, we introduce a new technique of algebraic pruning based on the algebraic approaches and eigenvalue formulation of the problem. The resulting algorithm corresponds to computing only selected eigenvalues in the domain of intersection. This is based on matrix formulation of the intersection problem, power iterations and geometric properties of Bézier curves and surfaces. The algorithm prunes the domain and converges to the solutions rapidly. It has been applied to intersection of parametric and algebraic curves, ray tracing and curve-surface intersections. The resulting algorithm compares favorably with earlier methods in terms of performance and accuracy.     

UNISURF,from styling to tool-shop

Since 1965, CAD has replaced the conventional system for defining free-form curves and surfaces. UNISURF, which has been widely used in the French car industry for designing car bodies since 1975, is briefly described.     

A New Paradigm for Geometric Processing

A new paradigm for geometric processing is proposed. The paradigm can be featured by the four key phrases: (1) Totally Four Dimensional Homogeneous Processing, (2) 4 × 4 Matrix Method and 4 × 4 Determinant Method, (3) Integer Arithmetic with Adaptive Data-Length Control Technique, (4) Systematic Paradigm Structures Based on the Duality.     

Automatic surface generation in computer aided design

A technique for smoothly blending algebraic surfaces and a language for syntactic specification of objects are developed. Their use in automated design is illustrated by a gate valve example in which all fillets, edge roundings and joining surfaces are automatically constructed. The resulting object has an internal representation that is particularly amenable to interactive editing.This work was supported in part by the National Science Foundation under grant ECS 83-12096 and MCS 82-17996     

Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least-Squares Data Fitting

This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, least-squares data fitting , and wavelets . We show how least-squares data fitting can be used to "reverse" a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization.
Some insights that this work brings forth are that the inner product used in a multiresolution analysis in uences the support of a wavelet, that wavelets can be constructed by straightforward matrix observations, and that matrix partitioning and factorization can provide alternatives to inverses or duals for building efficient decomposition and reconstruction processes. We illustrate our findings using an example curve, grey-scale image, and tensor-product surface.     

雕塑实体模型与多面体实体模型映射的研究

讨论了雕塑实体模型与多面体实体模型间映射问题 ,介绍了保持Brep拓扑结构一致性约束下面片合成、曲面离散等算法。     

Generic Geometric Programming in the Computational Geometry Algorithms Library

This paper describes a number of design issues and programming paradigms that affect the development of C gal , the computational geometry algorithms library. Genericity of the library is achieved by concepts such as templates, iterators, and traits classes. This allows the application programmer to plug in own types of containers and point types, for example. The paper gives an explanation of these concepts and examples of how they are used.     

Metis – An Object-Oriented Toolkit for Constructing Virtual Reality Applications

Virtual reality systems provide realistic look and feel by seamlessly integrating three-dimensional input and output devices. One software architecture approach to constructing such systems is to distribute the application between a computation-intensive simulator back-end and a graphics-intensive viewer front-end which implements user interaction. In this paper we discuss Metis, a toolkit we have been developing based on such a software architecture, which can be used for building interactive immersive virtual reality systems with computationally intensive components. The Metis toolkit defines an application programming interface on the simulator side, which communicates via a network with a standalone viewer program that handles all immersive display and interactivity. Network bandwidth and interaction latency are minimized, by use of a constraint network on the viewer side that declaratively defines much of dynamic and interactive behavior of the application.     

Designing emotional, metaphoric, natural and intuitive interfaces for interactive art, edutainment and mobile communications

We are artists working since 1991 on the creation of interactive computer installations for which we design metaphoric, emotional, natural, intuitive and multi-modal interfaces. The interactive experiences we create are situated between art, design, entertainment and edutainment. When creating our interactive systems we often develop novel interface technologies that match conceptual and metaphoric content with technically novel interface solutions. While our main focus is to design interactive systems for the art context, our interactive or immersive systems also often find use in edutainment and in mobile communications areas. The following article summarizes some of our key concepts for our interface designs and presents some of our interactive technologies in more detail.     

Design and manufacture of free-form surfaces by cross-sectional approach

Conventional methods for manual design and analysis are not necessarily the best methods for computer implementation, lofting techniques, or computer aided design to produce a satisfactory result for the design of a wide range of shapes and the general form of the B-spline curve with the defining polygon adequately fulfils most essential requirements. Fourth-order curves seemed to be best suited for most cases, as they provide a compromise between smoothness and ‘localness’, yet curve orders of varying degrees still have some merit in certain circumstances.The most attractive feature realized with this method is the simplicity of design and the determination of the main input elements. Surface interpolation curves are shown and the production of a mould for a plastic handle indicated.     

Progression of mental models throughout the phases of a computer-based instructional simulation: Supportive information,practice, and performance

Students of chemical engineering (n = 26) participated in an experiment using a computer-based simulation of a chemical plant. The progression of participants’ mental models was examined throughout a computer-based instructional experience as they acquired the complex cognitive skills of troubleshooting. Participants’ mental models of the complex learning task were matched against an expert mental model at five observation points through the instruction. Progressions of learners’ mental models were examined before and after three phases of the instructional process: supportive information presentation, problem solving practice, and performance test. The results indicated a significant change in participants’ mental models after receiving the supportive information and little change after practice or performance. This paper presents the results of this investigation and discusses the findings and their implications for computer-based instruction and training.     

Digital media: Bridges between data particles and artifacts

The field of visual communication is currently facing a period of transition to digital media. Two tracks of development can be distinguished; one utilitarian, the other artistic in scope. The first area of application pragmatically substitutes existing media with computerized simulations and adheres to standards that have evolved out of common practice. The artistic direction experimentally investigates new features inherent in computer imaging devices and exploits them for the creation of meaningful expression. The intersection of these two apparently divergent approaches is the structural foundation of all digital media. My focus will be on artistic explorations, since they more clearly reveal the relevant properties. The metaphor of adata particle is introduced to explain the general universality of digital media. The structural components of the data particle are analysed in terms of duality, discreteness and abstraction. These properties are found to have significant impact on the production process of visual information: digital media encourage interactive use, integrate different classes of symbolic representation, and facilitate intelligent image generation.     

On the aesthetics of inversion and osculation

The goal of this article is to present an informal introduction and tutorial on certain graphical aspects of inversion and osculation for the non-mathematician and to present artistic renditions using these methods.     

A note on inverted mandelbrot sets

A simple technique is described for demonstrating artistically interesting behavior in chaotic systems defined by complex dynamics. In particular, the Mandelbrot set for the iterative process is explored.     

3D representation of the Mandelbrot set

A new 3D representation of the Mandelbrot set is presented. Although the method employing the Douady Hubbard's potential function has been useful for the 3D representation of the Mandelbrot set, in our new method 3D pictures are generated by setting height components normal to the plane of the original Mandelbrot set. The pictures obtained look like natural landscapes with cliffs.     

浅谈计算机美工基础教育的意义和作用

作者通过介绍进行计算机美工基础教育的艺术欣赏、工作美工的需要和教学中培养学生创造性三个方面,阐述了当前信息化教育中计算机美工基础教育的意义和作用。     

Cleopatra's necklace and the aesthetics of osculatory growth

This paper provides an introduction to simple techniques for visualizing a large class of intricate shapes generated by osculatory packing of cylinders and spheres.     

Mental models and computer modelling

Abstract This paper is concerned with the place of mental models in the process of knowledge construction and in particular, the relationship between mental models and computer models in that process. It identifies what is meant by mental models and outlines why they might be seen to be central to the process of acquiring knowledge. In this context, the second part of the paper analyses and discusses children's use of a spreadsheet to build their own computer models. It is suggested that the process of building models on a computer may provide direct support to the cognitive processes of constructing mental models, although the relationship is not straight forward.     

Symmetry,beauty and chaos in Chebyshev's paradise

Chebyshev polynomials and Halley maps are used as a reservoir for the generation of several visually striking and intricate classes of symmetrical and chaotic patterns. Relatively simple numerical recipes are included to encourage reader involvement.     

Computers and Art

The use of computers in art is not new: examples are given of past and present applications. Three categories are mentioned: computer as tool, as origin of concepts and metaphors, and as controller. The use of the computer in art gives rise to the idea of computing as representation- rather than just information-processing. Thus the computer can be said to 'belong' to artists and designers, and can be seen as a qualitative device. It is argued that computing is 'really' an art or design activity, and that this has implications for art, design and computing.