Issue 4

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https://diglib.eg.org/handle/10.2312/75

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    Dynamics and Chaos: The Spherical Pendulum
    (Blackwell Science Ltd and the Eurographics Association, 1996) Palacios, Antonio; Gross, Lee M.; Rockwood, Alyn P.
    All but the simplest of dynamical systems contain nonlinearities that play an important role in modeling and simulating physical systems. They create unpredictable (chaotic) behavior that is often hidden or neglected in traditional solutions. A simple dynamical system, the spherical pendulum, is introduced to illustrate issues, principles, and effects of chaos in dynamics. The spherical pendulum is a two degrees of freedom nonlinear system with a pivot point in space. The equations of motion for the pendulum are derived, simulated, and animated. A periodical perturbation is applied to the pivot point producing radically different behavior.
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    Interactive Rendering of CSG Models
    (Blackwell Science Ltd and the Eurographics Association, 1996) Wiegand, T. E
    We describe a CSG rendering algorithm that requires no evaluation of the CSG tree beyond normalization and pruning. It renders directly from the normalized CSG tree and primitives described (to the graphics system) by their facetted boundaries. It behaves correctly in the presence of user defined,"near" and"far" clipping planes. It has been implemented on standard graphics workstations using Iris GL1 and Open GL2 graphics libraries. Modestly sized models can be evaluated and rendered at interactive (less than a second per frame) speeds. We have combined the algorithm with an existing B-rep based modeller to provide interactive rendering of incremental updates to large models.
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    SCROOGE:Perceptually-Driven Polygon Reduction
    (Blackwell Science Ltd and the Eurographics Association, 1996) Reddy, M.
    Many real-time 3D graphics renderers represent each object as a collection of simple polygons. The complexity of this polygon structure is of practical relevance because it can manifestly affect the performance of the graphics system. It is therefore common place to find techniques to reduce the polygonal complexity of a model with the ultimate aim of improving the interactivity of the application. In the past, many of these schemes have not been concerned with the perceptual side-effects of this reduction and as a result a number of visual incongruities are often perceivable when these correspondingly-reduced representations are employed. As an attempt to circumvent these problems, this paper presents a methodology for reducing the polygonal complexity of a model, whilst retaining a degree of perceptual predictability. This allows the visual consequences of the degradation to be quantified and accurately modelled.
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    Topologically exact evaluation of polyhedra defined in CSG with loose primitives
    (Blackwell Science Ltd and the Eurographics Association, 1996) Banerjee, Raja (P.K.); Rossignac, Jarek R.
    Floating point round-off causes erroneous and inconsistent decisions in geometric modelling algorithms. These errors lead to the generation of topologically invalid boundary models for CSG objects and significantly reduce the reliability of CAD applications. Previously known methods that guarantee topological consistency by relying on arbitrary precision rational arithmetic or on symbol-manipulation techniques are too expensive for practical purposes. This paper presents a new solution which takes as input a"fixed precision" regularized Boolean combination of linear half-spaces and produces a polyhedral boundary model that has the exact topology of the corresponding solid. Each half-space is represented by four homogeneous coefficients infixed precision format (La bits for the three direction cosines and Ld bits for the constant term, i.e. the distance from the origin). Exact answers to all topological and ordering questions are computed using a fixed length, 3 La+ Ld+ 2 bits, integer format. This new guaranteed tight limit on the number of bits necessary for performing intermediate calculations is achieved by expressing all of the topological decisions based on geometric computations in terms of the signs of 4 by 4 determinants of the input coefficients. The coordinates of intersection vertices are not required for making the correct topological decisions and hence vertices and lines are represented implicitly in terms of planes.
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    A Unified, Object-Oriented Graphics System and Software Architecture for Visualising CAD/CAM Presentations
    (Blackwell Science Ltd and the Eurographics Association, 1996) Kochhar, Sandeep; Hall, Jim
    Most object-oriented graphics systems (OOGS) either support general purpose graphics capabilities (drawing editors, ray tracing, etc.), or have targeted specific areas of computer graphics, for example, interface building, animation, and visualisation. However, the key concept in CAD/CAM graphics systems is that of presentations-pictures that convey information about products or parts of products. CAD/CAM graphics systems that create and manipulate presentations have specific graphical requirements that have not been addressed by existing OOGS. These requirements include the support of CAD/CAM concepts such as drawings, views and view-specific graphics, and layers, and the ability to allow external geometric modelers to be linked into the presentation. We describe an object-oriented presentation architecture that allows the application to describe the structure of the CAD/CAM presentation. This architecture provides a unified interface to drawings, views, layers and entities, and allows linkage to models created with an external geometric modeler, while isolating applications from details of the underlying traditional graphics rendering systems. It is our hope that this architecture provide the foundation for the architecture of next generation OOGS. We also present an implementation of this architecture and compare it to other OOGS.
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    Using a Convex Pyramid to Bound Surface Normal Vectors
    (Blackwell Science Ltd and the Eurographics Association, 1996) Daniel, M.
    Determining a tight bounding volume of all the surface normal vectors is of interest in surface modelling especially for intersection problems, in order to detect closed intersection curves. It is also important to determine quickly whether two such volumes intersect. This paper adresses both problems through the introduction of a pyramid with a convex planar base. For intersection problems, a different method has been proposed by M. Hohmeyer. The various solutions are discussed and compared.