A classic reference and text, this book introduces the foundations used to create an accurate computer screen image using mathematical tools. This comprehensive guide is a handbook for students and practitioners and includes an extensive bibliography for further study.
Modern industrial products feature a variety of complex shapes that go beyond mere functionality; they are also styled. While the importance of styling is well-known for items like cars, even simple consumer appliances must be aesthetically pleasing. Technical products, such as turbines or valves, are also designed with intricate shapes to enhance efficiency. Optimizing product shape is crucial in the development process. Various CAx systems have become essential tools for design, calculation, simulation, and manufacturing across industrial environments. However, shape improvement often occurs manually on physical models, creating a disconnect in the CAD information flow. This gap can be bridged using reverse engineering techniques, which reconstruct CAD surfaces (like Bezier or NURBS) from modified physical models. The 2nd Workshop on current CAx problems focused on reverse engineering, showcasing the latest research in surface reconstruction from point sets. It also covered methods and tools from leading CAD vendors, including Holometric Technology, IBM/Dassault, and others. Discussions included structural aspects of reverse engineering, potential future developments, and new research directions.
The content covers various aspects of curve and surface fairing and shape preservation. It begins with experiences in curve fairing, discussing co-convexity preserving curve interpolation and shape-preserving interpolation for both planar and three-dimensional curves, including a comparative study of two methods in Tribon Initial Design. The next section focuses on fairing B-spline curves and surfaces, introducing declarative modeling as an additional approach for computations. Shape preservation is further explored with variable degree polynomial splines, emphasizing the importance of maintaining shape integrity. The fairing of surfaces is addressed through functional aspects of fairness, including surface design based on brightness intensity and an overview of industrial challenges in fair surface blending. The text also delves into parametrizing wing surfaces using partial differential equations and algorithms for convexity-preserving interpolation of scattered data. It discusses abstract schemes for functional shape-preserving interpolation and tensor product spline interpolation under piecewise bilinear bounds. Additionally, it covers the construction of surfaces through shape-preserving approximation of contour data, B-spline approximation with energy constraints, curvature approximation for surface modeling, and scattered data approximation with triangular B-splines. Finally, benchmarks in planar shape-preserving
InhaltsverzeichnisI Presentations of CAD Systems.CATIA/IBM, Dassault.Curve and Surface Representation in Catia System.A Case for CAD.Digitising Sculptured Surfaces.ICEM / Control Data.Representations and Operations in the ICEM Systems.ICEM MESH — A Mesh Generation Tool for Free-Form Surfaces.STRIM/cisigraph.Practice of Computer Aided Geometric Design.SYRKO/Merces Benz.Car Body Design and Manufacturing with SYRKO.UNIGRAPHICS/McDonnel Douglas.Curves and Surfaces in Unigraphics and Parasolid.EUCLID / Matra.UNISURF IV — The advanced Solids & Surfaces Module of EUCLID-IS.II Visualisation System.WAVEFRONT — MENTAL RAY/mental images.High Quality Visualization of CAD Data.III Lectures on Developments for Interfaces.The Development Methodology of STEP and its Concept for Shape Representation.Integration of Physical “Phenomena” into CAD.General Matrix Representation for NURBS Curves and Surfaces for Interfaces.Approximate Conversion and Merging of Spline Surface Patches.IV Questionnaire on Curve/Surface/Volume Implementations.ANSWERS — Part I (EUCLID, STRIM, ICEM).ANSWERS — Part II (UNIGRAPHICS, SYRKO, CATIA).V Excerpts of the Panel Discussion.
Das Inhaltsverzeichnis umfasst mehrere zentrale Themen zur Transformation und Darstellung räumlicher Objekte. Der erste Abschnitt behandelt Transformationen, Projektionen und visuelle Techniken wie Stereobilder und Anaglyphen. Es folgen Grundlagen der Geometrie und Numerik, einschließlich Parameterdarstellungen, Interpolation und Approximation von Kurven und Flächen. Der dritte Teil widmet sich allgemeinen Splinekurven, deren Ideen und speziellen Typen wie kubischen und nichtlinearen Splines. Im vierten Abschnitt werden Bézier- und B-Spline-Kurven behandelt, einschließlich ihrer Anwendung in der Finite-Elemente-Technik. Der nächste Abschnitt fokussiert sich auf geometrische Splinekurven, die verschiedene Stetigkeitsbedingungen erfüllen. Daraufhin werden Spline-Flächen und deren verschiedenen Formen, wie Tensor-Produkt- und Bézier-Flächen, erläutert. Der Abschnitt über Gordon-Coons-Flächen zeigt deren Anwendung auf Vierecken und Dreiecken. Scattered Data Interpolation und Approximation werden in einem weiteren Kapitel behandelt, gefolgt von Basistransformationen für Kurven- und Flächendarstellungen. Multivariate Darstellungen und deren Visualisierung schließen die Themen ab. Schließlich wird das Schneiden und Glätten von Kurven und Flächen thematisiert, einschließlich der Erkennung und Beseitigung unerwünschter Bereiche. Ein Literaturverzeichnis und ein Stichwortverzeichnis runden das Werk ab.