Method of trimming PDE surfaces

A method for trimming surfaces generated as solutions to Partial Differential Equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order elliptic PDE on the parameter space. The chosen elliptic PDE is solved analytically, even in the case of a very general complex trim, allowing the design process to be carried out interactively in real time. To demonstrate the capability for this technique we discuss a series of examples where trimmed PDE surfaces may be applicable

A usability study on widget design for selecting boolean operations

Applying the correct set of Boolean operations is a fundamental task in constructive solid geometry (CSG), which is a staple in automated manufacturing systems. Although textual buttons and icons are the most common interfaces to apply such operations, these require an unnecessary cognitive load that hampers the solid modeling process. This study presents VennPad, a novel CSG widget that gathers all Boolean operations under the same user interface control element and is represented as a two-set Venn diagram. Contrary to conventional CSG widgets, VennPad supports a graphical interface that gives simultaneous access to several types of Boolean operations (intersection, union, difference, symmetric difference and split). A usability study was conducted to ascertain whether VennPad is a more natural interface compared to textual buttons and icon-based widgets for different solid modeling tasks. VennPad proved to be an effective interface to perform Boolean operations. Qualitative feedback places VennPad as the preferred interface, but efficiency results are operation dependent, thus, opening the way to new design iterations.info:eu-repo/semantics/publishedVersio

Generalized partial differential equations for interactive design

This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitrary set of boundary conditions. Both the boundary conditions which are defined as curves in 3-space and the spine of the corresponding PDE are utilized as interactive design tools for creating and manipulating geometry intuitively. In order to facilitate interactive design in real time, a compact analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme even in the case of general boundary conditions satisfies exactly the boundary conditions where the resulting surface has an closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples

Interactive Boolean Operations for Conceptual Design of 3-D Solids

Interactive modeling of 3-D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for interactive display of CSG models require expensive special-purpose hardware that is not easily available. In this paper we present a method for interactive display of CSG models using standard, widely available graphics hardware. The method enables the user to interactively modify the affine transformations associated with CSG sub-objects. The application we focus upon is that of conceptual design, a stage in the design process in which rapid, interactive visualization of the model and high-level design operations are of crucial importance, while the objects are relatively simple. The method converts the CSG graph to a novel Convex Differences Aggregate(CDA) representation. The CDA utili..

Towards a digitally conceived physical performance object

Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2007.Includes bibliographical references (p. 122-126).In the performing arts, the relationship that is established between what is seen and what is heard must be experienced to fully appreciate and understand the aesthetics of performance. Actual physical objects such as musical instruments, lights, elements of the set, props, and people provide the visual associations and a tangible reality which can enhance the musical elements in a performance. This thesis proposes that new and artistic physical objects can, in themselves, be designed to perform. It introduces the Chandelier, a kinetic sculpture, a central set piece for a new opera, a new kind of musical instrument, and an object that performs. The piece moves and changes shape through mechanical action and the designed interplay between surfaces and light. It is intended to be interacted with by musicians and players of the opera. This thesis also explores the design process and evolution of the Chandelier with a primary objective of realizing a constructible, physical performance object through an authentic and abstruse digital conception. It is a conception not of a static nature, but incorporates a dynamic sense of changeable form through coordinated elements of light, mechanics, and sculpture.Steven L. Pliam.S.M

An image-space algorithm for hardware-based rendering of constructive solid geometry

A new approach to image-space hardware-based rendering of Constructive Solid Geometry (CSG) models is presented. The work is motivated by the evolving functionality and performance of computer graphics hardware. This work is also motivated by a specific industrial application --- interactive verification of five axis grinding machine tool programs. The goal is to minimise the amount of time required to render each frame in an animation or interactive application involving boolean combinations of three dimensional shapes. The Sequenced Convex Subtraction (SCS) algorithm utilises sequenced subtraction of convex objects for the purpose of interactive CSG rendering. Concave shapes must be decomposed into convex shapes for the purpose of rendering. The length of Permutation Embedding Sequences (PESs) used as subtraction sequences are shown to have a quadratic lower bound. In ma ny situations shorter sequences can be used, in the best case linear. Approaches to subtraction sequence encoding are presented including the use of object-space overlap information. The implementation of the algorithm is experimentally shown to perform better on modern commodity graphics hardware than previously reported methods. This work also examines performance aspects of the SCS algorithm itself. Overall performance depends on hardware characteristics, the number and spatial arrangement of primitives, and the structure and boolean operators of the CSG tree

Generative Mesh Modeling

Generative Modeling is an alternative approach for the description of three-dimensional shape. The basic idea is to represent a model not as usual by an agglomeration of geometric primitives (triangles, point clouds, NURBS patches), but by functions. The paradigm change from objects to operations allows for a procedural representation of procedural shapes, such as most man-made objects. Instead of storing only the result of a 3D construction, the construction process itself is stored in a model file. The generative approach opens truly new perspectives in many ways, among others also for 3D knowledge management. It permits for instance to resort to a repository of already solved modeling problems, in order to re-use this knowledge also in different, slightly varied situations. The construction knowledge can be collected in digital libraries containing domain-specific parametric modeling tools. A concrete realization of this approach is a new general description language for 3D models, the "Generative Modeling Language" GML. As a Turing-complete "shape programming language" it is a basis of existing, primitv based 3D model formats. Together with its Runtime engine the GML permits - to store highly complex 3D models in a compact form, - to evaluate the description within fractions of a second, - to adaptively tesselate and to interactively display the model, - and even to change the models high-level parameters at runtime.Die generative Modellierung ist ein alternativer Ansatz zur Beschreibung von dreidimensionaler Form. Zugrunde liegt die Idee, ein Modell nicht wie üblich durch eine Ansammlung geometrischer Primitive (Dreiecke, Punkte, NURBS-Patches) zu beschreiben, sondern durch Funktionen. Der Paradigmenwechsel von Objekten zu Geometrie-erzeugenden Operationen ermöglicht es, prozedurale Modelle auch prozedural zu repräsentieren. Statt das Resultat eines 3D-Konstruktionsprozesses zu speichern, kann so der Konstruktionsprozess selber repräsentiert werden. Der generative Ansatz eröffnet unter anderem gänzlich neue Perspektiven für das Wissensmanagement im 3D-Bereich. Er ermöglicht etwa, auf einen Fundus bereits gelöster Konstruktions-Aufgaben zurückzugreifen, um sie in ähnlichen, aber leicht variierten Situationen wiederverwenden zu können. Das Konstruktions-Wissen kann dazu in Form von Bibliotheken parametrisierter, Domänen-spezifischer Modellier-Werkzeuge gesammelt werden. Konkret wird dazu eine neue allgemeine Modell-Beschreibungs-Sprache vorgeschlagen, die "Generative Modeling Language" GML. Als Turing-mächtige "Programmiersprache für Form" stellt sie eine echte Verallgemeinerung existierender Primitiv-basierter 3D-Modellformate dar. Zusammen mit ihrer Runtime-Engine erlaubt die GML, - hochkomplexe 3D-Objekte extrem kompakt zu beschreiben, - die Beschreibung innerhalb von Sekundenbruchteilen auszuwerten, - das Modell adaptiv darzustellen und interaktiv zu betrachten, - und die Modell-Parameter interaktiv zu verändern