Multi-scale space-variant FRep cellular structures

Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations

Systems Issues in Solid Freeform Fabrication

This paper is concerned with the systems aspects of the Solid Freeform Fabrication (SFF) technology, i.e., the issues that deal with getting an external geometric CAD model to automatically control the physical layering fabrication process as directly as possible, regardless ofthe source of the model. The general systems issues are described, the state of systems research is given, and open research questions are posed.Mechanical Engineerin

Rendering Curved Triangles on the GPU

This Thesis presents a new approach to render triangular Bézier patches in real time. The goal is to achieve a very good visual quality, avoid artifacts in the silhouette, and get in nite detail. Our approach consists in a ray casting technique to render tri- angular B ezier patches in real time. It is based on previous work explained in this document to implement a fast ray-surface intersec- tion technique. This previous work consists in adapting Newton's method to implement the intersections achieving interactive framer- ates ray casting di erent surfaces. The main contributions of our approach are adapting New- ton's method to perform intersections with triangular bicubic B ezier patches and implementing it in GPU to optimize performance using graphics hardware. Finally, we also contribute adapting the normal mapping tech- nique to shade the models and, thus, achieve even greater detail

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Direct Slicing of STEP Based NURBS Models for Solid Freeform Fabrication

Direct slicing of CAD models to generate process planning instructions for solid freeform fabrication may overcome inherent disadvantages of using STL format in terms of the process accuracy, ease of file management, and incorporation of multiple materials. This paper will present the results of our development of a direct slicing algorithm for layered freeform fabrication. The direct slicing algorithm was based on a neutral, international standard (ISO 10303) STEP-formatted NURBS geometric representation and is intended to be independent of any commercial CAD software. The following aspects of the development effort will be presented: 1) Determination of optimal build direction based upon STEP-based NURBS models; 2) Adaptive subdivision of NURBS data for geometric refinement; and 3) Ray-casting slice generation into sets of raster patterns. Feasibility studies applying the direct slicing algorithm to example models and the generation of fabrication planning instructions involving multi-material structures will also be presented.Mechanical Engineerin