After establishment of design requirements and creation of an initial shape, the design process of free-form shapes should include interrogation and fairing until a desired shape, with appropriate geometric and performance characteristics, is achieved. Afterwards, the quality of the manufactured product can be determined by comparing measured data to the design model. To permit automated design and manufacturing, mathematical methods and algorithms for the creation, interrogation, fairing, and inspection of curves and surfaces have been developed and integrated into a computer system called Praxiteles. The general layout of Praxiteles, along with a description of design capabilities, are presented. This description covers the areas of input, output, approximation and conversion for data exchange, a summary of some shape creation methods, and a description of some advanced interactive interrogation, fairing, and inspection methods for NURBS curves and surfaces. Examples illustrate some of the features of the system, as applied in the design and inspection of marine propellers. Recommendations for future development of the system are also presented.
Solid modelers have been used in computer aided design and manufacturing for more than one decade. However, current solid modelers based on Boundary Representation still encounter numerical instability and theoretical difficulties for ill-conditioned geometric computations involving intersections. In this thesis, numerically robust geometric representations and algorithms for numerically robust geometric interrogations, including ill-conditioned geometric intersections are developed. Interval polynomial objects are proposed for robust geometrical representations. A robust algorithm (solver) for solving unbalanced non-linear polynomial equation systems is developed. Based on this solver, a robust unified algorithm for general geometric intersections, including overconstrained intersections, is developed. For the effective and robust detection of intersection curve loops, a direct algorithm is developed to determine collinear normal points and isolated tangential contact points of two surfaces. Theory and algorithms are developed for ill-conditioned intersections, such as tangential intersections of curves, overlapping of curves and surfaces, and overlapping of surfaces. The End Point Theorem is presented to verify that if two ideal Bézier patches tangentially intersect along an open curve, the curve must start from and end at boundaries of either of the two patches. This theorem is extended to general C^{\infty} surface patches, and is followed by a corollary for surface overlapping.
An n-D novel non-manifold data structure for interval polynomial objects (points, curves, and surfaces) is developed to permit Boundary Representation of interval objects. It separates the manifold from the non-manifold parts of the object, and categorizes nodes into six types for Boolean operations. This separation allows the effective use of a new point classification algorithm for non-manifold objects. Based on the robust interval geometrical representations and computations and data structures, algorithms for Boolean operations are developed first for 2D manifold curved regions and then extended to 3D manifold curved solids. These algorithms are further extended to 2D and 3D non-manifold curved objects resulting from Boolean operations. In order to represent the geometric objects, such as trimmed surfaces, resulting from Boolean operations, the Extreme Orientation Theorem is introduced to determine the orientation of a piecewise smooth simple planar closed curve by an extreme point and its derivative at that point. Finally, examples illustrate the robustness and efficiency of the algorithms for geometric intersections and Boolean operations.Visualization and information modeling have played an effective role in supporting many engineering applications. This paper deals with visualization of roughness data for standard propeller surfaces and the information model for marine propeller blade surface roughness over the course of the propeller's life--cycle. For correlation of propeller surface roughness and fluid drag, we use two parameters, the center line average, R_a, as a height parameter and the peak count per inch, P_c, as a texture parameter. The standard Rubert surfaces for propeller roughness were measured using a surface profiling system and then preprocessed and exported to a graphics workstation. For each sample surface, points were selected and input into a geometric modeling and interrogation system, Praxiteles. These points were then approximated by a non-uniform rational B-spline (NURBS) which is the standard format for representing surfaces in modern geometric modeling systems. The surfaces were visualized and can be used as standard visual comparators to assess the roughness of measured manufactured and in-service propeller surfaces. To meet the requirements of industry and government for comprehensive and reliable information exchange mechanisms to effectively integrate existing computer systems and evolving information technologies, the ISO is developing a standard (ISO 10303, known informally as STEP) for digital product and manufacturing management data. Using the STEP (STandard for the Exchange of Product model data) EXPRESS information modeling language, an information model was developed that is intended to be the neutral form for representing and exchanging propeller surface roughness data. It can be easily integrated into the STEP standard and the application protocol for marine propulsors.
Keywords: EXPRESS and EXPRESS-G modeling language, geometric modeling and interrogation, information modeling, propeller life-cycle, product data exchange, propeller surface roughness, STEP standard, visual comparators, visualization.
MIT Ocean Engineering Design Laboratory
Copyright © 1997, Massachusetts Institute of Technology
URL: http://deslab.mit.edu/DesignLab/abstracts95.html
Revised: July 23, 1997